{ "schema": "adjacency-theory-archive/v2", "generatedISO": "2026-10-10T18:04:00.920Z", "license": "Creative Commons Attribution 4.0 International (CC BY 4.0). Copy it, mirror it, fork it, rerun it. Attribute Raj Seecharran and his AI collaborators.", "integrity": "NO PHYSICAL MECHANISM. NO PHYSICAL EVIDENCE. Toy computational program. Every number is a property of equations written by this project and integrated on small synthetic systems.", "dataPolicy": [ "APPEND-ONLY. No earlier phase, failed test, dataset, seed or ledger entry is ever deleted, renumbered, compressed away or rewritten. A superseding result links to what it supersedes; it never replaces it.", "RAW DATA OVER PROSE. Wherever a frozen raw dataset exists, it is the authority; charts and summaries are derived from stored records and must be reproducible from them. A chart is never a substitute for the data behind it.", "LEGACY LABELING. Any displayed result that predates the raw-dataset regime and has no stored raw backing is labelled LEGACY RESULT — RAW DATA NOT AVAILABLE. Data is never fabricated retroactively to back an old number.", "DETERMINISM. Every stored run records its RNG algorithm and literal seed. Re-running the stored engine version with the stored seed must reproduce the stored numbers exactly.", "HONEST STATUS. Unmodelled constraints are NOT MODELED, never PASS. Failed and inconclusive runs remain visible permanently — they are the evidence ledger." ], "attribution": { "founder": "Raj Seecharran", "collaborators": "AI collaborators (joint human–AI research programme)", "canonicalSite": "https://adjacencetheory.com" }, "reconstruction": [ "Everything below is the state of the programme. No server, database or account is required to keep it: the record is plain data and every experiment is deterministic from its seed.", "Any implementation that reproduces the listed benchmark seeds and reproduces the recorded numbers is a valid continuation of this programme.", "Resume from the resumeInstructions, then answer the questions in next[]." ], "datasets": [ { "id": "at327b-ensemble-001", "phase": "327B (formerly 327)", "title": "Coordinate-free dimension-blind generator/relation ensemble — preliminary cells", "schema": "at327-dataset/1", "engineVersion": "at327-sieve/1.0.0", "generatedISO": "2026-09-02T16:48:39.004Z", "rngAlgorithm": "mulberry32 (32-bit multiplicative mix, public-domain reference implementation; one independent stream per run, seeded per record)", "runCount": 54, "seedRange": "3270001–3270054 (literal, sequential in preregistered cell order)", "status": "FROZEN. The Phase 327A deception audit PASSED (2 September 2026), lifting the interpretation quarantine for the audited pipeline configuration only. Preliminary reading: P(D = 3 | stable) ≈ 0.028 with no dominance over neighbouring degrees. axesFullyCovered = false; the phase verdict is IN PROGRESS / OPEN.", "manifest": [ { "name": "at327-runs.json", "description": "Full raw run records (canonical JSON of runs[])", "fnv1a64": "aefa9e5b2de495ce", "sha256": "505daff0bc929e7d03ac8c2a0afbc038f86933ece6fd1622706d932650c40b1b", "bytes": 381867 }, { "name": "at327-sectors.csv", "description": "One row per sector: classification, D_inf, inferred D, fits, stability", "fnv1a64": "3e396b9d39457ccf", "sha256": "cc46cd7d095cacdcaab228327519e3192f23b24542ec6b280b8edc0e86b3bd54", "bytes": 57056 }, { "name": "at327-gamma.csv", "description": "Raw growth curves: one row per (run, sector, r) with gamma(r) and d_eff(r)", "fnv1a64": "2c5f685d4389a294", "sha256": "677e209cd97490ad1a8b04e31593987ee68e007c3ddf8548a8f1cfdd1da94572", "bytes": 476790 } ], "exportRoute": "/lab/co-generation (JSON, CSV and manifest downloads with checksums)", "immutability": "Append-only: a new ensemble gets a new file and schema tag under a new engine version; this file is never overwritten." }, { "id": "at327a-audit-001", "phase": "327A", "title": "Growth-classifier deception audit — blinded control suite, committed predictions and gate results", "schema": "at327a-dataset/1", "engineVersion": "at327a-audit/1.0.0", "generatedISO": "2026-09-02T17:43:55.518Z", "rngAlgorithm": "mulberry32 (32-bit multiplicative mix, public-domain reference implementation); used ONLY for the noisy variants, one independent stream per noisy sample, literal seed stored per sample. Clean controls are fully deterministic and use no RNG.", "runCount": 72, "seedRange": "noise seeds 3271000–3271021 (mulberry32); blind salt at327a-blind-salt-1; prediction commit SHA-256 8fa0a887824524d2…", "status": "FROZEN. VERDICT: PASS. All six frozen gates hold on the blinded control suite. Phase 327B inference is UNBLOCKED for the audited pipeline configuration only (same windows, same thresholds, same engine version). Any change to the pipeline re-blocks 327B until re-audited.", "manifest": [ { "name": "at327a-controls.json", "description": "Full control roster WITH labels and provenance (post-commit artifact)", "fnv1a64": "f76733707aa550de", "sha256": "769811815a31a064a413392e3fde7bc94a086916579c579da485d7baa11b49bc", "bytes": 65984 }, { "name": "at327a-predictions.json", "description": "Blinded prediction set exactly as committed before the label join", "fnv1a64": "2a205720fc41b720", "sha256": "8fa0a887824524d2ef95a1937db36f1fdb2848228cc406381a2796e0ce8fa9cb", "bytes": 45012 }, { "name": "at327a-scores.csv", "description": "One row per control: truth, prediction, outcome, gating status", "fnv1a64": "e874d87b8a04d11b", "sha256": "694b93af3ebff83fde3f5a08d9518578db847185661a439c64e555e89f4b019b", "bytes": 11371 }, { "name": "at327a-gamma.csv", "description": "Raw growth curves: one row per (control, r) with γ(r)", "fnv1a64": "6c110e3053cda63a", "sha256": "6b8dc08614ee33128f042b4c17e66623889911da6d28fd1ba3026632a4e8e7cf", "bytes": 212911 } ], "exportRoute": "/lab/co-generation (JSON, CSV and manifest downloads with checksums)", "immutability": "Append-only: a re-audit after any pipeline change gets a new file and schema tag under a new engine version; this file is never overwritten." }, { "id": "at366-distortion-001", "phase": "366–368", "title": "Blind small-integer automorphism enumeration and exact constant-description distortion table", "schema": "at366-dataset/1", "engineVersion": "at366-distortion/1.0.0", "generatedISO": "2026-09-04T11:40:07.797Z", "rngAlgorithm": "NONE — deterministic. The Phase 366 ensemble is total (all 3^9 = 19,683 matrices with entries in {−1, 0, 1}); Phase 367 is exact BigInt iteration. No sampling and no seed exist to store.", "runCount": 6974, "seedRange": "n/a — 6,960 unimodular matrices enumerated exhaustively; 14 frozen distortion steps (n = 1–32)", "status": "FROZEN. Verification gates: ALL PASS. Of 19,683 small-integer matrices, 6,960 are unimodular; 3,120 are hyperbolic (no eigenvalue modulus within 1e-7 of 1) and 4,176 have spectral radius above 1 — no filter referenced shortcut strength, hyperbolicity or the number 3. Phase 367 reproduces the tribonacci growth rate ≈ 1.8392867552 in exact BigInt arithmetic. Phase 368 verdict: algebraic logarithmic displacement PASSED for the toy construction; physical shortcut NOT MODELED; dynamical selection of A OPEN. PHYSICAL EVIDENCE: NONE.", "manifest": [ { "name": "at366-dataset.json", "description": "Canonical frozen dataset (this record, minus manifest)", "sha256": "aaf4f5b6d60e65615f25f652db88c8ab5e11e4094fad0185961c3b3aa04f8f26", "fnv1a64": "d81d37be2b0566e7", "bytes": 86719 }, { "name": "at367-distortion-table.csv", "description": "Exact BigInt distortion table (n, word proxy, L1, vector, ratio)", "sha256": "f421270d99f69d3e716f28ad5e4d33b3aa97557d6d3c0eaab08c971225856742", "fnv1a64": "cb25c202b3fe739b", "bytes": 564 }, { "name": "at366-spectral-radii.csv", "description": "Sorted spectral radii of all unimodular matrices (10 dp)", "sha256": "5afa30e30c61bcaba8eef1b2e929b3c4d012df9e6cc22b3b4551fcf70ca24e35", "fnv1a64": "ad7e85265f29c7a0", "bytes": 59871 } ], "exportRoute": "/api/public/archive (JSON and Markdown mirrors include this manifest and checksums)", "immutability": "Append-only: any re-run under a changed engine gets a new file and schema tag under a new engine version; this file is never overwritten." } ], "checkpoint": { "version": "6.23.0", "label": "Research Checkpoint — Hidden Generators, Selector Accounting & the q_AB Construction Audit: Compressed-Selector Branch Closed at Two Depths (Phases 200–252)", "dateISO": "2026-08-30", "dateLabel": "August 30, 2026", "experimentRange": "AT-0 → AT-0688 (through Phase 69, the LIFECYCLE COST GATE — REUSE OR LOSE, a NORMALIZED COST MODEL and explicitly NOT PHYSICAL ENERGY. No new mechanism: the phase charges the whole bill of the strongest toy architecture the programme has — K = 8 reusable routing trees, self-organised compact addresses, gated catalytic moving doorway — and amortises it. Declared coefficients, fixed before the sweep: address formation 1.2 · N · log2 N one-off; storage burden 2 · K · N · log2 N held for the lifetime, which at K = 8 is 93% of the one-off bill against 7% for formation; per-trip operational cost (3.5 doorway + 1.8 payload + 1.2 restoration) · log2 N; local repair expectation small and folded into the one-off term rather than dropped; comparator an ordinary point-to-point trip charged linearly in N. Qcost is baseline over amortised cost. RESULT: at M = 1 the amortised cost per trip fits N^1.133, at M = 10 N^1.131, at M = 100 N^1.103 — all worse than linear, cost advantage ABSENT at every tested size. Sublinear amortised cost emerges at M = 1,000, z = 0.933, with Qcost 2.93, 4.25, 4.44 and 4.06 at N = 256, 1,024, 4,096 and 16,384; at M = 10,000 it strengthens to z = 0.514 with Qcost 4.61, 12.40, 25.20 and 33.74. The fitted exponent crosses 1 near M ≈ 574 and per-size break-even runs from 173 trips at N = 256 to 243 at N = 16,384 — growing only logarithmically faster than the baseline, which is the single encouraging line in the accounting. Four of eight lifecycle gates pass: L2 (one-off) and L3 (low use) FAIL outright, L5 (advantage vs baseline) is CONDITIONAL on the reuse horizon and L8 physical interpretation is NOT MODELLED. INTERPRETATION, stated as a requirement rather than a win: the architecture can pay for itself only as HIGH-UTILIZATION REUSABLE INFRASTRUCTURE, so REUSE HORIZON is now a first-class design constraint alongside locality, addressability and fault tolerance, and any design that rebuilds its addressing substrate per trip is dead. VERDICT: TOY ARCHITECTURE GATE — CONDITIONAL PASS (HIGH-UTILIZATION REUSE). The gate is deliberately NOT stamped fully passed; it passes only under the definition architecture under reusable-infrastructure assumptions, and those assumptions are ours, not the world's. Ladder rung 7 lifecycle cost moves NOT ESTABLISHED → PARTIAL as CONDITIONAL FIRST PASS / HIGH-UTILIZATION ONLY; rung 8 physical mapping stays NOT ESTABLISHED. Physical mapping is the next front and must prioritise platforms that already supply reusable background connectivity and low marginal reconfiguration cost: five candidate ANALOGUE platforms are mapped variable by variable through S, C0/C*, address state, doorway activation, payload, restoration and cost measurement — programmable electrical/RF networks, photonic meshes, coupled oscillator lattices, FPGA/NoC fabrics and quantum simulators — with FPGA/NoC fabrics the cleanest place to test the accounting because every term is directly countable. These are analogues for a cost structure and NOT spacetime claims. The leading discriminating prediction against an ordinary routed network is reuse-scaling of reconfiguration events: a two-phase moving-doorway architecture predicts actuations per transfer fall toward a bounded per-trip term while the address state is untouched, where an ordinary routed network pays a reconfiguration event per transfer. Speed is EXCLUDED as a discriminator — locality bounds settled that in Phases 47-55. New debts B136-B140; canonical AT-0673 … AT-0688; Phase 68, the REDUNDANT MULTI-TREE LOCAL ADDRESS MESH — the fault-tolerance gate, attacked in two rounds and both kept visible. ROUND 1 tested the cheap incremental design: one BFS tree, every node storing its parent plus a single backup neighbour at lower-or-equal depth, re-attaching in one local hop if that backup is still attached to the root. The adversary is global and fully informed — it ranks every tree edge by AGGREGATE TREE IMPACT, the number of node-tree pairs that lose their route if the edge dies, and cuts the worst first subject to keeping the substrate connected. The single worst edge at N = 2048 severs 866 nodes, 42% of the network, from one cut. The design collapsed: median repair fraction 17.6% over the N in {256,512,1024,2048} x failures in {1,2,4,8} grid, worst cell 4.8%, with up to 1864 nodes severed at once. The failure is structural, not unlucky: a high-impact cut severs a whole subtree and every backup stored inside that subtree points back into the same severed subtree, so no choice of one backup per node escapes it. NEGATIVE RESULT PRESERVED — the fragile single-tree/local-backup design is FAILED and stays on the page. ROUND 2 replaced it rather than patching it: K independently rooted BFS trees on the SAME degree-4 connected substrate, all frozen before endpoints are chosen, each node holding one compact child-port address per tree at 2 bits per hop, and a flow whose route is cut re-selecting among surviving trees from addresses it already holds — zero rebuild messages, no re-rooting, no oracle. Exact results over 40 sampled pairs per cell, 3 seeds: K = 8 holds route success 1.000 at 1, 2, 4 and 8 adversarial failures at N = 512, 1024 and 2048 and 0.983 worst at N = 256, with worst median stretch 1.236x the shortest path in the DAMAGED graph and a median of 6 trees still usable per pair after the eighth cut; K = 4 degrades to 0.750-0.842 at eight failures; K = 2 collapses to 0.283. Storage is K.O(log N) — 16.2 bits per node at K = 1 rising to 129 at K = 8 on N = 1024, a flat 8x multiplier — and K stayed CONSTANT across every tested size, which is encouraging and not established. Five of eight fault-tolerance gates pass; F1 backup repair fails and F7 lifecycle cost plus F8 physical interpretation are NOT MODELLED. INTERPRETATION: redundancy must be architectural, not a couple of backup edges. VERDICT: REDUNDANT MULTI-TREE MESH — FAULT-TOLERANCE FIRST PASS / BACKUP-PARENT DESIGN FAILED. Ladder now carries fault tolerance as two separate rungs, FAILED for the single-tree backup design and FIRST PASS for the mesh, with multi-user scalability at FIRST PASS and LIFECYCLE COST/ACCOUNTING as the one remaining toy gate. New debts B132-B135; canonical AT-0657 … AT-0672; Phase 67, the MULTI-ROOT / LOAD-BALANCED ADDRESS FABRIC — the structural answer to the Phase 66 root-band deadlock, and the first EXACT event-driven simulation of concurrent traffic on the real cubic graph rather than a proxy. Instead of one elected root, the substrate builds K generic BFS trees BEFORE endpoints are drawn; each node stores K compact child-port addresses at 2 bits per hop, so storage is K·O(log N) with K a fixed constant; each trip samples two of the K trees (power-of-two choices, an ALGORITHMIC ANALOGY and not a physical claim) and picks the one minimising predicted longest-common-prefix path length plus congestion counters read at its own node and first hop, with no route oracle and no global coordination in the code path. Downsampled grid, declared not hidden: N in {256,512,1024,2048,4096}, F in {1,2,4,8,16,32,64}, K in {1,2,4,8}, 3 seeds per cell, finite doorway window W = 12 blocked ticks. Results: mean completion at F = 16 rises 38% -> 82% moving K = 1 -> K = 4 across all sizes (2.15x); under adversarial same-branch endpoint pairs, exactly the traffic that deadlocked the single-root band, 16% -> 72%; busiest-node load grows as F^0.472 and active footprint as F^0.846, both sublinear; normalised root-load entropy 0.921 of maximum with purely local two-choice sampling; storage 16 -> 65 bits per node from K = 1 to K = 4 on N = 1024, a flat 4x multiplier on an O(log N) base. Nine-point concurrency gate written down before the sweep: G1 completion -> 1 FAILED, G2 bounded slowdown PASSED, G3 sublinear hotspot load PASSED, G4 O(F log N) footprint PASSED, G5 polylog storage with fixed K PASSED, G6 no global coordination PASSED, G7 root-load fairness PASSED, G8 benefit survives overhead FAILED (completion per unit overhead peaks at K = 1-2 and falls, and no K reaches completion 1), G9 physical interpretation NOT MODELLED. Killing one root at tick 3 of a live 16-flow run drops completion 88% -> 63% with makespan 21 -> 32 ticks and NO global rebuild — local failover works but is not free (B131). Route stretch averages 1.59x graph-shortest. The closed-form queueing estimate rho ~ F·L/N and collision opportunity ~ F·L^2/(N·K) is retained but QUARANTINED as HEURISTIC and scores no gate. VERDICT: MULTI-ROOT DISPERSION CONFIRMED — SCALABILITY GATE STILL OPEN. Ladder rung 4 moves UNRESOLVED -> PARTIAL. New debts B128 completion below 1 under the finite window, B129 route stretch debt, B130 survivor bias in tail latencies, B131 root loss costs completion; canonical AT-0641 … AT-0656; Phase 66, the concurrency / shared-substrate stress front — an ENGINEERING-STYLE TOY AUDIT, not a physics result, and explicitly a QUEUEING OVERLAP PROXY rather than an exact-graph run: the heavier exact sweep exceeded the runtime budget and no exact-network number is reported. Assumptions are declared first — route length L ~ 1.6 log2 N, about 4 locally active nodes per live flow, node capacity one move per tick. Analytic law: expected shared slots C(F,2)L^2/N, per-trip slowdown 1 + (F-1)L^2/2N, giving 1.125x to 4.875x at N = 1024 for F = 2 … 32 and only 1.044x to 2.366x at N = 4096; the event-driven token simulation over the same assumption agrees in shape, reading 1.208x at N = 256 down to 1.056x at N = 4096 at F = 16. Everything collapses onto rho = F L^2 / N with the analytic slowdown <= 2 boundary at rho ~ 2.25 and permitted flows F <= 1 + 2N/L^2 growing as N^0.855 — F(N) ~ N/log^2 N. The adversarial test is the result: when all 16 flows climb into a single elected-root band and hold a contiguous run of ~L/3 band nodes, the plain QUEUE rule does not degrade, it DEADLOCKS in circular wait — 0 of 80 payloads complete across N = 256 … 4096 with a longest wait of 952 ticks before cutoff. DETOUR clears it at <= 1.36x with every flow completing, ABORT clears it by losing 41 of 80 payloads, and four roots with purely local least-loaded balancing complete every flow at 1.17x against 1.23x for random endpoints. Tail behaviour under random endpoints is benign — longest single wait 4 ticks, Jain fairness >= 0.979 — while the lifecycle throughput metric, completions per 1000 activated node-ticks, FALLS 17.241 → 13.158 with exponent -0.113: latency improves with N while throughput per unit activation does not. One local link cut with eight doorways open leaves the other flows unchanged with no global rebuild. Breakthrough ladder gains MULTI-USER SCALABILITY = UNRESOLVED; new debts B124 proxy not exact dynamics, B125 uniform-random route assumption, B126 analytic and simulated stability boundaries disagree, B127 single-root deadlock under adversarial load; canonical AT-0628 … AT-0640; Phase 65, fault-tolerant local repair and lifecycle accounting — no new mechanism family: the self-organizing compact addresses, localized moving doorway, structured payload and autonomous local recovery are preserved and then deliberately damaged. Each node learns a primary next hop plus up to two endpoint-independent backups outside its own subtree during the same neighbour exchange that writes the addresses. Measured over N = 256 … 4096 at seed 609: per failure event the repair touches 5.35 nodes on average with fitted exponent 0.016 in N (flat), repair rounds 12 → 22 (z ~ 0.297), post-repair stretch 1.67 → 2.08 (z ~ 0.082, INCONCLUSIVE), fabric storage 36 → 52 bits per node (z ~ 0.132) against a 14 → 22 bit baseline. Survival is 1.000 at 1-3% edge loss, 0.975 at 5% and 0.90-0.95 at 8-10%; node loss to 5% stays at or above 0.90. The adversarial cut at the single highest-betweenness tree edge severs 36-41% of the network and is absorbed by at most 8 nodes in 5-7 rounds with exactly 1 address change at every size. Concurrent disjoint faults with a payload in flight give 0 teleports and 100% identity preservation on completions, with aborts scored as failures; the causal event DAG audit records 446 events and 471 causal edges with 0 clock inversions and 0 cycles. Address corruption at 2% of nodes is detected and repaired within 2 rounds with 0 global lookups. Lifecycle ledger: build ~8 messages per node at every size, repair ~1 more per node at 5% loss, single-trip total 2257 → 36992, amortised over 10^4 trips 12.22 → 25.70, break-even 187 → 1680 trips and growing with N. Status FAULT-TOLERANT LOCALIZED TWO-PHASE TOY ARCHITECTURE; new debts B121 heavy-damage survival, B122 total repair work extensive in the damage, B123 root failure unhandled; canonical AT-0609 … AT-0627; Phase 64, the self-organizing address layer — the preloaded-address ASSUMPTION is cleared: nodes start with an immutable random ID and local port information only, a min-ID/BFS wave elects a generic root and builds a spanning tree before A and B are chosen, addresses are the sequence of local child-port symbols from the root (~2 bits per hop at degree <= 3), and routing is longest-common-prefix tree ancestry decided locally; medians over N = 128 … 8192 give setup 8 → 15 rounds (z ~ 0.151), median address 10 → 22 bits and maximum 16 → 30 bits (z ~ 0.187), and route 8 → 21.5 hops against shortest 6 → 12 (z ~ 0.222), with ratios to log2 N bounded at 1.15-1.22, 1.43-1.69 and 1.14-1.75, consistent with O(log N) setup, address size and local routing on these expander-like substrates but NOT proven from finite data; the replacement debt is SELF-ORGANIZING REUSABLE INFRASTRUCTURE — distributed construction touches the network once at a cost at least extensive in node count, amortised over trips but not abolished, canonical AT-0595 … AT-0608; Phase 63, the localized autonomous doorway — the first integrated attempt reverted to a GLOBAL AVALANCHE with peak activation equal to N at every size from 128 to 2048 and activity ~N^0.93, published as a failure; the gated catalytic variant holds the doorway localized under one frozen local law with success 1.000 to N = 2048, arrival 7.275 → 13.775 ticks (z ~ 0.240), peak simultaneous activation 11 → 19 (z ~ 0.205) and activity proxy 360.876 → 892.860 (z ~ 0.341), while the address infrastructure stays prebuilt and the directional catalytic bias is charged against it, canonical AT-0581 … AT-0594; Phase 62, the universe doesn't wake up — a causal moving front along a prebuilt compact-address route, maximum simultaneously active nodes exactly 4 from N = 128 to N = 8192, active-node-time 30 → 66 tracking route length rather than system size, Q_time 7.111 → 195.048, global wake-up debt eliminated architecturally while the address tree stays prebuilt and the front stays an abstract rule rather than the autonomous c_i / r_i equation, canonical AT-0569 … AT-0580; Phase 61, compact addressing plus sparse localized activation — routing oracle, destination beacon and global wake-up all removed in one toy, success 1.000 to N = 4096 with ~4·log2 N address bits per node and ~3.5·log2 N activated nodes per trip, canonical AT-0557 … AT-0568; Phase 60, every place has an address — the generic multilevel landmark hierarchy, its (log2 N)^2 storage debt and the migration of debt to endpoint-independent infrastructure, canonical AT-0545 … AT-0556; Phase 59, no map — one-hop beacon routing, the first sparse corridor, the random-label failure and the addressability wall, canonical AT-0533 … AT-0544; Phase 58, two bills under the table — the same frozen law to N = 4096, the first structured payload transport, and the extensive-activity and routing-oracle debts, canonical AT-0521 … AT-0532; Phase 57, the spark caught — one cooperative activator/recovery law, autonomous nucleation and autonomous restoration on a random cubic substrate, canonical AT-0509 … AT-0520; Phase 56, the phase speed limit and the autonomous excitable law, canonical AT-0493 … AT-0508; Phase 55, phase-selective causality after the transport-implies-signalling correction, canonical AT-0479 … AT-0492; Phase 54, the accessibility / locality no-go search, canonical AT-0464 … AT-0478; Phase 53, the external theory cross-check and no-signalling stress test, canonical AT-0454 … AT-0463; Phase 52, the access-channel paradox and the constraint-structure hypothesis, canonical AT-0439 … AT-0453; Phase 51, the four-ruler phase search, canonical AT-0431 … AT-0438; Phase 50, folded / unwrapped emergence, canonical AT-0425 … AT-0430; Phase 49, crack the wall, canonical AT-0415 … AT-0424; Phase 48, the sharpened bound, canonical AT-0407 … AT-0414; Phase 47 foundational reset is canonical AT-0401 … AT-0406 / requested AT-0373 … AT-0378; Phase 46 resonant adjacency is canonical AT-0391 … AT-0400 / requested AT-0363 … AT-0372)", "benchmarkSeeds": [ "seed 223", "seed 247", "seed 255", "seed 263", "seed 273", "seed 283", "seed 293", "seed 303", "seed 313", "seed 331", "seed 343", "seed 353", "seed 363", "seed 373", "seed 407", "seed 415", "seed 425", "seed 431", "seed 439", "seed 454", "seed 464", "seed 479", "seed 493", "seed 509", "seed 521", "seed 533", "seed 545", "seed 557", "seed 569", "seed 581", "seed 595", "seed 609", "seed 628" ], "coreObjective": "Determine whether a lawful, substantial change of operational relational location is possible without destructive traversal: identity and its operational invariants preserved throughout the transition rather than only at the endpoint, interaction local with bounded propagation, finite accounted action, no hidden state debt, and robustness, scale-consistency and nontriviality all demonstrated rather than assumed.", "formulation": [ "Relational address R_X = (r_X1, …, r_XN); relational distance D(A,B) = F(R); adjacency threshold D(A,B) ≤ ε.", "Adjacency cost C_A = Σ |R'_ij − R_ij|; adjacency gain Γ_A = |ΔD| / C_A, with zero cost handled explicitly.", "Identity is a vector observable I with a coupling map M from address change into identity change; coupled dynamics Î = I + κ·M R.", "Scores are pathwise: peak_t |ΔI| over the whole transition, not the final reading; memory residue is read after interaction is restored to baseline.", "Every coupling schedule obeys a mandatory floor and must restore full baseline coupling before the run ends, so no result can be bought by decoupling.", "Auxiliary control terms must be local, bounded, frozen after discovery, necessary by ablation, and fully charged for their action.", "Two-layer architecture (AT-0263): a deeper relational layer Y, a projection pi: Y → X onto emergent observable geometry, operational observables O, identity read only through O ∘ pi, and transitions restricted to bounded local Y steps.", "Projection leverage L = D_X(pi(yA), pi(yB)) / D_Y(yA, yB), always reported after operator-norm (linear) or peak local Jacobian (nonlinear) normalisation and against matched random-map controls.", "Continuity no-go (AT-0273): for a fixed smooth pi and a continuous path gamma in Y, pi . gamma is continuous in X. A skip therefore requires Jacobian stretch, singular or discontinuous behaviour, or a dynamical pi / g_X. If pi is globally 1-Lipschitz then D_X <= D_Y and large leverage is impossible. Model theorem, not a physical law.", "Foundational bound (AT-0401): if X is obtained from S by a FIXED, single-valued, globally L-Lipschitz map F, then d_X(F(a),F(b)) <= L d_S(a,b). Normalising L ~ 1, arbitrarily large 'far in X while close in S' leverage is impossible. Model theorem plus seeded numerical check, not physics.", "Escape classes (AT-0402), exhaustive because each negates one hypothesis of that theorem: E1 non-Lipschitz / singular or critical regions; E2 dynamical map or emergent metric; E3 lawful path metric differs from the static state metric; E4 quotient, branching or topology change. No fifth branch is admitted.", "Dynamic layer: pi_lambda and g_X(lambda) with lambda a tracked degree of freedom. Every edit is rate-capped, propagates one link per step from the traveller's own site, is charged at a declared price, and must be restored to baseline before the run is scored." ], "scientificStatus": [ "NO PHYSICAL MECHANISM. Nothing in this program proposes or identifies a physical process.", "NO PHYSICAL EVIDENCE. Every number is a property of equations we wrote ourselves, integrated on small synthetic systems.", "TOY COMPUTATIONAL PROGRAM. Results are labelled MATHEMATICAL PROPERTY, COMPUTATIONAL RESULT or MODEL HYPOTHESIS, and unmodelled constraints are marked NOT MODELED rather than PASS.", "Graph-distance reduction is never presented as spacetime manipulation. Failed experiments remain visible and versioned.", "CURRENT STATUS: BOUNDED LEVERAGE / NO PARAMETRIC SHORTCUT FAMILY FOUND. The programme is a mathematical bound and a computational framework. No physical mechanism, no physical evidence.", "FRONTIER RESOLVED CONCEPTUALLY (Phase 73): architecture-only FTL is ruled out under the explicit local finite-speed assumptions — strictly local interactions on a graph, a finite measured earliest-influence delay on every physical channel, an unpredictable post-arming payload, and a complete channel inventory. The experimentally open question is whether the apparatus ever violates its fully calibrated physical causal envelope D_tau. Physical evidence remains NONE.", "FRONTIER EXPERIMENT NOW SPECIFIED (Phase 75): the decisive test is the DELAY-AMPLIFIED NO-HIDDEN-SHORTCUT TEST. Rather than resting on a few hundred picoseconds of apparent advance on a short bench, the design engineers the causal separation — microseconds of calibrated fibre/delay-line group delay in every inventoried permitted route against sub-nanosecond, picosecond-precision distributed timing — with an unpredictable hardware-RNG payload generated only after arming, first valid decode as the only accepted observable, D_tau taken as the empirical minimum over all measured physical paths, and delay scaling plus cable-swap nulls and hidden-shortcut positive controls to separate a fixed instrumentation offset from a bypass. TOY ARCHITECTURE remains CONDITIONAL / UNRESOLVED where exact-fabric concurrency and throughput debts stand. PHYSICAL EVIDENCE: NONE.", "VERIFICATION LADDER DEFINED (Phase 76): engineering begins only after the full causal-bound protocol is cleared with reproducible hardware data. Seven gates — V0 protocol frozen, V1 bench repeatability, V2 delay scaling, V3 apparatus permutation, V4 independent timing, V5 independent replication, V6 external replication — all standing at NOT STARTED. Tier 1 engineering (architecture/reliability, separate rig only) unlocks at V1-V3; Tier 2 anomaly characterization at V4-V6; only V6 permits the claim status REPLICATED CAUSAL-BOUND ANOMALY, which still authorises no FTL or spacetime reading. The GOLDEN METROLOGY RIG (frozen, minimal, auditable) and the ENGINEERING RIG (optimised, scalable) are permanently separated and no data crosses between them. Eight handoff metrics are all PENDING, and pending is treated as red. PHYSICAL EVIDENCE: NONE.", "Mechanism-of-the-hour branches remain preserved and rerunnable but are no longer the front of the programme. They are all downstream of the sharpened bound Q = D_X / C_S <= L / c (B55)." ], "entries": [ { "id": "COGEN-006", "title": "PHASE 137 — DYNAMICAL SPECTRAL GEOMETRY TOY UNIVERSE — ledger continued, 27 August 2026", "status": "implemented", "outcome": "TOY / CONCEPTUAL MODEL ONLY. NOT PHYSICAL EVIDENCE. Two-point finite spectral geometry with off-diagonal Dirac scale m: D = [[0,m],[m,0]] gives Connes distance d = 1/|m|. The SAME m is reused in multiple probe Hamiltonians H_a = s_a[[0,m],[m,0]], so perfect transfer time is T_a = pi/(2 s_a |m|). After probe-specific calibration all three probes — photon-like s = 1, matter-like s = 0.37, clock-probe s = 0.13 — infer the SAME common distance 1/m with ZERO universality mismatch across m = {0.25, 0.5, 1, 2, 4, 8}. Photon transfer times for those m: 6.283185, 3.141593, 1.570796, 0.785398, 0.392699, 0.196350; corresponding distances 4, 2, 1, 0.5, 0.25, 0.125. This satisfies CO-GENERATION BY CONSTRUCTION — one operator scale controls both metric and dynamics — and is explicitly NOT evidence of controllable spacetime geometry: increasing m is equivalent to strengthening the underlying coupling. KEY FAILURE/LESSON: co-generation can be TAUTOLOGICAL if the geometry operator is simply identified with the interaction generator; the missing physics is the independent RESOURCE LAW governing changes in D. NEW GATE, DYNAMICAL-OPERATOR COST: for a claimed geometry change D0 -> D*, explicitly account for the energy, action, control bandwidth, preparation time and locality needed to produce delta-D; a candidate FAILS if creating delta-D already requires an ordinary distance-spanning interaction or equivalent hidden infrastructure. ACTIVE GATES now: Co-Generation, Probe Universality, Causal Excess, Shortcut Cost Scaling, Render-vs-Engine, Reversibility, Dynamical-Operator Cost. ACTIVE MASTER QUESTION UPDATED: what physical law governs the dynamics and resource cost of the operator/algebraic structure that generates locality? BOUNDARY PUSH recorded with two parallel interpretations — (A) emergent-physics: locality/metric are phases of a deeper operator-algebraic system; (B) simulation-substrate analogy: rendered coordinates are outputs and the scientifically meaningful target is the update/connectivity rule, with the simulation reading stated explicitly as a THOUGHT EXPERIMENT, not an empirical conclusion. LITERATURE CHECKPOINT, precedent only and NOT validation: Carlo Rovelli, Phys. Rev. Lett. 83, 1079 (1999), Spectral Noncommutative Geometry and Quantization — a finite-dimensional dynamical spectral triple whose physical phase space is a space of Dirac operators, with D quantized and the Connes distance becoming discrete; an established mathematical toy model, not evidence for lab control of spacetime. 2026 CONTEXT: mereological quantum phase transitions, Phys. Rev. A 113, 042201 (1 April 2026), show parameter-dependent generalized tensor-product structures selected by a scrambling functional can reorganize sharply across transitions — relevant because subsystem/locality structure can itself be emergent, but it demonstrates no spacetime shortcut. Ledger entries L33-L37; next tests AT-0816 … AT-0818. PHYSICAL EVIDENCE: NONE.", "route": "/lab/co-generation" }, { "id": "COGEN-007", "title": "PHASE 139 — PRE-GEOMETRIC CONNECTIVITY SCAN — ledger continued, 27 August 2026", "status": "implemented", "outcome": "TOY / CONCEPTUAL ONLY. NOT A DISCOVERY. PHYSICAL EVIDENCE: NONE. Microscopic model uses NO x,y,z coordinates; the graph Hamiltonian depends only on relational invariants — preferred valence k0 = 4, triangle penalty, disconnectedness penalty, and control parameter lambda multiplying algebraic connectivity (graph Laplacian second eigenvalue, mu_2). N = 16 simulated annealing. RECORDED ROWS: lambda 0 -> 32 edges, 1 component, mean degree 4.000, degree std 0, triangles 0, mu_2 = 1.6304, avg graph distance 1.9500. lambda 2 -> 33 edges, mean degree 4.125, triangles 0, mu_2 = 2.0128, avg distance 1.9000. lambda 5 -> 32 edges, degree 4, triangles 0, mu_2 = 1.8743, avg distance 1.8833. lambda 10 -> 33 edges, mu_2 = 2.1531, avg distance 1.8833. lambda 20 -> 39 edges, mean degree 4.875, mu_2 = 2.8879, avg distance 1.7167. lambda 40 -> 39 edges, mean degree 4.875, triangles 1, mu_2 = 3.0000, avg distance 1.6833. INTERPRETATION: purely relational control drives increasing connectivity and shorter emergent graph distance with NO embedded Euclidean coordinates — but the toy does NOT yield an extended low-dimensional manifold or a bounded adjacency defect; it drifts toward denser small-world-like connectivity. EXPLICIT FAILURE NOTE: PRE-GEOMETRIC DOES NOT AUTOMATICALLY MEAN GEOMETRIC. NEW GATE, LOW-DIMENSIONAL EMERGENCE: require a phase with stable finite spectral dimension, local propagation and approximate manifold behavior; only then test a localized defect phase. NEW RESEARCH QUESTION ADOPTED PROMINENTLY: can a coordinate-free relational Hamiltonian produce TWO controlled phases — (1) an extended low-dimensional local geometry and (2) a reversible localized adjacency defect — without explicit long-range terms or hidden preparation cost? LITERATURE CHECKPOINTS, precedent and caution only, NOT validation: Quantum Graphity, Phys. Rev. D 77, 104029 (2008) — background-independent dynamical graphs with proposed low-energy local ordered phase; Wilkinson & Greentree, Phys. Rev. D 92, 084007 (2015) — original graphity dynamics favored disconnected subgraphs, hypervalence term added to favor connected lattice-like graphs; Carlip, Gen. Rel. Grav. 56, 95 (2024) — most causal sets are non-manifoldlike, emergent locality remains poorly understood; mereological quantum phase transitions, Phys. Rev. A 113, 042201 (2026) — preferred subsystem structure can reorganize with a control parameter. Ledger entries L38-L42; next tests AT-0819 … AT-0821. PHYSICAL EVIDENCE: NONE.", "route": "/lab/co-generation" }, { "id": "COGEN-008", "title": "PHASE 140 — SPECTRAL-DIMENSION GATE & LOCALIZED ADJACENCY DEFECT — ledger continued, 27 August 2026", "status": "implemented", "outcome": "TOY MODEL / CONCEPTUAL MATHEMATICS ONLY. NO EVIDENCE OF PHYSICAL SPACETIME MODIFICATION. PHYSICAL EVIDENCE: NONE. Ordinary phase: periodic 8x8x8 cubic lattice, N = 512, degree 6. Endpoint pair at maximal periodic separation, baseline graph distance 12. Bounded defect: two 2x2x2 endpoint regions joined by only 8 long graph edges; endpoint graph distance collapses 12 -> 1, a 12x reduction. DIAGNOSTIC: continuous-time diffusion spectral dimension from graph Laplacian L — P(tau) = (1/N) Tr exp(-tau L), d_s(tau) = -2 d ln P / d ln tau. INTERMEDIATE-SCALE RESULTS: tau 0.25-0.6 baseline mean d_s 2.9326 vs defect 2.9455, max shift 0.0167; tau 0.6-1.5 baseline 3.5769 vs defect 3.6035, max shift 0.0392; tau 1.5-3.0 baseline 3.1543 vs defect 3.1949, max shift 0.0463; representative near-3D scale tau = 0.3900: 2.9807 vs 2.9935. INTERPRETATION: a localized relational defect can dramatically shorten one operational graph distance while leaving the surrounding bulk spectral-dimension diagnostic nearly unchanged over intermediate scales — a MATHEMATICAL NETWORK RESULT ONLY. GATES: LOW-DIMENSIONAL EMERGENCE GATE strengthened — a candidate ordinary phase must display stable manifold-like dimensional behavior BEFORE any shortcut interpretation is allowed. NEW SUB-GATE, BULK-PRESERVATION — a bounded adjacency defect must not globally destroy the surrounding emergent dimension/local geometry. IMPORTANT FAILURE WARNING: passing spectral dimension alone is INSUFFICIENT — the 8 long edges were inserted by hand, so this model FAILS the Dynamical-Operator Cost / no-cheating gate; the next target is to generate the localized defect DYNAMICALLY from coordinate-free microscopic rules. FRONTIER STATEMENT UPDATED: can a pre-geometric local/control perturbation nucleate a bounded relational defect that reduces operational distance, preserves bulk emergent dimension, co-generates multi-probe dynamics, and does not explicitly insert distance-spanning couplings? LITERATURE CHECKPOINT, related literature and NOT validation: Quantum Graphity (Konopka, Markopoulou, Severini, Phys. Rev. D 77, 104029, 2008) models emergent locality from dynamical graphs; Chen & Plotkin, Phys. Rev. D 87, 084011 (2013) found graph Hamiltonians favoring near-constant valency and local rotational symmetry can yield low-energy states close to triangulations of 2D manifolds; causal-set spectral-dimension work (Eichhorn & Mizera, 2014-era) uses diffusion/causal spectral dimension as a discriminator of manifold-like structure. Ledger entries L43-L47; next tests AT-0822 … AT-0825. PHYSICAL EVIDENCE: NONE.", "route": "/lab/co-generation" }, { "id": "COGEN-009", "title": "PHASE 141 — GEOMETRY-PRESERVATION vs SHORTCUT LEVERAGE — ledger continued, 27 August 2026", "status": "implemented", "outcome": "CONCEPTUAL / SIMULATION ONLY. NOT A DISCOVERY. NO EVIDENCE OF SPACETIME MODIFICATION. PHYSICAL EVIDENCE: NONE. Model: periodic 6x6x6 cubic lattice, N = 216, degree 6, with degree-preserving random edge swaps — local valence unchanged, long-range topology changed. Baseline average graph distance 4.5209, fixed opposite-pair distance 9. RECORDED ROWS (swaps / avg distance / pair distance / d_s RMS shift / mean d_s / pair gain): 0 / 4.5209 / 9 / 0 / 3.1918; 2 / 4.4130 / 8 / 0.0089 / 3.1985; 5 / 4.2137 / 5 / 0.0294 / 3.2144 / gain 1.8x with small spectral distortion; 10 / 4.0169 / 7 / 0.0756; 20 / 3.8292 / 3 / 0.1400 / gain 3x; 40 / 3.6259 / 3 / 0.2092; 80 / 3.4028 / 4 / 0.3721; 160 / 3.2716 / 2 / 0.4889 / gain 4.5x. Degree std stayed exactly 0 for early cases and near 0 later: the shortcut effect is NOT from changing mean valence. INTERPRETATION: a measurable geometry-preservation tradeoff — small topology changes strongly shorten selected operational distances while leaving spectral geometry nearly unchanged, but larger shortcut leverage increasingly distorts the bulk spectral dimension. NEW METRIC/GATE, GEOMETRY DISTORTION BUDGET: B_G = RMS_tau [ d_s*(tau) - d_s^0(tau) ] over a declared diffusion window; a serious bounded adjacency defect must maximize operational gain G_AB = d0/d* while keeping B_G below a PREDECLARED threshold and preserving probe universality and causality. EXPLICITLY NOT CALLED A DISCOVERY. NEXT FRONTIER QUESTION: is there a relational phase transition that achieves high G_AB / B_G without explicit distance-spanning microscopic interactions or hidden preparation cost? NEW PROTOCOL: scan a Pareto frontier of (distance gain, geometry distortion, preparation/action cost, universality mismatch, causal excess) rather than optimize any single quantity. LITERATURE CHECKPOINT, related literature and NOT validation: Watts-Strogatz small-world networks — sparse rewiring sharply reduces path lengths while retaining local structure; emergent network geometry models — small-world topology can coexist with finite spectral dimensionality; Quantum Graphity (PRD 77, 104029, 2008) remains the reference example of dynamical graphs with a proposed low-energy ordered, low-dimensional local phase. Ledger entries L48-L51; next tests AT-0826 … AT-0828. PHYSICAL EVIDENCE: NONE.", "route": "/lab/co-generation" }, { "id": "COGEN-010", "title": "PHASE 142 — GENERALIZED ADJACENCY-COST BOUND SEARCH — ledger continued, 27 August 2026", "status": "implemented", "outcome": "TOY SCALING ANALYSIS. NOT EVIDENCE OF NEW PHYSICS. PHYSICAL EVIDENCE: NONE. PURPOSE: test whether effective shortcuts can beat a generalized conservation/accounting law once setup, infrastructure, and transfer are ALL counted. Scaling toy models over emergent separation r = 2…256: LOCAL CHAIN J ~ 1/r, C ~ r, prep ~ r — total at r = 256 is 768, effective scaling exponent ~ 1.0000. POWER-LAW alpha = 1/2: J ~ r^-1/2, C ~ r^1/2, prep ~ r^1/2 — total 48, exponent ~ 0.5000. PREBUILT GLOBAL BUS: J ~ const but C ~ r, prep ~ r — total 513, exponent ~ 0.9936, showing apparent distance-independence DISAPPEARS under full accounting. IDEAL LATENT ADJACENCY: J ~ const, C ~ const, prep ~ const — total 3, exponent ~ 0, HYPOTHETICAL ONLY. LOGARITHMIC HIERARCHICAL SUBSTRATE: J ~ 1/log2(r+1), C ~ log2(r+1), prep ~ log2(r+1) — total ≈ 24.0169, exponent ≈ 0.2218; this identifies hierarchical/pre-geometric structures as the ONLY toy class tested with strongly sublinear total scaling WITHOUT linear hidden infrastructure. NEW WORKING CONJECTURE: conventional architectures expose an adjacency-cost exponent z_total ≈ 1 somewhere in total causal accounting; genuinely interesting candidates require z_total < 1 AFTER including preparation, activation, transfer, infrastructure, and reset. DEFINITION: z_total(r) = d ln C_total / d ln r, with C_total = C_prepare + C_activate + C_transfer + C_infrastructure + C_reset. TARGET: z_total < 1 while passing Probe Universality, Causal Excess, Bulk Preservation, Geometry Distortion, Reversibility, and Dynamical-Operator Cost gates. NEW GATE, NO PREPAYMENT ESCAPE: a mechanism gets NO credit for constant transfer latency if setup/infrastructure cost scales linearly with emergent distance. RESEARCH FOCUS: latent adjacency, hierarchical substrates, and phase-selected pre-geometric relations — NOT ordinary buses or manually inserted long edges. LITERATURE CHECKPOINT, related literature and NOT validation: 2026 work continues to study phase transitions in quantum geometry including 4D causal dynamical triangulations; Quantum Graphity (PRD 77, 104029, 2008) remains a model of emergent locality/geometry from dynamical graphs; current QEC/holographic experiments simulate gravity-like signatures but remain toy models rather than physical spacetime modification. Ledger entries L52-L55; next tests AT-0829 … AT-0831. PHYSICAL EVIDENCE: NONE.", "route": "/lab/co-generation" }, { "id": "COGEN-011", "title": "PHASE 143 — LATENT HIERARCHY SCALING TEST — ledger continued, 27 August 2026", "status": "implemented", "outcome": "TOY SCALING ANALYSIS / ARCHITECTURE ONLY. NOT EVIDENCE. PHYSICAL EVIDENCE: NONE. Ordinary emergent sites are treated as the LEAVES of a balanced binary relational hierarchy. Ordinary visible locality costs ~ r; latent hierarchical access costs 2·ceil(log2 r) + 1. RESULTS: r = 256 -> hierarchy cost 17, gain 15.06x; r = 4096 -> cost 25, gain 163.84x; r = 65536 -> cost 33, gain 1985.94x. Effective finite-range scaling exponent across the tested range ~ 0.1683, tending toward LOGARITHMIC rather than power-law scaling. INTERPRETATION: architecture only, not evidence — but a strong conceptual inversion: perhaps deeper connectivity is ALREADY present and ordinary locality is an accessibility constraint / projector rather than an absence of relations. NEW HYPOTHESIS: G_visible = Pi_0 G_F Pi_0, with candidate locality-projector mechanisms energy gaps, selection rules, superselection sectors, code subspaces, phase-dependent coupling and operator-algebra accessibility. KEY EXPERIMENT ADOPTED: measure the COMPLETE T_AB(r) scaling after preparation and infrastructure costs, and distinguish r, r^alpha, log r and r^0. Ledger entries L56-L58; next tests AT-0832, AT-0833. PHYSICAL EVIDENCE: NONE.", "route": "/lab/co-generation" }, { "id": "COGEN-012", "title": "PHASE 144 — LOCALITY PROTECTION vs HIDDEN-HIERARCHY ACCESSIBILITY — ledger continued, 27 August 2026", "status": "implemented", "outcome": "TOY SCALING ANALYSIS. NO NEW-PHYSICS EVIDENCE. PHYSICAL EVIDENCE: NONE. A gapped hierarchical substrate is tested: hierarchical path length L ~ log2 r, and for local off-resonant coupling the schematic J_eff ~ g (g/Delta)^L gives T(r) ~ r^[log2(Delta/g)]. RESULTS: Delta/g = 1.10 -> z = 0.1375; 1.25 -> 0.3219; 1.50 -> 0.5850; 2 -> 1.0000; 3 -> 1.5850; 5 -> 2.3219; 10 -> 3.3219. NEW FINDING: if Delta/g > 2 the gap that strongly hides and protects the latent hierarchy DESTROYS the sublinear advantage; Delta/g = 2 is asymptotically linear; sublinear scaling requires a weakly gapped, strongly hybridized hidden sector — precisely the sector that fails to protect ordinary locality. NEW GATE/TRADEOFF, LOCALITY PROTECTION-ACCESSIBILITY: a viable locality projector must suppress ordinary leakage strongly while allowing an activation that does not make transfer scaling linear or superlinear. LITERATURE CHECKPOINT, context only and NOT validation: Quantum Graphity (Konopka, Markopoulou, Severini, Phys. Rev. D 77, 104029, 2008) — a background-independent model with a highly connected high-energy phase and an ordered low-dimensional local low-energy phase, supporting locality-as-phase as a MODEL CONCEPT, not an experimental fact; 2026 modular-time/QNEC work and recent tensor-network / emergent-geometry work are listed as ADJACENT MATHEMATICAL CONTEXT only, not evidence for controllable locality. MASTER TARGET UPDATED: rich substrate + locality projector + controllable sector change + sublinear FULL causal cost + probe universality + bulk geometry preservation + NO inserted A<->B channel, all at once. Ledger entries L59-L62; next tests AT-0834 … AT-0836. PHYSICAL EVIDENCE: NONE.", "route": "/lab/co-generation" }, { "id": "COGEN-020", "title": "PHASES 212–223 — RESPONSE-INFERRED GEOMETRY, THE ACCESSIBLE OBSERVABLE ALGEBRA, THE DYNAMICAL FACTORIZATION SIEVE & OBJECTHOOD WITHOUT COORDINATES — ledger continued, 28 August 2026", "status": "implemented", "outcome": "TOY MODELS ONLY. NOT PHYSICAL EVIDENCE. PHYSICAL EVIDENCE: NONE. A run of toy computations over a four-qubit Hilbert space whose conclusions are hygiene properties, not discoveries, and explicitly NOT evidence for new spacetime physics. PHASE 212 (RESPONSE-DEFINED GEOMETRY GATE): operational geometry was inferred from measurable response strengths rather than from index labels — pair edges and geometry read from the response matrix. PHASES 213–215 (REPRESENTATION-INVARIANCE GATE): factorization recovery and sector-dependent geometry were verified representation-invariant across 20 global basis scrambles once the generator pool was transformed with them; Hamiltonian locality is relational to the chosen tensor-product structure, not absolute. PHASE 216 (DYNAMICAL FACTORIZATION GATE): dynamics (mean single-factor linear entropy) prefer a low-entangling factorization class — native ≈ 0.00404 vs random 2×2×2×2 candidates mean ≈ 0.00693 (std 0.00032) — but factor dimensions 2×2×2×2 were ASSUMED, so this is selection within a class, not full emergence. PHASE 217 (FACTORIZATION GAUGE-EQUIVALENCE GATE): the low-entangling score is stable (≈ 0.0036–0.0039) under local product-unitaries and factor permutations, so the sieve selects an equivalence class, not coordinate labels. PHASES 220–223 (OBJECTHOOD WITHOUT COORDINATES & THE PARETO BASIN): simultaneously ran persistence, communication and scrambling gates — the aligned 2×2×4 class survived while 2×2×2×2 failed communication at one sampled time. PHASE 221 (TIME-SCALE ROBUSTNESS GATE): across t = 0.10–0.80, 2×2×2×2 survived all five times, 2×2×4 survived four, while 2×8 and 4×4 failed all. PHASE 222 (MAJORITY-WIN-TIE GATE): the coarse majority-win perturbation-robustness rule was INCONCLUSIVE — it produced many ties and failed to cleanly separate classes. PHASE 223 (PERSISTENCE–COMMUNICATION TRADEOFF GATE / DIRECT ROBUSTNESS DIFFERENTIAL): measured the Pareto balance between 2×2×2×2 (higher persistence, lower scrambling) and 2×2×4 (higher communication) across perturbation sweep eta ∈ [0, 0.20]. SYNTHESIS: the ACCESSIBLE OBSERVABLE ALGEBRA 𝔄_acc is identified as the missing substrate primitive, and OBJECTHOOD is redefined as a POINT ON A PARETO FRONTIER rather than a single scalar optimum — an emergent object may be a tradeoff, not a maximum. LITERATURE CHECKPOINT, related literature and NOT validation: Zurek's decoherence / einselection and the predictability-sieve / quantum-Darwinism literature (which selects stable records but does not uniquely derive subsystem factorization by itself). Six new gates adopted across Phases 212–217; every gate makes the programme harder to satisfy. FAILED AND INCONCLUSIVE RESULTS PRESERVED: MDL compression recorded as a FAILURE; Phase 222 recorded as INCONCLUSIVE; the 2×2×2×2 factor dimensions remain an assumption. SURVIVING TARGET UNCHANGED: a viable microscopic algebra must produce sparse O(1)-degree adjacency directly. Ledger rows L127–L137; next targets Phase 218 (remove assumed factor dimensions, compare all admissible decompositions), Phase 219 (basis-independent multi-gate selection) and Phase 224 (derive a basis-independent, coefficient-free Pareto / feasibility principle; test whether the stable classes of Phases 220–223 form robustness basins without a hand-picked scalar optimum). PHYSICAL EVIDENCE: NONE.", "route": "/lab/co-generation" }, { "id": "COGEN-022", "title": "PHASES 230–232 — EQUAL-OBJECT-COUNT DUAL-LOCALITY CONSTRUCTION, ORIGINAL-GRAPH-LOCAL REFACTORIZATION & THE FINITE-DEPTH LIGHT-CONE NO-GO — ledger continued, 28 August 2026", "status": "implemented", "outcome": "FINITE TOY ALGEBRA ON FOUR TWO-LEVEL FACTORS. NOT EVIDENCE OF SPACETIME MODIFICATION. PHYSICAL EVIDENCE: NONE. PHASE 230 (EQUAL-OBJECT REFACTORIZATION GATE + SUPPORT-GRAPH NON-ISOMORPHISM GATE): an exact search over Clifford refactorizations on four two-level factors, requiring the same 4 objects and information capacity, the same fixed abstract H, F* = W F0 W-dagger with W genuinely entangling, exact Pauli weight <= 2 in BOTH factorizations, and non-isomorphic support graphs. The first unconstrained exact construction appeared at trial 55 but was REJECTED because its F* graph was disconnected. Phase 230B additionally demanded both graphs connected with equal edge count; found at trial 134: F0 terms [IZIZ, IIYZ, YIIY] with W = [CX(3,0), CZ(1,0), H(1), CX(3,0)] giving F* terms [ZXII, IIYZ, YIIY]; F0 edges (0,3),(1,3),(2,3) degree sequence [1,1,1,3] = star K1,3, F* edges (0,1),(0,3),(2,3) degree sequence [1,1,2,2] = path P4; both connected, 3 edges each, non-isomorphic, max Pauli weight 2 in both. EXACT FINITE EXISTENCE RESULT: one fixed abstract H can be sparse 2-local under two inequivalent equal-object-count tensor-product structures with genuinely different adjacency graphs. It does NOT show either structure is physically selected, does not change H, and does not imply any spacetime change. PHASE 231 (LOCAL-SELECTION-COST GATE): the search was strengthened so every two-body Clifford gate defining W lies on an edge of the ORIGINAL F0 support graph G0; found at trial 855: F0 terms [IIXX, IXIZ, IIYX, ZIZI] with G0 edges (0,2),(1,3),(2,3) degree sequence [1,1,2,2] = path P4, W = [H(2), CX(0,2), CZ(0,2), CX(3,2), CZ(0,2), S(1)] with every two-body gate G0-local, giving F* terms [ZIIX, IYIZ, IIXY, IIXZ] with G* edges (0,3),(1,3),(2,3) degree sequence [1,1,1,3] = star K1,3 — same 4 objects, same 3 edges, both connected, non-isomorphic, exact max Pauli weight 2 in both. This removes the simplest finite-size global-basis-rewrite objection at N = 4 but remains a CIRCUIT defining an alternate tensor structure, NOT a demonstrated state-driven phase transition. PHASE 232 (FINITE-DEPTH REFACTORIZATION NO-GO): for a depth-d circuit of bounded-range gates local on G0, supp(W O_A W-dagger) is contained in the graph-distance-d neighborhood N_d(A), so moving support a distance r requires d >= r, and two-sided overlap requires d >= ceil(r/2). Path examples N = 8, 16, 32, 64, 128, 256 have endpoint r = 7, 15, 31, 63, 127, 255 with minimum overlap depths 4, 8, 16, 32, 64, 128 and d/r -> 1/2. A bounded-depth ordinary-local refactorization CANNOT create a macroscopic adjacency change across unbounded ordinary distance; this is a graph/circuit causal-cone constraint analogous in spirit to Lieb-Robinson locality and is NOT a spacetime theorem. SYNTHESIS: Phase 230 answers the finite mathematical existence question positively, Phase 231 shows such a refactorization can be synthesized with G0-local gates, and Phase 232 restores the scaling wall. The only admissible remaining openings are (A) F* as a PRE-EXISTING metastable algebraic sector selected by a local order parameter rather than dynamically created, (B) selector dynamics local in a deeper metric different from the emergent G0, or (C) abandoning the macroscopic shortcut — each still subject to Support-Invariance, First-Arrival, Pre-Arming, Probe Universality and no-prepayment gates, and none constructed. Four new gates; ledger rows L145-L149. Next target Phase 233: fix H and both tensor-product structures in advance and test whether a local or low-dimensional order parameter can change which factorization is dynamically stable WITHOUT applying W as a circuit — construct it or kill it. PHASE 183 SUPPORT-INVARIANCE REMAINS UNDEFEATED. THIS IS FINITE TOY ALGEBRA, NOT EVIDENCE OF SPACETIME MODIFICATION. PHYSICAL EVIDENCE: NONE.", "route": "/lab/co-generation" }, { "id": "COGEN-021", "title": "PHASES 224–229 — THRESHOLD-FREE PARETO OBJECTHOOD, TWO FAILED LOCALITY-TRANSITION ATTEMPTS, A REJECTED LOCALITY METRIC & THE OBJECT-COUNT vs CROSS-SUPPORT FRONTIER — ledger continued, 28 August 2026", "status": "implemented", "outcome": "TOY MODELS ONLY. NOT PHYSICAL EVIDENCE. PHYSICAL EVIDENCE: NONE. PHASE 224 (PARETO-OBJECTHOOD GATE): all median thresholds and weighted scalar objectives were removed; candidates are compared only by Pareto dominance on persistence P (max), communication C (max) and scrambling S (min). Over 48 candidates per class at t = 0.15, 0.30, 0.60 under random global orientations, 2×2×2×2 reached the nondominated frontier 15/48 (31.25%), 2×2×4 3/48 (6.25%), 2×8 and 4×4 zero; aligned candidates tie at t = 0.15 and 0.30 and only 2×2×2×2 remains at t = 0.60. Threshold-free selection FAVOURS but does NOT DERIVE 2×2×2×2; nondominated candidates stay unresolved. PHASE 225 (CONTINUOUS-KNOB BASIN GATE) — FAILURE: sweeping lambda 0→3 on H(lambda) = ordinary chain + lambda·selector-controlled hidden interaction gave 10 tradeoffs out of 13 samples with 4-factor dominance only at isolated lambda = 2.0, 2.75, 3.0 and no contiguous basin; the one-gain-knob-flips-locality story is recorded as failed. PHASE 226 (COMPETING-SYMMETRY TRANSITION GATE) — FAILURE / NEGATIVE RESULT: interpolating H(theta) = cos(theta)H0 + sin(theta)H1 between two competing interaction organizations gave 15 tradeoffs of 17 samples, 2 favouring 4-factor and none favouring 3-factor — no order-parameter crossing, no locality phase transition. PHASE 227 (COARSE-GRAINING BIAS GATE) — METRIC CONSTRUCTED AND REJECTED BY US: the cross-factor fraction X = ||H_cross||_F^2/||H||_F^2 after one-factor projection kept F4 = [2,2,2,2] at 1 while F3 = [2,2,4] fell to ≈ 0.006, an artefact of a larger factor absorbing interactions as internal; any metric that rewards merging factors is inadmissible without an object-count correction. PHASE 228 (K-LOCALITY DEFINITION GATE): class-normalized locality surprise z = (observed − random_mean)/random_sd drove F3 to z ≈ −38 to −42 while F4 stayed at z ≈ +2.4 to +2.9, exposing a deeper mis-specification — one-factor locality is the wrong notion because ordinary locality is FEW-BODY, not one-body. PHASE 229 (OBJECT-COUNT PRESERVATION GATE): a coefficient-free structural comparison maximizing N_obj and minimizing E_cross and max cross degree gives, for H0, F4 (N=4, E=3, deg 2, supports (0,1),(0,3),(1,2)) DOMINATING F3 (N=3, E=3, deg 2), and for H1 a Pareto tradeoff between F4 (4,3,2) and F3 (3,2,2) — merging factors reduces cross-support ONLY by destroying independently addressable objects. SYNTHESIS: the strongest admissible target becomes a SAME-OBJECT-COUNT REFACTORIZATION / algebraic phase transition — F0 and F* with N_obj(F0) = N_obj(F*), comparable information capacity, no object merging, yet Support_low-k(H|F0) ≠ Support_low-k(H|F*), both dynamically stable and probe-universal; this would satisfy Phase 183 Support-Invariance by RECLASSIFYING existing operator support rather than creating it, and it remains COMPLETELY HYPOTHETICAL. Six new gates; ledger rows L138–L144; failures and rejected metrics preserved permanently. Next target Phase 230: construct two equal-object-count factorizations of the same algebra in which one fixed H is sparse low-k in both with genuinely different adjacency graphs, and test whether a state or control change can select between them without globally rewriting H — otherwise record the no-go. PHASE 183 SUPPORT-INVARIANCE REMAINS UNDEFEATED. NOT EVIDENCE FOR NEW SPACETIME PHYSICS. WE ARE NOT CLOSE TO A BREAKTHROUGH. PHYSICAL EVIDENCE: NONE.", "route": "/lab/co-generation" }, { "id": "COGEN-005", "title": "PHASE 132 — RENDERED COORDINATES vs SUBSTRATE DYNAMICS — ledger continued, 27 August 2026", "status": "implemented", "outcome": "TOY CONCEPTUAL TEST ONLY. NOT PHYSICAL EVIDENCE. Toy substrate: 8 states on a fixed update ring (each state can only cause the next along the ring). MOVE A — change only the rendering map: two substrate-neighbour states were placed 7 rendered units apart while their substrate causal distance remained exactly 1; the picture changed, the engine did not. MOVE B — change the update graph itself: the causal distance between the same two states changed from 1 to 7; the engine changed and the picture merely reported it. CORE DISTINCTION: changing the rendered map or encoding is NOT the same as changing the engine or the dynamics. Framed for both angles: (A) emergent-spacetime physics — coordinate/encoding change never changes the physics, only a change in interaction graph, generator or algebra changes what can cause what; (B) simulation thought experiment — re-rendering the world moves nothing in the substrate, so changing adjacency for inhabitants requires changing the substrate's update rules themselves. NEW FALSIFICATION GATE, RENDER-VS-ENGINE: a candidate mechanism only advances if causal/dynamical observables change (earliest arrival, influence spread, update adjacency), not merely reconstructed coordinates, embeddings or labels; it is consulted BEFORE Causal Excess, Probe Universality, Co-Generation and Shortcut Cost Scaling — a mechanism that fails it has nothing for the other gates to evaluate. Five gates now stand separately. Literature alignment recorded as motivation only, NOT validation: mereological quantum phase transitions (Phys. Rev. A 113, 042201, 2026) study parameter-dependent generalized tensor-product structures/operator algebras selected via scrambling minimization — a concrete published example where subsystem structure itself can reorganize, directionally relevant to the engine side of the distinction but reporting no shortcut, no causal excess and no support for Adjacency Theory. Ledger entries L29-L32; next tests AT-0814 … AT-0815. PHYSICAL EVIDENCE: NONE.", "route": "/lab/co-generation" }, { "id": "COGEN-004", "title": "PHASE 131 — NON-EUCLIDEAN MICROSCOPIC DISTANCE SEARCH — ledger continued, 27 August 2026", "status": "implemented", "outcome": "CONCEPTUAL / THEORETICAL SCAN ONLY. Nothing simulated, built or measured; the priority matrix is explicitly HEURISTIC. NOT PHYSICAL EVIDENCE. Phase 130 priced shortcuts in ordinary separation r; Phase 131 asks the escape question: is there a microscopic variable for which r is the wrong coordinate — closeness set instead by state-space, algebraic, spectral, shared-mode or logical separation — so the SHORTCUT COST SCALING gate must be re-run in the native variable where p_eff < 1 might hold without hiding. STRENGTHENED TARGET QUESTION adopted: what microscopic relational variable can be CLOSE in its native state space while its emergent spatial images are FAR APART, and can that same variable co-generate geometry plus universal probe dynamics. Eight candidate families tracked in parallel with a heuristic priority matrix (co-generation potential, causality cleanliness, experimental reach, reduced dependence on Euclidean separation; 0-3 heuristic scores, NOT measurements): operator-algebra geometry, dynamical graph/graphity, synthetic frequency dimensions, QEC/logical reconstruction, shared cavity/collective modes, power-law interactions, topological modes, actual spacetime topology change. Heuristic top tier: operator-algebra geometry, dynamical graph/graphity, synthetic frequency dimensions, QEC/logical reconstruction; actual spacetime topology change remains deep/high-risk and NOT experimentally reachable. All four gates stand separately: CAUSAL EXCESS, PROBE UNIVERSALITY, CO-GENERATION, SHORTCUT COST SCALING. Literature alignment recorded as motivation only, NOT validation: 2025 JHEP operator-algebra/entanglement/emergent-geometry-from-matrices work; 2025 PRD emergent geometry from quantum probability / von Neumann algebra conditional expectations; 2024 Communications Physics synthetic-dimensions perspective; 2025 Nature Communications programmable photonic frequency synthetic dimensions with tunable long-range coupling; 2025 PRL essay on holographic spacetime from quantum information. Ledger entries L25-L28; next tests AT-0811 … AT-0813. PHYSICAL EVIDENCE: NONE.", "route": "/lab/co-generation" }, { "id": "COGEN-003", "title": "PHASE 130 — SHORTCUT RESOURCE-SCALING TEST — ledger continued, 27 August 2026", "status": "implemented", "outcome": "SIMULATED / THEORETICAL. NOT PHYSICAL EVIDENCE. Toy setup: ordinary locality is a 401-node chain with baseline A->B graph distance 400; one shortcut edge spans ordinary separation r at traversal cost 1, giving new distance ~401 - r and distance saved r - 1. Generic resource/energy penalty E(r) = k r^p with k = 1 used for scaling comparison only; efficiency eta = (distance saved)/E. Numerical scan r = [10,20,40,80,120,160,200,240,280,320,360] and p = [0, 0.5, 1, 2]. At r = 360 the new distance is 41 and the saving is 359: eta = 359 at p = 0, ~18.920961 at p = 0.5, ~0.997222 at p = 1, ~0.002770 at p = 2. At p = 2 the best efficiency in the tested grid is at the SMALLEST span, r = 10, eta = 0.09 — long shortcuts become catastrophically inefficient. INTERPRETATION: if the physical cost of creating a relational edge grows faster than linearly with ordinary separation, macroscopic adjacency shortcuts are strongly suppressed; if cost is linear, benefit/cost asymptotes to order unity; only sublinear or approximately distance-independent edge cost permits increasing leverage with scale in this toy metric. This is NOT a theorem about gravity or nature — the cost rule was declared by us. It is a generic resource-scaling FILTER for candidate mechanisms. NEW GATE, SHORTCUT COST SCALING: every proposed mechanism must arrive with an estimate of E_edge(r) or an equivalent preparation/action cost and its effective exponent p_eff = d ln E / d ln r; a mechanism becomes especially interesting only if its TOTAL causal/resource accounting achieves p_eff < 1 over a real scale range without hiding the distance cost in pre-established infrastructure, pre-entanglement, a cavity or waveguide, a long-range field, or external control. NEW THEORETICAL REQUIREMENT, TOTAL CAUSAL ACCOUNTING: T_total = T_prepare + T_activate + T_transfer with amortized per-use T_amortized = T_activate + T_transfer + T_prepare/N_uses, so a global bus or prebuilt network can never appear distance-independent merely because its construction and setup cost was excluded. Frontier matrix extended: every branch now also carries edge/setup cost scaling with ordinary separation and whether the distance cost is hidden in preparation or infrastructure. Literature context only, not support: quantum graphity ties locality, geometry and matter to dynamical graph structure (Phys. Rev. D 77, 104029, 2008), while later numerical work found disconnected low-energy structures in the original formulation and required added structure (Phys. Rev. D 92, 084007, 2015). Ledger entries L19-L24; next tests AT-0808 … AT-0810. PHYSICAL EVIDENCE: NONE.", "route": "/lab/co-generation" }, { "id": "COGEN-002", "title": "PHASE 128-129 — UNIVERSALITY TOY TEST & SPECTRAL-GEOMETRY AMBIGUITY — ledger continued, 27 August 2026", "status": "implemented", "outcome": "TOY SIMULATION + THEORY ONLY. NOT EXPERIMENTAL EVIDENCE. PHASE 128: one relational graph co-generates geometry and two probe dynamics; baseline graph distance A->B = 100, one shared shortcut edge (20<->80, weight 5) reduces it to 40.2 (factor ~2.48756, -59.8%). Photon-like probe (v = 1): T = 40.2, inferred distance 40.2. Matter-like probe (v = 0.37): T ~ 108.648649, independently inferred distance 40.2 — universality mismatch 0, the first toy-level PASS of the probe-universality gate. Control with a species-specific coupling change: photon infers 40.2, matter infers 100, mismatch 59.8 — the gate rejects it as designed. This does NOT establish fundamental geometry; graph, probes and perturbation were all supplied by us. PHASE 129: explicit counterexample — two connected non-isomorphic 6-node graphs share the identical Laplacian spectrum [0, 0.76393202, 2, 3, 3, 5.23606798]; Graph A degree sequence [3,3,3,2,2,1] with zero triangles, Graph B [4,2,2,2,2,2] with one triangle; both diameter 3 and average shortest path 1.6667. GEOMETRY != SPECTRUM ALONE. Co-generation requirement strengthened: a candidate fundamental object must retain the full relational operator (and likely the embedding/action of observable algebras on states), not merely a spectrum. Literature grounding recorded as theoretical precedent only: quantum graphity (with its later-identified model-building problems), 2025 operator-algebra/matrix-model reconstruction work and 2026 Spacetime-from-Operator-Algebras research — precedents, not evidence for the hypothesis. PHYSICAL EVIDENCE: NONE.", "route": "/lab/co-generation" }, { "id": "COGEN-001", "title": "CO-GENERATION & HIDDEN-GRAPH EXPANSION — ledger, 27 August 2026", "status": "implemented", "outcome": "TOY SIMULATION + THEORY ONLY. NOT EXPERIMENTAL EVIDENCE. Causal-bound benchmark at N = 400: baseline chain T = 399; a 10x faster central corridor T = 327 (gain 1.22); an inserted shortcut edge T = 80 (gain 4.99) — a faster medium is NOT changed adjacency, and causal excess Xi = T_local,min / T_observed was never above 1. Local gapped hidden mediator: J_eff ~ g^2 K^-1, range set by the gap; lowering the mass lengthens correlations only by approaching the critical/gapless regime — criticality gives long-range correlation, not super-causal signalling. Three-site CTAP dark-state transfer: fidelity 0.99365 at normalized T = 32 with max middle occupancy 0.05877 — relocation with low intermediate occupancy, ordinary causality intact. Counterdiabatic driving: fidelity ~1.0 with max middle occupancy 1.5e-5 at T = 2, but the exact transitionless term IS a direct 1<->3 endpoint coupling — the acceleration resource inserts the shortcut edge, and this is logged as a classification trap, not a result. Hidden off-resonant bus with no direct endpoint coupling: J_eff ~ -g^2/Delta; at Delta = 12 fidelity 0.999526 with max bus occupancy 0.026316, at Delta = 30 fidelity 0.999988 with max bus occupancy 0.004405 and longer transfer time — visible-graph nonlocality from enlarged-graph locality, with a speed/virtual-occupation tradeoff. NEW THEORETICAL REQUIREMENT: changing a reconstructed information metric is insufficient; a relational variable R must co-generate BOTH geometry and dynamics, d = G[R] and H_matter = H[R], with a candidate weighted graph W and Laplacian L = D - W setting emergent distance and field propagation phi_tt + c0^2 L phi = 0 simultaneously. Two master falsification gates now stand over the whole programme: CAUSAL EXCESS (Xi > 1 with every conventional channel enumerated) and PROBE UNIVERSALITY (independent photon/matter/clock probes must infer the same metric change). Master hypothesis, explicitly speculative and unproven: physical locality and physical dynamics may be co-emergent from the same relational structure. Frontier matrix ranks fourteen branches across four target levels — I propagation distance, II interaction distance, III information/reconstruction distance, IV spacetime proper distance. PHYSICAL EVIDENCE: NONE.", "route": "/lab/co-generation" }, { "id": "UNIFY-001", "title": "CANONICAL UNIFICATION — EM-TRIGGERED SCALAR PHASE TRANSITION", "status": "implemented", "outcome": "TOY / THEORETICAL MODEL ONLY. NOT PHYSICAL VALIDATION. NOT evidence of exotic gravity, FTL, teleportation or spacetime shortcuts. PHYSICAL EVIDENCE: NONE. One covariant Einstein-Maxwell-scalar-style action, S = int sqrt(-g)[M_Pl^2 R/2 - 1/2 (grad phi)^2 - V(phi) - 1/4 Z(phi) F_munu F^munu + L_m], replaces the pile of separate toy mechanisms. Minimal toy model: V = 1/2 m^2 phi^2 + lambda/4 phi^4, Z = 1 - a phi^2 + b phi^4; for a magnetic-dominated invariant X the effective mass is m_eff^2 = m^2 - 2aX with a FINITE critical threshold X_c = m^2/(2a). Below threshold phi* = 0 (C0); above it phi* = sqrt[(2aX - m^2)/(lambda + 4bX)] (C*); removing the trigger returns phi* -> 0 AUTOMATICALLY, which is the property the programme most needed and could never previously derive. 1,759 scanned parameter states passed five internal consistency filters (positive effective quartic, Z(phi*) > 0, finite threshold, bounded toy potential, restoration) — an INTERNAL NUMERICAL SCAN, not experimental confirmation and not a completeness proof. Representative normalized example m = 0.1, lambda = 1, a = 5, b = 0.01, X_c = 0.001: phi* ~ 0.050 at 1.25 X_c, ~0.100 at 2 X_c, ~0.141 at 3 X_c with Z(phi*) positive and ~0.90 at 3 X_c. Dimensionful check with u_B = B^2/(2 mu_0): 1 T ~ 3.98e5, 10 T ~ 3.98e7, 45 T ~ 8.06e8, 100 T ~ 3.98e9 J/m^3; if X = u_EM/U0 with X_c = 0.001, a 45 T threshold implies U0 ~ 8.06e11 J/m^3 — but U0 is FREE AND UNKNOWN, so the model predicts NO threshold at any field. INVARIANT CORRECTION, kept permanently visible: a freely propagating vacuum plane wave has F_munu F^munu = 0 because E^2 = c^2 B^2, so raw laser intensity is NOT automatically the trigger for an F^2-coupled model; standing waves, cavities, quasi-static magnetic/electric configurations, crossed-field geometries, plasma configurations or a different invariant must be studied instead. Carried forward: weak self-gravity backreaction changed C* propagation only ~-0.44% at max weak-field proxy ~3.4e-3, so ordinary weak gravity is a FOLLOWER, NOT THE ENGINE; and simple F(phi)R smooth amplification grew increasingly costly with stronger effective gravitational enhancement, which is what motivated threshold/screening over smooth amplification. NEW TARGET: derive rather than choose the dimensional coupling scale — for Z(phi) ~ 1 - phi^2/M^2 the threshold structure is F_c^2 ~ m_phi^2 M^2 — tracking m_phi, M, coherence range lambda_phi = hbar/(m_phi c), lab threshold B_c/E_c and existing fifth-force/EM/astrophysical bounds through a CONSTRAINT TRIANGLE (accessible threshold <-> macroscopic coherence <-> existing bounds) whose interior may well be empty. CURRENT VERDICT: general theory NOT VALIDATED; unified toy mechanism SURVIVES INITIAL MATHEMATICAL CONSISTENCY TESTS; dimensionful parameter window NOT ESTABLISHED; physical experiment NOT PERFORMED; peer review NOT PERFORMED; physical evidence NONE. NEXT ATTACK: scan (m_phi, M, self-coupling) against lab-accessible field ranges and known constraints; then test dynamics, nucleation and interface energy; design hardware only after both gates are survived. 2026 literature alignment, explicitly NOT validation of our laboratory hypothesis: July 2026 Phys. Rev. D work derives phase-transition behaviour for scalarized solutions from an energy functional, and 2026 Einstein-Maxwell-scalar literature shows electromagnetic coupling can induce scalarization under specific strong-field (astrophysical) conditions.", "route": "/lab/unification" }, { "id": "EXP-001", "title": "EXPERIMENT 001 — LOCALLY COUPLED NONLINEAR OSCILLATOR FABRIC", "status": "planned", "outcome": "HARDWARE DESIGN READY / BUILD NOT STARTED / PHYSICAL EVIDENCE: NONE. First physical primitive test: can a locally coupled medium create, move and erase a bounded coherent state? C0 = incoherent oscillator state, C* = locally phase-coherent cluster. Platform: bench-scale programmable electronic relaxation oscillators, 8x8 then 16x16 planar, nearest-neighbour coupling only, boundary drive only. Order parameter R_local = |(1/m) sum exp(i theta_j)|; metrics v_C*, w_C*, tau_form, tau_decay, E_transition, locking range, failure rate. Ten-step sequence T1-T10, six provisional engineering gates G1-G6, five falsification criteria. Literature grounding (programmable CMOS relaxation-oscillator arrays; synchronized spin-torque oscillator arrays) validates COMPONENT PHYSICS ONLY and is not evidence for this programme.", "route": "/lab/experiment-001" }, { "id": "AT-0701", "title": "PERSISTENT LOCAL FIELD", "status": "implemented", "outcome": "OBSERVED IN SIMULATION. A destination field produced only by local neighbour relaxation persisted across trips in the tested toy model; routing after field maturity completed 100% of sampled trips with median stretch improving as the field relaxed. The p95 ~1.5 tail is UNRESOLVED and stays visible. TOY COMPUTATIONAL MODEL / NOT PHYSICAL EVIDENCE.", "route": "/lab/persistent-field" }, { "id": "AT-0702", "title": "DESTINATION MOVE UPDATE", "status": "implemented", "outcome": "OBSERVED IN SIMULATION. Destination moves of ~2-3 graph hops needed typically 4-8 local relaxation sweeps in the tested samples versus a ~8-sweep cold start in that experiment. Interpretation held loosely: nearby destination changes can often reuse the existing distributed field rather than rebuild it. Far moves not characterised.", "route": "/lab/persistent-field" }, { "id": "AT-0703", "title": "DAMAGE / SELF-REPAIR", "status": "implemented", "outcome": "OBSERVED IN SIMULATION, SAMPLES ONLY. With a mature field, removing 5%, 10% or 20% of nodes often left routing inside the provisional gate with zero repair sweeps at N = 512-2048. Representative N = 4096 draws: 5% -> 8 sweeps, 10% -> 4, 20% -> 1, against a 32-sweep cold start. NOT a scaling law; larger replication required.", "route": "/lab/persistent-field" }, { "id": "AT-0704", "title": "LIFECYCLE NARRATIVE REWRITTEN", "status": "implemented", "outcome": "PASS (MODEL-LEVEL). The architecture narrative moves from per-trip field construction to C_total = C_cold-start + sum(C_local-update) + sum(C_trip): a field that exists continuously, deforms locally after a change, and guides a transient C* front. Candidate control stack: persistent distributed field -> local differential sensing -> sequential-confidence decision rule -> transient C* recruitment -> local recovery/self-restoration.", "route": "/lab/persistent-field" }, { "id": "AT-0705", "title": "LOCAL REPAIR CONE — the new wall", "status": "planned", "outcome": "NOT YET VALIDATED. Every result so far measures T_repair. The decisive quantity is N_repair, the number of nodes that change state at all under a bounded disturbance. Required: N_repair << N and ideally N_repair / N -> 0. If it does not fall, the persistent field is a global object and this milestone is a caching trick.", "route": "/lab/persistent-field" }, { "id": "AT-0673", "title": "The normalized cost model, declared before the sweep", "status": "implemented", "outcome": "PASS. Setup 1.2 · N · log2 N, storage 2 · K · N · log2 N at K = 8, per-trip (3.5 doorway + 1.8 payload + 1.2 restoration) · log2 N, small local repair folded into the one-off term, comparator an ordinary point-to-point trip charged linearly in N. Every unit is a dimensionless count of modelled operations and bit-hops. NORMALIZED COST, NOT PHYSICAL ENERGY.", "route": "/lab/lifecycle" }, { "id": "AT-0674", "title": "Where the one-off bill actually goes", "status": "implemented", "outcome": "PASS. At N = 1,024 the K = 8 storage burden is 93% of the one-off cost and address formation only 7%. Redundancy, not discovery, is what has to be paid off. Both terms carry the same 1/M amortisation factor, which is why heavy reuse helps them equally — and why lowering K would lower the bill and the fault tolerance together.", "route": "/lab/lifecycle" }, { "id": "AT-0675", "title": "M = 1 — a single trip", "status": "implemented", "outcome": "FAIL. Amortised cost per trip fits N^1.133, worse than the linear baseline, with Qcost 0.0075 at N = 256 falling to 0.0004 at N = 16,384. COST ADVANTAGE ABSENT. Building a whole addressing fabric for one journey is the most expensive thing in the model, and this is the case that kills any per-trip-substrate reading of the architecture.", "route": "/lab/lifecycle" }, { "id": "AT-0676", "title": "M = 10 — occasional use", "status": "implemented", "outcome": "FAIL. z = 1.131. Ten trips barely move the exponent because the one-off term still dominates by two orders of magnitude. Occasional use is indistinguishable from one-off use in this accounting.", "route": "/lab/lifecycle" }, { "id": "AT-0677", "title": "M = 100 — moderate use", "status": "implemented", "outcome": "FAIL. z = 1.103 — bending, and still above 1. Best Qcost 0.63 at N = 256, which is an improvement and not an advantage. Bending is not crossing; reported as a failure of the gate.", "route": "/lab/lifecycle" }, { "id": "AT-0678", "title": "M = 1,000 — sublinear amortised cost emerges", "status": "implemented", "outcome": "PASS. z = 0.933. Qcost 2.93 at N = 256, 4.25 at N = 1,024, 4.44 at N = 4,096 and 4.06 at N = 16,384 — a broad advantage roughly flat in N rather than growing. Sublinear in a normalized model; this is not a physical energy statement.", "route": "/lab/lifecycle" }, { "id": "AT-0679", "title": "M = 10,000 — the reuse advantage strengthens", "status": "implemented", "outcome": "PASS. z = 0.514 with Qcost 4.61, 12.40, 25.20 and 33.74 at the four headline sizes. The advantage now grows with N because the one-off term has been spread thin and only the log-scaling per-trip term remains. The asymptote is 6.5 · log2 N against a linear baseline.", "route": "/lab/lifecycle" }, { "id": "AT-0680", "title": "Where the exponent crosses 1", "status": "implemented", "outcome": "PASS. Fitting on a fine grid of horizons, the amortised exponent crosses z = 1 at M ≈ 574 lifetime trips. Below that the fabric is a liability; above it, an asset — in normalized units, and only for the declared coefficients.", "route": "/lab/lifecycle" }, { "id": "AT-0681", "title": "Break-even trips per size", "status": "implemented", "outcome": "PASS. Break-even rises from 173 trips at N = 256 to 243 at N = 16,384, growing only logarithmically faster than the baseline because the one-off bill and the baseline both scale with N. Break-even is identified, not assumed.", "route": "/lab/lifecycle" }, { "id": "AT-0682", "title": "REUSE OR LOSE", "status": "implemented", "outcome": "INCONCLUSIVE. The architecture is not cheap and not expensive — it is reuse-dependent. Reuse horizon becomes a first-class requirement of the toy, on the same footing as locality, addressability and fault tolerance. A design that rebuilds its addressing substrate per trip is dead in this accounting regardless of how elegant its local law is.", "route": "/lab/lifecycle" }, { "id": "AT-0683", "title": "The lifecycle gate, scored", "status": "implemented", "outcome": "INCONCLUSIVE. Four of eight gates pass. L2 and L3 FAIL — no advantage at one-off or low use — L5 is CONDITIONAL on the reuse horizon, L8 physical interpretation is NOT MODELLED. Lifecycle cost is therefore CONDITIONAL FIRST PASS / HIGH-UTILIZATION ONLY. Conditional means the condition is stated, not that anything real satisfies it.", "route": "/lab/lifecycle" }, { "id": "AT-0684", "title": "The toy architecture gate is not stamped passed", "status": "implemented", "outcome": "INCONCLUSIVE. With locality, sublinear activity, self-organised addressability, multi-user dispersion, fault tolerance and now lifecycle accounting all showing first passes, the temptation is to stamp the toy architecture gate PASSED. It is not. The correct verdict is TOY ARCHITECTURE GATE — CONDITIONAL PASS (HIGH-UTILIZATION REUSE).", "route": "/lab/lifecycle" }, { "id": "AT-0685", "title": "Not physical energy", "status": "implemented", "outcome": "PASS. Nothing on the page has been converted to joules, seconds, bandwidth or channel capacity, and no conversion factor exists. A Qcost of 33 means the toy ledger charges 33x less than the toy baseline. It does not mean anything is 33x more efficient in any laboratory. The overclaim scanner treats energy language here as a defect.", "route": "/lab/lifecycle" }, { "id": "AT-0686", "title": "Physical mapping must prioritise reusable connectivity", "status": "implemented", "outcome": "INCONCLUSIVE. Because rebuilding the addressing substrate per trip is dead, candidate platforms must supply reusable background connectivity and low marginal reconfiguration cost. That single criterion eliminates most systems we would otherwise have examined, which is what makes it useful. OPEN PHYSICAL QUESTION.", "route": "/lab/lifecycle" }, { "id": "AT-0687", "title": "Candidate analogue platforms, mapped variable by variable", "status": "implemented", "outcome": "INCONCLUSIVE. Five candidates — programmable electrical/RF networks, photonic meshes, coupled oscillator lattices, FPGA/NoC fabrics and quantum simulators — each mapped through S, C0/C*, address state, doorway activation, payload, restoration and cost measurement. FPGA/NoC fabrics are the cleanest place to test the accounting because every term is directly countable. Analogues for a cost structure, not models of spacetime.", "route": "/lab/lifecycle" }, { "id": "AT-0688", "title": "What would distinguish us from an ordinary routed network", "status": "implemented", "outcome": "INCONCLUSIVE. The leading discriminator is reuse-scaling of reconfiguration events: the two-phase moving-doorway architecture predicts actuations per transfer fall toward a bounded per-trip term on an untouched address state, where an ordinary routed network pays a reconfiguration event per transfer. Speed is EXCLUDED as a discriminator — locality bounds settled that in Phases 47-55. No such measurement has been performed; physical mapping remains NOT ESTABLISHED.", "route": "/lab/lifecycle" }, { "id": "AT-0657", "title": "The Adversary — Rank Every Tree Edge By Aggregate Impact", "status": "implemented", "outcome": "PASS. Each tree edge is scored by the number of (node, tree) pairs that lose their route if it dies, summed across trees, and the worst are cut first subject to keeping the substrate connected. The single highest-impact edge severs 111 of 256 nodes, 217 of 512, 435 of 1024 and 866 of 2048 — up to 42% of the network from one cut. The attack is global and fully informed; the defence is local and blind. That asymmetry is the test.", "route": "/lab/mesh" }, { "id": "AT-0658", "title": "ROUND 1 — One Tree, One Backup Parent, Under Targeted Attack", "status": "implemented", "outcome": "FAIL. Median repair fraction is 17.6% across the whole N x failures grid and 4.8% at eight targeted failures, with up to 1864 nodes severed at once. The majority of severed nodes never re-attach. This kills the fragile single-tree / local-backup design; the result is preserved rather than deleted. Note: the originally reported reproduction recorded a median repair fraction of exactly 0; this implementation measures a small non-zero fraction because boundary nodes sometimes hold a backup pointing at a surviving sibling branch. Same conclusion, discrepancy recorded rather than smoothed.", "route": "/lab/mesh" }, { "id": "AT-0659", "title": "Why The Backup Edge Cannot Help", "status": "implemented", "outcome": "PASS. A high-impact cut severs an entire subtree, and every backup edge stored strictly inside that subtree points to another node inside the same severed subtree. Only boundary nodes can repair, and the adversary selects exactly the edges whose subtrees have fewest boundary nodes relative to their size. No choice of one backup per node escapes this. Adding a second or third spare edge shifts the numbers, not the argument.", "route": "/lab/mesh" }, { "id": "AT-0660", "title": "ROUND 2 — K Independent Trees On One Shared Substrate", "status": "implemented", "outcome": "PASS. K BFS trees rooted generically on the same degree-4 connected substrate, all frozen before any endpoint is chosen, each node storing one compact child-port address per tree at 2 bits per hop for K·O(log N) bits total. A flow whose route is cut re-selects among surviving trees from addresses it already holds. Independence means independently rooted on one graph, not disjoint graphs.", "route": "/lab/mesh" }, { "id": "AT-0661", "title": "Route Success At N = 256", "status": "implemented", "outcome": "PASS. K = 8: 1.000, 1.000, 0.992, 0.983 at 1, 2, 4 and 8 adversarial failures. K = 4: 1.000, 1.000, 0.983, 0.833. K = 2 falls to 0.283. Forty sampled pairs per configuration, three seeds.", "route": "/lab/mesh" }, { "id": "AT-0662", "title": "Route Success At N = 512", "status": "implemented", "outcome": "PASS. K = 8 holds 1.000 at every tested failure count with median stretch at or below 1.000x the damaged-graph shortest path. K = 4 falls to 0.750 and K = 2 to 0.308 under identical damage. Same substrate, same adversary, three architectures.", "route": "/lab/mesh" }, { "id": "AT-0663", "title": "Route Success At N = 1,024", "status": "implemented", "outcome": "PASS. K = 8 holds 1.000 at 1, 2, 4 and 8 failures with median stretch 1.045-1.163x. K = 4 degrades to 0.767 and K = 2 to 0.417. Constant K, larger network, unchanged survival in the sampled range.", "route": "/lab/mesh" }, { "id": "AT-0664", "title": "Route Success At N = 2,048", "status": "implemented", "outcome": "PASS. K = 8 holds 1.000 at eight adversarial failures with median stretch 1.183x. K = 4 gives 0.842, K = 2 gives 0.408. Beyond N = 2048 the exact damage sweep was not run and nothing is claimed there.", "route": "/lab/mesh" }, { "id": "AT-0665", "title": "K = 2 Degrades Sharply", "status": "implemented", "outcome": "FAIL. Two trees survive a single cut everywhere and then collapse: worst sampled success 0.283 after multiple high-impact failures. A pair of alternatives is not a mesh — the adversary only has to break both. This is the quantitative form of the phase's interpretation.", "route": "/lab/mesh" }, { "id": "AT-0666", "title": "K = 4 Is Better And Still Not Enough", "status": "implemented", "outcome": "FAIL. Four trees hold 1.000 through two targeted failures at every size, then fall to 0.750-0.842 at eight. Not a collapse and not survival either; reported as a failure of the gate, not of the idea.", "route": "/lab/mesh" }, { "id": "AT-0667", "title": "K = 8 Survives Every Tested Attack", "status": "implemented", "outcome": "PASS. Worst sampled cell across N = 256 … 2048 and 1 … 8 adversarial high-impact failures is route success 0.983, with a median of 6 trees still usable per pair after the eighth cut. Sampled route success, not a proof of universal reachability (B132).", "route": "/lab/mesh" }, { "id": "AT-0668", "title": "Route Stretch Under Adversarial Damage", "status": "implemented", "outcome": "INCONCLUSIVE. Worst median stretch at K = 8 is 1.236x the shortest path in the damaged graph, rising with size over four points. Modest in range and trending upward; recorded as debt B134 rather than passed on its own.", "route": "/lab/mesh" }, { "id": "AT-0669", "title": "Storage Overhead Of Architectural Redundancy", "status": "implemented", "outcome": "PASS. Address storage is K·O(log N): 16.2 bits per node at K = 1 and 129.4 at K = 8 on N = 1024, a flat 8x multiplier, with K·N one-off build messages. K remained constant across every tested size — encouraging, and not established beyond the measured box (B133).", "route": "/lab/mesh" }, { "id": "AT-0670", "title": "Failure Handling Stays Local", "status": "implemented", "outcome": "PASS. Re-selection reads addresses the flow already carries. No node outside the affected route is notified, no tree is re-rooted and no flood is triggered by a cut: zero rebuild messages. The mesh does not repair damage, it routes around it — which is why long-run degradation under accumulating faults is untested (B135).", "route": "/lab/mesh" }, { "id": "AT-0671", "title": "The Fault-Tolerance Gate, Scored", "status": "implemented", "outcome": "INCONCLUSIVE. Five of eight gates pass on the exact layer. F1 fails and kills the backup-parent design; F7 lifecycle cost and F8 physical interpretation are NOT MODELLED. Fault tolerance is therefore FIRST PASS: architectural redundancy works inside the tested box and is not proved outside it. First pass means survived the test we designed, not solved.", "route": "/lab/mesh" }, { "id": "AT-0672", "title": "No Promotion", "status": "implemented", "outcome": "INCONCLUSIVE. Everything measured here is a property of a router we wrote, attacked with an adversary we wrote, on a graph we generated. No substrate, no channel, no energy, no experiment. Programme status remains LOCALIZED AUTONOMOUS DOORWAY — TOY CANDIDATE / PHYSICAL EVIDENCE NONE. Good toy results are the easiest place to lose the label.", "route": "/lab/mesh" }, { "id": "AT-0641", "title": "Generic Roots Before Endpoints Exist", "status": "implemented", "outcome": "PASS. K roots elected from the lowest immutable identifiers and spread by a local max-min rule, then K BFS waves freeze the infrastructure before any endpoint is drawn. Ordering is enforced in code. At K = 4 on N = 1024 the build costs 4096 messages and leaves 65 address bits per node.", "route": "/lab/multiroot" }, { "id": "AT-0642", "title": "K Compact Addresses Per Node", "status": "implemented", "outcome": "PASS. Per-node storage is K·2·depth bits: 16 bits at K = 1 rising to 129 at K = 8 on N = 1024, a constant multiplier on an O(log N) base rather than a change of order. K is a fixed constant of the architecture; if it had to scale with N the front would be closed as failed.", "route": "/lab/multiroot" }, { "id": "AT-0643", "title": "Local Tree Selection Without A Route Oracle", "status": "implemented", "outcome": "PASS. A source samples two of the K trees and compares predicted path length, computed by longest common prefix from addresses it already holds, plus congestion counters read at itself and its first hop. No global route computation is reachable from the selection path. Power-of-two choices is an ALGORITHMIC ANALOGY from load balancing theory, not a physical claim.", "route": "/lab/multiroot" }, { "id": "AT-0644", "title": "Exact Event-Driven Sparse Simulation", "status": "implemented", "outcome": "PASS. The Phase 66 proxy is replaced: payloads move along real LCA tree paths on the real cubic graph, one move per node per tick, with node occupancy, round-robin service order and a finite doorway window of W = 12 blocked ticks. Route overlap is now structural, exactly the correlation a random-sample proxy underestimates by construction. Grid declared: N in {256 … 4096}, F in {1 … 64}, K in {1,2,4,8}, 3 seeds per cell.", "route": "/lab/multiroot" }, { "id": "AT-0645", "title": "K = 1 Versus Multi-Root Across Size", "status": "implemented", "outcome": "PASS. At F = 16 the single elected root completes 38% of payloads on average across N = 256 … 4096; four generic roots complete 82%, a 2.15x improvement holding at every size tested (39->81, 35->85, 37->85, 41->75, 35->81). Improvement, not resolution.", "route": "/lab/multiroot" }, { "id": "AT-0646", "title": "Offered-Load Sweep At N = 2048", "status": "implemented", "outcome": "INCONCLUSIVE. Median slowdown with four roots stays near 1.0-1.3x from F = 1 to F = 64 and the tail is mild, but latencies are measured over completed flows only — a survivor bias that flatters the tail while completion is below 1 (B130).", "route": "/lab/multiroot" }, { "id": "AT-0647", "title": "Hotspot Load Sublinear In F", "status": "implemented", "outcome": "PASS. Busiest-node load fits F^0.472 over F = 1 … 64 at N = 2048 with four roots. Sublinear: the fabric spreads rather than funnels. Seven points, three seeds each, treated as a fit over a measured range and not a converged exponent.", "route": "/lab/multiroot" }, { "id": "AT-0648", "title": "Active Footprint Scaling", "status": "implemented", "outcome": "PASS. Touched nodes fit F^0.846 at N = 2048 on top of the measured O(log N) tree route, and no global wake-up appears at any offered load: the rest of the substrate is never activated.", "route": "/lab/multiroot" }, { "id": "AT-0649", "title": "Adversarial Same-Branch Endpoint Pairs", "status": "implemented", "outcome": "PASS. Endpoints drawn from different top-level branches of tree 0 force every single-tree route across the root band — the traffic that deadlocked Phase 66. One root completes 16% of those payloads; four roots complete 72% (1024: 33->79, 16->70, 6->65; 4096: 20->83, 16->75, 5->58) with root-load entropy 0.96-0.98 of maximum. The adversary's branch structure does not survive the choice of tree.", "route": "/lab/multiroot" }, { "id": "AT-0650", "title": "Root-Load Entropy And Fairness", "status": "implemented", "outcome": "PASS. Normalised root-load entropy averages 0.921 of maximum across the size sweep. Purely local two-choice sampling keeps the K roots near evenly loaded with no coordinator assigning anybody a tree.", "route": "/lab/multiroot" }, { "id": "AT-0651", "title": "Route Stretch Debt", "status": "implemented", "outcome": "FAIL. Multi-root tree paths average 1.59x the graph-shortest path. Dispersion is bought with distance; entered as debt B129 rather than netted off against the concurrency gain.", "route": "/lab/multiroot" }, { "id": "AT-0652", "title": "Root Failure During Active Traffic", "status": "implemented", "outcome": "FAIL. Tree 0 destroyed at tick 3 of a 16-flow run on N = 1024: only flows riding it react, re-selecting from addresses they already hold at their current node, with NO global rebuild and no other flow informed. Completion nevertheless falls 88% -> 63% and makespan rises 21 -> 32 ticks (B131).", "route": "/lab/multiroot" }, { "id": "AT-0653", "title": "Lifecycle — Does The Benefit Survive The Overhead?", "status": "implemented", "outcome": "FAIL. Completion per unit of address overhead is 0.38 at K = 1, 0.34 at K = 2, 0.21 at K = 4 and 0.10 at K = 8: eight roots cost 8x the storage for no further completion. Because no K reaches completion 1, the gate is not bought at any price in this grid. A cheaper failure is still a failure.", "route": "/lab/multiroot" }, { "id": "AT-0654", "title": "HEURISTIC Queueing Estimate, Kept Separate", "status": "implemented", "outcome": "INCONCLUSIVE BY CONSTRUCTION. Sparse random route overlap suggests node occupancy rho ~ F·L/N and pairwise collision opportunity ~ F·L^2/(N·K); since L ~ log N, fixed or slowly growing F should get easier at larger N while high F can still build hotspots. Labelled HEURISTIC, quarantined in its own panel, plotted on its own axes and scoring no gate.", "route": "/lab/multiroot" }, { "id": "AT-0655", "title": "The Concurrency Gate, Scored", "status": "implemented", "outcome": "FAIL. 6 of 9 gates pass on the exact layer — bounded slowdown, sublinear hotspot load, near-linear footprint, polylog storage with fixed K, no per-trip global coordination, root-load fairness. G1 completion -> 1 and G8 benefit-survives-overhead FAIL; G9 physical interpretation is NOT MODELLED. MULTI-USER SCALABILITY: OPEN. Structural resolution is not empirical resolution.", "route": "/lab/multiroot" }, { "id": "AT-0656", "title": "No Promotion", "status": "implemented", "outcome": "INCONCLUSIVE. Everything in this phase is a property of a router we wrote, measured in ticks and bits, with no substrate, energy, channel or experiment. Programme status remains LOCALIZED AUTONOMOUS DOORWAY — TOY CANDIDATE / PHYSICAL EVIDENCE NONE.", "route": "/lab/multiroot" }, { "id": "AT-0628", "title": "One Trip Is Not A Network — Stating The Proxy Before The Numbers", "status": "implemented", "outcome": "PASS AS A DECLARATION. The exact-graph concurrency sweep exceeded the runtime budget, so no exact-network result is reported. What is published instead is a labelled queueing overlap proxy: route length L ~ 1.6 log2 N, ~4 locally active nodes per live flow, node capacity one move per tick. The assumptions are stated before any figure so no number here can be mistaken for the fabric itself.", "route": "/lab/concurrency" }, { "id": "AT-0629", "title": "The Analytic Congestion Law", "status": "implemented", "outcome": "PASS. Expected shared slots C(F,2)·L²/N and per-trip slowdown 1 + (F−1)L²/2N. At N = 1,024 that is 1.125×, 1.375×, 1.875×, 2.875×, 4.875× for F = 2, 4, 8, 16, 32; at N = 4,096 only 1.044× to 2.366×, because the same traffic spreads over more substrate.", "route": "/lab/concurrency" }, { "id": "AT-0630", "title": "Event-Driven Simulation Over The Same Assumption", "status": "implemented", "outcome": "PASS. Tokens stepped over sampled routes with longest-waiting-first local arbitration and counted rather than predicted overlap. At F = 16 the simulated slowdown reads 1.208× at N = 256 falling to 1.056× at N = 4,096, agreeing in shape with the analytic law and running consistently below it because a token holds a node for one tick rather than for the whole trip.", "route": "/lab/concurrency" }, { "id": "AT-0631", "title": "The Load Parameter ρ = F L² / N", "status": "implemented", "outcome": "PASS. Congestion collapses onto a single load parameter: pairs (N, F) with equal ρ predict equal slowdown, so 'how many users' is really 'how much of the substrate is occupied'. Points with occupancy F·L/N above 25% are flagged as leaving the sparse regime rather than extrapolated through.", "route": "/lab/concurrency" }, { "id": "AT-0632", "title": "Collision Policies As Explicit Local Rules", "status": "implemented", "outcome": "PASS. QUEUE, DETOUR, MERGE and ABORT are written as local rules using only information at the contended node, then run at F = 16. Under random endpoints they are nearly indistinguishable (1.06-1.08× at N = 1,024 and 4,096); the differences only appear under adversarial load. ABORT's dropped payloads are scored as failures, never hidden in a latency average.", "route": "/lab/concurrency" }, { "id": "AT-0633", "title": "Adversarial Hotspot Endpoints — The Root Band DEADLOCKS", "status": "implemented", "outcome": "FAIL, AND WORSE THAN EXPECTED. Random endpoints are benign at 1.23× worst case. Forcing every route to climb into the single elected-root band and hold a contiguous run of ~L/3 band nodes — what a real tree path does — makes the plain QUEUE rule stop rather than slow: 0 of 80 payloads complete across N = 256 … 4,096, tokens hold band nodes while waiting for band nodes held by others, longest wait 952 ticks before cutoff. Circular wait, not congestion (B127).", "route": "/lab/concurrency" }, { "id": "AT-0634", "title": "Two Local Fixes — DETOUR And Multi-Root Balancing", "status": "implemented", "outcome": "INCONCLUSIVE, BOTH WORK IN THE PROXY. Under the identical load that deadlocked the fabric, DETOUR completes every flow at ≤ 1.36× with no topology change; ABORT clears the deadlock only by losing 41 of 80 payloads; four elected roots with 2 extra address bits and a purely local least-loaded band choice complete every flow at 1.17× against 1.23× for random endpoints, with addresses still O(log N) and the sender still blind to the destination. INCONCLUSIVE because neither is implemented in the real fabric and inter-root consistency is NOT MODELLED.", "route": "/lab/concurrency" }, { "id": "AT-0635", "title": "Tail Latency, Starvation And Fairness", "status": "implemented", "outcome": "PASS UNDER RANDOM ENDPOINTS. p95 tracks the mean at low ρ and separates as ρ grows; longest single wait anywhere in the sweep is 4 ticks and the lowest Jain fairness index is 0.979. Longest-waiting-first arbitration is what prevents starvation, and it is a local rule.", "route": "/lab/concurrency" }, { "id": "AT-0636", "title": "Lifecycle Throughput — Transfers Per Unit Activation", "status": "implemented", "outcome": "INCONCLUSIVE AND UNFLATTERING. Charging ≈ 4 active nodes per live flow per tick, completions per 1,000 activated node-ticks FALL from 17.241 to 13.158 across N = 256 … 4,096 at F = 16, exponent −0.113. Latency improves with N while throughput per unit activation does not. Latency alone flatters any design that keeps a neighbourhood awake.", "route": "/lab/concurrency" }, { "id": "AT-0637", "title": "One Local Failure While Many Doorways Are Open", "status": "implemented", "outcome": "PASS. Eight doorways active, one link cut at tick 3 on one route. At every size the other flows complete unchanged, no global rebuild is triggered, and the damaged flow pays a bounded 4-hop detour under the Phase 65 local repair rule. Concurrency does not turn a local fault into a global event.", "route": "/lab/concurrency" }, { "id": "AT-0638", "title": "The Stable Throughput Region — What Would Count As Success", "status": "implemented", "outcome": "INCONCLUSIVE, WITH THE GATE STATED. Success requires an F(N) growing with N at bounded per-trip slowdown on the exact fabric. The conservative analytic bound F ≤ 1 + 2N/L² gives 5 → 24 flows across N = 256 … 4,096, exponent 0.855 in N — the shape F(N) ~ N/log²N. The token simulation permits far more (48 → 256 within the same slowdown bound), and that disagreement between two defensible accounting choices is itself recorded as a debt (B126) rather than resolved in favour of the flattering number.", "route": "/lab/concurrency" }, { "id": "AT-0639", "title": "Specification For The Exact Sparse Simulation", "status": "implemented", "outcome": "INCONCLUSIVE BY CONSTRUCTION. Written as a contract before the run: adjacency-list substrate, priority-queue event stepping with no per-tick scan over N, real route overlap on the actual tree, node AND edge capacity, and the same seeds. Publishing the specification before the result is what stops the exact run from being tuned toward the proxy.", "route": "/lab/concurrency" }, { "id": "AT-0640", "title": "Phase 66 Verdict — MULTI-USER SCALABILITY: UNRESOLVED", "status": "implemented", "outcome": "UNRESOLVED. The congestion law behaves exactly as expected under uniform-random routes, and that is the whole of the good news. Route overlap in the real fabric is structural rather than random; the single-root band deadlocks outright under adversarial load; throughput per unit activation falls with N; and no exact-graph sweep has been run. The breakthrough ladder gains MULTI-USER SCALABILITY = UNRESOLVED. Programme status unchanged: LOCALIZED AUTONOMOUS DOORWAY — TOY CANDIDATE / PHYSICAL EVIDENCE NONE.", "route": "/lab/concurrency" }, { "id": "AT-0609", "title": "The Redundant Address Fabric — Backups Learned Before Anything Breaks", "status": "implemented", "outcome": "PASS. Each node keeps its primary parent plus up to two backup next-hops drawn from its own neighbours and restricted to nodes outside its own subtree, so a graft can never create a cycle. All of it is learned during the same neighbour exchange that writes the addresses, before A and B are chosen. Backups are endpoint-independent and reusable.", "route": "/lab/repair" }, { "id": "AT-0610", "title": "Random Edge Failure — 1%, 3%, 5%, 8%, 10%", "status": "implemented", "outcome": "PASS WITH A GRADED CURVE. Survival 1.000 at 1-3% edge loss at every size, 0.975 at 5%, 0.900-0.950 at 8-10%. Post-repair stretch 1.5-2.3. The degraded end is reported as prominently as the clean end.", "route": "/lab/repair" }, { "id": "AT-0611", "title": "Random Node Failure Up To 5%", "status": "implemented", "outcome": "PASS. Node loss orphans every tree child at once and is strictly harder than edge loss; survival stays at or above 0.90 to 5% node loss. One 4096-node run at 5% exceeded the local chain bound and was charged as a REBUILD EVENT rather than hidden.", "route": "/lab/repair" }, { "id": "AT-0612", "title": "Repair Scope Per Event Is Flat In N", "status": "implemented", "outcome": "PASS. 5.35 nodes learn anything per failure event on average, fitted exponent 0.016 in N — flat, better than logarithmic. Repair rounds 12 → 22 with exponent 0.297, consistent with logarithmic depth. The mechanism is the bounded upward prefix announcement stopping at the first common ancestor.", "route": "/lab/repair" }, { "id": "AT-0613", "title": "Total Repair Work Is Extensive In The Damage", "status": "implemented", "outcome": "FAIL AGAINST THE ACCOUNTING OBJECTIVE. A fixed PERCENTAGE of failed edges means the number of repair events grows with N, so total touched nodes grow roughly linearly with the damage: 83 at N = 256 and 1039 at N = 4096 at 5% loss. Locality holds per event, not per epidemic (B122).", "route": "/lab/repair" }, { "id": "AT-0614", "title": "No Silent Flood — Rebuild Events Are Charged", "status": "implemented", "outcome": "PASS. The prefix announcement is bounded; exceeding it increments a visible REBUILD EVENT counter. Zero at 1-5% edge loss, appearing only at 8-10% and in one 5% node-failure run. Nothing is repaired by flooding without being counted.", "route": "/lab/repair" }, { "id": "AT-0615", "title": "Descendants Keep Their Addresses", "status": "implemented", "outcome": "PASS. Only the grafted branch head changes its parent; reachability is restored by a redirect at the ancestor, not by renaming the subtree. Address changes are a small fraction of repair scope, and an adversarial cut can rescue 40% of the network while changing exactly one address.", "route": "/lab/repair" }, { "id": "AT-0616", "title": "Adversarial Single Cut At The Highest-Betweenness Tree Edge", "status": "implemented", "outcome": "PASS. Cutting the tree edge with the largest subtree severs 36-41% of the network from the root. Survival 1.000, repair touches at most 8 nodes in 5-7 rounds, exactly 1 address changes, at every size from 256 to 4096. The expected spanning-tree fragility does not appear because the rescue is a local re-graft plus a short announcement rather than a re-rooting.", "route": "/lab/repair" }, { "id": "AT-0617", "title": "Route Stretch After Repair", "status": "implemented", "outcome": "INCONCLUSIVE. Stretch against true shortest paths runs 1.55 → 2.29 across sizes and damage levels, fitted exponent 0.082 in N at 5% loss. Five sizes cannot separate a bounded constant from a very slow logarithmic climb.", "route": "/lab/repair" }, { "id": "AT-0618", "title": "The Moving Doorway Reroutes Without A Global Restart", "status": "implemented", "outcome": "PASS. Edges are killed while the doorway advances with a structured payload. It reroutes under the same local repair rule at a median added cost of 3-6 hops and never restarts the fabric; where no local continuation exists it stops. There is no case in which the doorway resumes elsewhere.", "route": "/lab/repair" }, { "id": "AT-0619", "title": "Added Storage For Redundancy And Repair", "status": "implemented", "outcome": "PASS. Baseline addresses 14 → 22 bits per node; with two backups 36 → 52 bits per node, exponent 0.132 — the same logarithmic family at a constant factor of roughly 2.4. Repair state adds a further 1.3 → 31.7 bits per node depending on damage, and that term grows with the epidemic rather than with N.", "route": "/lab/repair" }, { "id": "AT-0620", "title": "Concurrent Failures During Payload Transit", "status": "implemented", "outcome": "PASS. Zero payloads teleported at any size. Every completed trip preserved its structured identity exactly; the remainder aborted in place and were scored as failures. Nothing is respawned, skipped forward, or partially arrived.", "route": "/lab/repair" }, { "id": "AT-0621", "title": "Address Corruption And One-Hop Consistency", "status": "implemented", "outcome": "PASS. With 2% of nodes given a bogus parent pointer, a single neighbour handshake exposes every inconsistency: 100% detected and repaired within 2 rounds, 0 global lookups, route survival back to 1.000. Defeats random corruption; a consistently lying neighbour is NOT MODELLED.", "route": "/lab/repair" }, { "id": "AT-0622", "title": "The No-Bounce Rule — Why Repair Stopped Looping", "status": "implemented", "outcome": "PASS, FAILURE KEPT VISIBLE. The first repair rule installed a detour around the break itself, which needs a short cycle through the failed edge: 41 of 53 repairs at N = 1024 degenerated into rebuild events and 10% of trips looped. Two local corrections fixed it — announce the moved prefix upward until the branches meet, and never leave by the arrival port. Loops and rebuild events both went to zero at that damage level.", "route": "/lab/repair" }, { "id": "AT-0623", "title": "Lifecycle Ledger — Single Trip Versus Amortised", "status": "implemented", "outcome": "INCONCLUSIVE. Build ~8 messages per node at every size; repair adds ~1 more per node at 5% edge loss. A single trip costs 2257 at N = 256 and 36992 at N = 4096. Amortised over 10^4 trips the per-trip cost falls to 12.22 → 25.70, essentially transit itself. Break-even 187 → 1680 trips and growing with N, which is the unsettled part (B117).", "route": "/lab/repair" }, { "id": "AT-0624", "title": "What The Repair Layer Does Not Do", "status": "implemented", "outcome": "PASS BY CONSTRUCTION. No global beacon, no per-trip routing oracle, no global wake-up, no knowledge of N, no shortest-path information used for decisions, no re-addressing of healthy branches. What remains is a bounded-degree graph whose routing tables survive edits — an engineering-style property, not evidence about spacetime.", "route": "/lab/repair" }, { "id": "AT-0625", "title": "Ladder And Debt After Local Repair", "status": "implemented", "outcome": "MIXED. B119 (fault tolerance unmeasured) CLEARED for edge and node failure. B117 QUANTIFIED, still open. New: B121 heavy-damage survival, B122 total repair work extensive in the damage, B123 root failure unhandled. The physical-content gate remains FAILED.", "route": "/lab/repair" }, { "id": "AT-0626", "title": "Phase 65 Verdict", "status": "implemented", "outcome": "LOCAL SELF-HEALING ADDRESS FABRIC — MATHEMATICAL TOY LEAD. Programme status FAULT-TOLERANT LOCALIZED TWO-PHASE TOY ARCHITECTURE. Damage is repaired locally: ~5.3 nodes per event at exponent 0.016, rounds at 0.297, and a deliberate cut severing ~40% of the network absorbed by at most 8 nodes. Survival degrades under heavy damage and total repair work scales with the damage. No advance toward physical mapping is claimed from graph robustness. PHYSICAL EVIDENCE: NONE.", "route": "/lab/repair" }, { "id": "AT-0627", "title": "Causal / Event DAG Audit Under Concurrent Repair", "status": "implemented", "outcome": "PASS, HYGIENE ONLY. Eight disjoint faults injected at each size while a payload is in transit; every local state change recorded as an event with a Lamport clock over reads only. 446 events, 471 causal edges, 0 clock inversions, 0 cycles, complete topological sort, payload hop clock strictly increasing, maximum causal depth 23, and 6597 genuinely concurrent event pairs left unordered. Consistency is a requirement, not progress (B42).", "route": "/lab/repair" }, { "id": "AT-0595", "title": "Removing The Assumption — Nodes Start With An ID And Nothing Else", "status": "implemented", "outcome": "PASS BY CONSTRUCTION. Every node begins with one immutable random identifier and its own neighbour / port information on a fresh connected random cubic substrate. No coordinates, no tables, no knowledge of N, no knowledge that a trip will ever be requested. Phases 60-63 all depended on an address book we wrote off-model; this phase removes it.", "route": "/lab/self-address" }, { "id": "AT-0596", "title": "Root Election By Minimum Identifier", "status": "implemented", "outcome": "PASS. Each node forwards the smallest identifier it has seen; the global minimum wins and becomes the root. Generic and endpoint-independent — election completes before A and B exist and would give the same root for any later trip, which is what makes the resulting structure chargeable as reusable background. One root is also one point of failure and it has never been killed (B119).", "route": "/lab/self-address" }, { "id": "AT-0597", "title": "Setup Rounds — 8 → 15 Over Six Doublings", "status": "implemented", "outcome": "PASS, WINDOW OBSERVATION. Election plus BFS-tree construction completes in 8, 9, 11, 12, 13, 14, 15 rounds at N = 128 … 8192; finite-size exponent 0.151 and rounds/log2 N flat at 1.15-1.22. Consistent with the mechanism (logarithmic diameter on an expander-like cubic graph). Rounds are synchronous local-message rounds in this model, not seconds.", "route": "/lab/self-address" }, { "id": "AT-0598", "title": "Address Size — One Extra Symbol Per Doubling", "status": "implemented", "outcome": "PASS, WINDOW OBSERVATION. Median addresses 10, 12, 14, 16, 18, 20, 22 bits and maxima 16 → 30 bits; exponent 0.187, bits/log2 N in 1.43-1.69. Exactly one extra port symbol per doubling, as a tree of depth ~log N with <= 2 bits per hop should give. First scheme in the programme with storage linear in depth rather than Phase 60's (log2 N)^2.", "route": "/lab/self-address" }, { "id": "AT-0599", "title": "Routing By Longest Common Prefix", "status": "implemented", "outcome": "PASS. The traveller carries B's address; each node ascends to the parent until it is an ancestor of B, then descends by B's next symbol. No shortest-path oracle, no destination beacon, no table beyond the node's own parent and child ports, no communication beyond the next hop. Routes 8, 12.5, 14, 15, 19, 21, 21.5 hops; exponent 0.222, route/log2 N in 1.14-1.75.", "route": "/lab/self-address" }, { "id": "AT-0600", "title": "Stretch — What The Tree Detour Costs", "status": "implemented", "outcome": "PARTIAL, REPORTED RATHER THAN FOLDED IN. Shortest paths 6, 5.5, 8, 8, 10, 10.5, 12 against tree routes up to 21.5, so stretch reaches ~2.3. Logarithmic but consistently long is a different object from near-optimal. Bounded-stretch compact routing retaining O(log N) bits and local decisions is the standing target (B118).", "route": "/lab/self-address" }, { "id": "AT-0601", "title": "The Three Logarithms Together", "status": "implemented", "outcome": "PARTIAL. Setup, storage and route all grow by roughly a constant per doubling with exponents 0.151, 0.187 and 0.222 and bounded ratios to log2 N. Consistent with O(log N) setup, O(log N) address size and O(log N) local routing on these substrates. Seven sizes over six doublings cannot separate a logarithm from a slow power: THE ASYMPTOTICS ARE NOT PROVEN.", "route": "/lab/self-address" }, { "id": "AT-0602", "title": "Audit — No Endpoint-Targeted Infrastructure Anywhere", "status": "implemented", "outcome": "PASS ON STRUCTURE. Identifiers are random and immutable and cannot encode position; election reads only identifiers; tree construction reads only ports; all of it completes before endpoints exist, so no setup quantity can depend on them; and every per-trip decision reads local ports plus the carried destination address. Necessary, and nowhere near sufficient — it says the logarithms are not bought by a hidden oracle, not that the construction is physical.", "route": "/lab/self-address" }, { "id": "AT-0603", "title": "The Bill — Distributed Construction Is Extensive, Once", "status": "implemented", "outcome": "FAIL AGAINST THE ACCOUNTING OBJECTIVE. A distributed build must reach every node once, so it carries a one-time communication and work cost at least extensive in node count. It is reusable and endpoint-independent and therefore amortises over trips, but amortisation is not abolition, maintenance under change is unmeasured, and no lifecycle ledger yet reports build plus repair against M trips (B117).", "route": "/lab/self-address" }, { "id": "AT-0604", "title": "Debt Tracker Update — One Assumption Cleared, One Debt Created", "status": "implemented", "outcome": "MIXED. CLEARED IN TOY: routing oracle, destination beacon, global wake-up (inherited from the Phase 63 moving-doorway variant, not re-earned here). CLEARED AS ASSUMPTION: preloaded address infrastructure — replaced by SELF-ORGANIZING REUSABLE INFRASTRUCTURE DEBT (B117). OPEN: tree-route stretch (B118), untested fragility (B119), one frozen physical-law mapping, physical evidence NONE.", "route": "/lab/self-address" }, { "id": "AT-0605", "title": "Objective Scorecard After The Address Layer", "status": "implemented", "outcome": "PARTIAL. MET: addresses not written by us, endpoint independence, local next-hop decisions, no shortest-path oracle, no destination beacon. PARTIAL: address size, setup time, route length. UNMET: one-time construction cost, physical mapping. UNMEASURED: self-healing, root failure, dynamic topology, integration with the doorway. Four unmeasured clauses say one thing — nothing has broken yet.", "route": "/lab/self-address" }, { "id": "AT-0606", "title": "Breakthrough Ladder — Address Emergence Moves To First Pass", "status": "implemented", "outcome": "MIXED. Address emergence, the top unresolved structural gate since Phase 62, moves to FIRST PASS. Address size / setup time and local routing are STRONG TOY LEAD and TOY LEAD WITH A CAVEAT. Infrastructure accounting FAILED, energy and action accounting FAILED, robustness and self-healing NOT TESTED, physical mapping and laboratory evidence NONE.", "route": "/lab/self-address" }, { "id": "AT-0607", "title": "Next Attacks — Break It On Purpose", "status": "implemented", "outcome": "QUEUE FIXED BY THE DEBTS. (A) delete 1% / 5% / 10% of edges and measure route failures, local repair radius and time, address churn and rebuild pressure; (B) kill the elected root and charge distributed re-election and re-addressing; (C) bounded-rate rewires with maintenance messages per node per unit time; (D) integrate self-organized addresses with the Phase 63 gated doorway and a structured payload, no precomputed path object exposed to the dynamics; (E) bounded-stretch compact routing at O(log N) bits; (F) full lifecycle ledger amortising build and maintenance across M trips.", "route": "/lab/self-address" }, { "id": "AT-0608", "title": "Phase 64 Verdict", "status": "implemented", "outcome": "SELF-ORGANIZING ADDRESSABLE DOORWAY — MATHEMATICAL TOY LEAD. The network elects a generic root and writes its own compact addresses from local IDs and ports alone, before endpoints exist, with setup, address size and route all consistent with O(log N) across six doublings. The preloaded-address assumption is cleared and replaced by a charged, reusable one-time construction debt. No asymptotic proof, no integration with the transport rule, nothing yet survived a failure. PHYSICAL EVIDENCE: NONE.", "route": "/lab/self-address" }, { "id": "AT-0581", "title": "The Integration Point — One Law, One Address, One Doorway", "status": "implemented", "outcome": "PASS BY CONSTRUCTION. The Phase 57 autonomous activator / recovery law, the compact address relation and the moving doorway combined into one frozen local rule on a random cubic substrate, with the generic BFS address infrastructure frozen before endpoints are drawn. Protocol fixed before any number below. The infrastructure is charged as reusable background and is still something we built rather than something that grew (B113).", "route": "/lab/doorway" }, { "id": "AT-0582", "title": "GLOBAL AVALANCHE REVERSION — The First Integrated Attempt Failed", "status": "implemented", "outcome": "FAIL, PUBLISHED AT FULL SIZE. N = 128, 256, 512, 1024 and 2048 all reached the destination with success 1.000 — and maximum simultaneous activation equalled N exactly at every size, with the activity proxy scaling ~N^0.93. The whole toy universe entered the special phase to move one traveller. Under the localized-doorway objective, arrival bought that way is not partial credit; the objective was missed while a headline number looked healthy.", "route": "/lab/doorway" }, { "id": "AT-0583", "title": "The Gated Catalytic Doorway", "status": "implemented", "outcome": "PASS. Base dynamics subcritical and decaying everywhere; catalytic drive admitted only at the locally designated next hop of a currently active node; the same autonomous recovery law closing behind. One frozen law, nothing retuned between sizes, success 1.000 at N = 128 … 2048 over ten runs per size on fresh random connected cubic substrates.", "route": "/lab/doorway" }, { "id": "AT-0584", "title": "Peak Activation 11 → 19 Instead Of 128 → 2048", "status": "implemented", "outcome": "PASS, WINDOW OBSERVATION. Maximum simultaneous activation 11, 11.5, 15.5, 16, 19 against exactly N for the failed attempt; finite-size exponent 0.205 against 1; peak awake fraction falling 8.59% → 0.93%. The O(N) global wake-up is gone in this variant because of the gating clause and only because of it. Four doublings cannot separate a logarithm from a small power (B116).", "route": "/lab/doorway" }, { "id": "AT-0585", "title": "Arrival Time Sublinear Across The Window", "status": "implemented", "outcome": "PASS, WINDOW OBSERVATION. Arrival 7.275, 7.675, 10.925, 11.325, 13.775 ticks while N grows sixteenfold; finite-size exponent 0.240. Route length 10, 10.5, 14.5, 15, 18 hops reproduces Phase 62 routing behaviour under a different activation rule. The exponent is not converged and no asymptotic claim is made.", "route": "/lab/doorway" }, { "id": "AT-0586", "title": "Activity Proxy — Sublinear, And Steeper Than We Would Like", "status": "implemented", "outcome": "INCONCLUSIVE. Activity 360.876, 389.150, 640.798, 674.967, 892.860; finite-size exponent 0.341 against the failed attempt's ~0.93. A genuine improvement, markedly steeper than Phase 62's hand-written front, and high enough that three more doublings could change the reading. Dimensionless proxy with no separation between trigger, catalytic work, recovery and stored medium (B115).", "route": "/lab/doorway" }, { "id": "AT-0587", "title": "Q And Identity Must Not Be Over-read", "status": "implemented", "outcome": "INCONCLUSIVE, STATED EXACTLY. Q climbs 8.797 → 74.338 and is a ratio between two clocks defined inside this model — not a speed, a factor or an advantage. Identity error reads exactly zero because the payload representation is idealised and deterministic with no decoherence, dispersion, loss or noise mechanism in it. A self-consistency check, never a fidelity result (B116).", "route": "/lab/doorway" }, { "id": "AT-0588", "title": "Avalanche Against Doorway — The Full Comparison", "status": "implemented", "outcome": "PASS. One clause separates them: supercritical any-neighbour spreading against subcritical dynamics with catalysis restricted to the designated next hop. Arrival identical, locality opposite — exactly N against 11 → 19, 100% against 0.93% awake fraction, N^0.93 against N^0.341, whole-network restoration against recovery closing behind the traveller. Both attempts published at the same size.", "route": "/lab/doorway" }, { "id": "AT-0589", "title": "Debt Audit — Wake-Up Cleared, Addresses Still Red", "status": "implemented", "outcome": "MIXED. CLEARED: routing oracle, destination beacon, global wake-up (gated variant only) and Phase 62's hand-written front rule. PREBUILT AND RED: the BFS address infrastructure (B113) and the directional catalytic bias that reads from it (B114). OPEN: activity-as-energy (B115) and physical mapping. A mechanism that requires a pre-existing map still requires a mapmaker.", "route": "/lab/doorway" }, { "id": "AT-0590", "title": "Objective Scorecard — Four Met, Five Unmeasured", "status": "implemented", "outcome": "INCONCLUSIVE. MET: routing success, one frozen local law, autonomous advance, autonomous recovery. PARTIAL: peak activation, total activity, arrival time. UNMET: address emergence, physical mapping. UNMEASURED: infrastructure construction cost, robustness, concurrency, larger N, identity under noise. Unmeasured is not a soft pass (B116).", "route": "/lab/doorway" }, { "id": "AT-0591", "title": "Breakthrough Ladder After Integration", "status": "implemented", "outcome": "MIXED. Autonomous local phase front → FIRST PASS. Localized activity scaling and time scaling → STRONG TOY LEAD on exponents 0.205 / 0.341 and 0.240. Address emergence UNRESOLVED. Energy and action accounting FAILED. Robustness and concurrency NOT TESTED. Physical mapping and laboratory evidence NONE.", "route": "/lab/doorway" }, { "id": "AT-0592", "title": "What Would Falsify This", "status": "implemented", "outcome": "PREREGISTERED. Peak activation turning over toward N at 4096-16384; the activity exponent rising once the proxy is decomposed; the energy audit showing path-proportional injected work; two crossing doorways deadlocking or violating the causal DAG; one corrupted address entry requiring a global lookup; or the hierarchy proving to need per-trip reconstruction. Six falsifiers, all scheduled as next attacks.", "route": "/lab/doorway" }, { "id": "AT-0593", "title": "Next Attacks After The Doorway", "status": "implemented", "outcome": "QUEUE FIXED BY THE DEBTS. Sparse runs at 4096 / 8192 / 16384; removing the prebuilt BFS dependency via a self-organising reusable hierarchy with construction charged; robustness across rewires, noise and edge failure; two crossing doorways; misaddress and local rerouting; an energy landscape audit separating trigger, catalytic work, recovery and stored medium; and a four/five-ruler before-during-after audit.", "route": "/lab/doorway" }, { "id": "AT-0594", "title": "Phase 63 Verdict", "status": "implemented", "outcome": "LOCALIZED AUTONOMOUS DOORWAY — TOY CANDIDATE. The first integrated attempt reverted to a global avalanche and is published as a failure. The gated catalytic variant keeps the doorway localized and autonomous with peak activation 11 → 19 and both time and activity sublinear over the tested window. Address infrastructure remains prebuilt, activity remains a dimensionless proxy, and no asymptotic proof or physical mechanism is claimed. PHYSICAL EVIDENCE: NONE.", "route": "/lab/doorway" }, { "id": "AT-0569", "title": "Infrastructure Frozen Before A And B Exist", "status": "implemented", "outcome": "PASS BY CONSTRUCTION. Random connected cubic substrate, generic BFS addressing tree, local parent / child relations written to every node — and only then are A and B drawn. Each node knows the next hop from its own tree relation plus the destination address. No global beacon, no shortest-path oracle, no destination-wide search at any point in the trip.", "route": "/lab/front" }, { "id": "AT-0570", "title": "Exactly Four Nodes Awake At Any Instant", "status": "implemented", "outcome": "PASS, ARCHITECTURAL. Maximum simultaneously active nodes is 4 at N = 128, 256, 512, 1024, 2048, 4096 and 8192 — a 64-fold change in system size with no change in instantaneous activity. This is a consequence of the moving-front rule (one catalysing node plus the tau = 3 refractory tail), not a measurement that could have come out otherwise, and it is stated as such.", "route": "/lab/front" }, { "id": "AT-0571", "title": "Active-Node-Time Tracks Route, Not System Size", "status": "implemented", "outcome": "PASS, WINDOW OBSERVATION. Median active-node-time 30, 36, 40.5, 48, 54, 64.5, 66 node-ticks over N = 128 … 8192; finite-size exponent z ~ 0.197; active-node-time / log2 N holds between 4.29 and 5.38. Against Phase 58's extensive N^1.031 activity proxy this is the first construction where total work follows the trip. Node-ticks are not action (B111).", "route": "/lab/front" }, { "id": "AT-0572", "title": "Route Length And Transit Over Seven Sizes", "status": "implemented", "outcome": "PASS, WINDOW OBSERVATION. Median route length equals transit at every size: 9, 11, 12.5, 15, 17, 20.5, 21 hops. Finite-size exponent z ~ 0.211; route / log2 N between 1.29 and 1.71 with no monotone drift. Consistent with logarithmic-like scaling in this finite range. Seven sizes cannot separate a logarithm from a small power and no asymptotic claim is made.", "route": "/lab/front" }, { "id": "AT-0573", "title": "Q_time Reaches 195 At N = 8192", "status": "implemented", "outcome": "COMPUTATIONAL RESULT, MODEL-INTERNAL. Q_time 7.111, 11.636, 20.513, 34.133, 60.235, 99.962, 195.048. Time leverage continues growing strongly in this toy because the ordinary-phase baseline grows with N while transit does not. It is a ratio between two clocks we defined and carries no physical content.", "route": "/lab/front" }, { "id": "AT-0574", "title": "Global C* Against Moving C*", "status": "implemented", "outcome": "PASS ON THE ARCHITECTURE CLAUSE. Peak simultaneous activity N against 4; total activity O(N) against O(route); awake fraction falls from 3.1% at N = 128 to 0.049% at N = 8192. The global wake-up debt can be removed architecturally rather than argued away — established here in a routing / activation toy only.", "route": "/lab/front" }, { "id": "AT-0575", "title": "Fifty Runs Per Size, Fresh Substrates", "status": "implemented", "outcome": "METHOD. Every figure is a median over 50 runs per size on fresh random connected cubic substrates with A and B drawn after infrastructure freeze. Firmer than the 20-run windows of Phases 59 to 61, and still a finite window on seven sizes.", "route": "/lab/front" }, { "id": "AT-0576", "title": "Three Debts Cleared, Three Carried", "status": "implemented", "outcome": "MIXED, STATED EXACTLY. CLEARED: routing oracle, destination beacon, global wake-up. PREBUILT: the BFS address infrastructure (B109). OPEN: autonomous equation integration (B110) and physical energy mapping (B111). No debt is described as discharged that has only been renamed.", "route": "/lab/front" }, { "id": "AT-0577", "title": "The Front Rule Is Hand-Written", "status": "implemented", "outcome": "SELF-LIMITING CLASSIFICATION. Each active node catalyses exactly its addressed next hop and recovers after a hand-set refractory lifetime tau = 3. This is a local causal rule chosen to isolate the architecture question, NOT the cooperative c_i / r_i activator-recovery equation that passed the Phase 57 spark test. Two separately working models are not one working model (B110).", "route": "/lab/front" }, { "id": "AT-0578", "title": "What Was Not Tested", "status": "implemented", "outcome": "OPEN. No noise, no trigger threshold, no C0 stability check, no failure or rewiring after freeze, no concurrent routes, no identity payload and no integrated drive. Each of these is a property the Phase 57 law had to earn and this front has not been asked for (B112).", "route": "/lab/front" }, { "id": "AT-0579", "title": "Integration Objective Scorecard", "status": "implemented", "outcome": "INCONCLUSIVE. Instantaneous activity, total activity, per-trip preparation and endpoint independence MET; route length and address bits PARTIAL; autonomous phase dynamics and physical mapping UNMET; infrastructure construction, integrated action, resilience and concurrency UNMEASURED. Best architectural position this line has recorded; still not an integrated solution.", "route": "/lab/front" }, { "id": "AT-0580", "title": "Phase 62 Verdict", "status": "implemented", "outcome": "LOCALIZED MOVING-PHASE ARCHITECTURE / TOY LEAD — NOT AN INTEGRATED SOLUTION. The universe does not have to wake up for a trip: instantaneous activity can be held at O(1) by construction while total activity tracks the route. The address tree is still prebuilt and the front is still not the autonomous equation. PHYSICAL EVIDENCE: NONE.", "route": "/lab/front" }, { "id": "AT-0557", "title": "Generic Tree Built Before Endpoints", "status": "implemented", "outcome": "PASS. Random connected cubic substrate, then a generic BFS / landmark tree, then compact hierarchical ancestor data written to every node — and only then are A and B drawn. The traveller carries B's compact address and reads the stored data of the node it occupies and of that node's immediate neighbours. No shortest-path oracle, no destination beacon, no per-trip global search. Ordering is the guarantee: nothing in the address space can have been arranged around the pair later measured.", "route": "/lab/localized" }, { "id": "AT-0558", "title": "Success 1.000 To N = 4096 With No Oracle And No Beacon", "status": "implemented", "outcome": "PASS. Twenty graph and pair trials per size on fresh substrates: success 1.000 at N = 128, 256, 512, 1024, 2048, 4096. Phase 60's residual ~1.4% failure rate is absent in this scheme. Control comparison unchanged: Phase 59 frozen random labels collapse to 0.38-0.50 by N = 1024 under the identical greedy discipline.", "route": "/lab/localized" }, { "id": "AT-0559", "title": "Route Length Tracks log2 N", "status": "implemented", "outcome": "PASS, WINDOW OBSERVATION. Median route 10, 10, 14, 14.5, 17.5, 19 hops; finite-size power fit z ~ 0.203; route / log2 N holds between 1.25 and 1.59 with no monotone drift. Strongly consistent with O(log N)-like growth over the tested window. NOT an asymptotic proof — six sizes cannot separate a logarithm from a small power.", "route": "/lab/localized" }, { "id": "AT-0560", "title": "Only The Path And Its Halo Wake Up", "status": "implemented", "outcome": "PASS, AND THE FIRST LAWFULLY CAUSED SPARSE ACTIVATION. Activated nodes 23, 24, 32, 33, 39, 42 across N = 128 … 4096 — the traversed path plus a one-hop halo, about 1% of the network at 4096. Finite-size z ~ 0.185, active / log2 N between 3.00 and 3.56. Unlike Phase 59's corridor the activated set is caused by the trip, not selected with global distances. GLOBAL WAKE-UP DEBT removed in this toy; counting nodes is still not integrating action (B108).", "route": "/lab/localized" }, { "id": "AT-0561", "title": "Address Storage At Four Times The Information Floor", "status": "implemented", "outcome": "PASS. Per-node address size 28, 32, 36, 40, 44, 48 bits — exactly 4 · log2 N at every size, against Phase 60's 49, 64, 81, 100 which was (log2 N)^2. Naming one of N destinations requires at least log2 N bits, so this sits at a constant multiple of an unavoidable floor. The fitted power near 0.155 is the artefact of fitting a line to a logarithm and is not the description.", "route": "/lab/localized" }, { "id": "AT-0562", "title": "Stretch Flatter But Still Above One", "status": "implemented", "outcome": "INCONCLUSIVE. Median stretch 1.67, 1.67, 2.00, 1.71, 1.75, 1.90 — 19 hops against a true shortest 10 at N = 4096. Flatter and measured over a longer window than Phase 60's climbing 1.50 → 2.88, and flat over six sizes is not bounded. The O(1) stretch clause is PARTIAL, not MET.", "route": "/lab/localized" }, { "id": "AT-0563", "title": "Three Debts Removed In One Construction", "status": "implemented", "outcome": "PASS. ROUTING ORACLE DEBT removed — no shortest-path call during the trip. DESTINATION BEACON DEBT removed — the destination does nothing and the network is never told a trip is happening. GLOBAL WAKE-UP DEBT removed — activation is the path plus a one-hop halo. Two remain: INFRASTRUCTURE DEBT (reduced and reshaped, still open, B105) and PRECOMPUTED TABLE DEBT (newly named, B106).", "route": "/lab/localized" }, { "id": "AT-0564", "title": "The Infrastructure Ledger", "status": "implemented", "outcome": "INCONCLUSIVE, SELF-REPORTED. Charged: storage ~4·log2 N bits per node, per-trip preparation zero, activated nodes ~3.5·log2 N, stretch 1.67-2.00. NOT MEASURED: construction of the tree itself, integrated action of the trip, maintenance after topology change. The debt is one-time, endpoint-independent and reusable so it can in principle amortise, but the amortisation crossover has not been computed. Argued, not demonstrated.", "route": "/lab/localized" }, { "id": "AT-0565", "title": "Why This Is Not An Address-Emergence Result", "status": "implemented", "outcome": "SELF-LIMITING CLASSIFICATION. Each hop resolves against precomputed tree parent and ancestor tables produced by a global construction. Local at runtime, global at build time — an honest description of any real routing infrastructure, and not autonomous self-organised address emergence. Classification: COMPACT-ADDRESS INFRASTRUCTURE TOY, not a fundamental solution.", "route": "/lab/localized" }, { "id": "AT-0566", "title": "What Was Not Tested", "status": "implemented", "outcome": "OPEN. No node or edge failed, no rewiring after freeze, no two simultaneous routes, no false-address or collision rate measured, and no audit of whether the address system exposes latent structure S as an ordinary readable channel in C0. Each can individually invalidate the sparse-activation reading (B107).", "route": "/lab/localized" }, { "id": "AT-0567", "title": "Joint Objective — Three Of Twelve Met", "status": "implemented", "outcome": "INCONCLUSIVE. MET: routing success, zero per-trip preparation, endpoint independence. PARTIAL: route length, activated nodes, address bits, stretch. UNMET: autonomous phase dynamics driving the front, physical mapping. UNMEASURED: construction and maintenance cost, integrated action, resilience and contention. Best score this line has recorded, and still three of twelve.", "route": "/lab/localized" }, { "id": "AT-0568", "title": "Phase 61 Verdict", "status": "implemented", "outcome": "LOCALIZED ADDRESSABLE TWO-PHASE ARCHITECTURE — TOY LEAD. Routing oracle resolved in this toy; localized activity first pass; addressability first pass with reusable infrastructure debt; energy/action for the localized phase still must be measured and the gate stays FAILED; autonomous phase-dynamics integration still pending. PHYSICAL EVIDENCE: NONE.", "route": "/lab/localized" }, { "id": "AT-0545", "title": "Every Place Has An Address — The Generic Hierarchy", "status": "implemented", "outcome": "PASS. Multilevel landmark hierarchy built from the substrate alone and frozen before endpoint selection; the payload holds B's compact address and reads neighbour addresses only. No oracle, no beacon, no global distance table during the trip.", "route": "/lab/hierarchy" }, { "id": "AT-0546", "title": "Neighbour-Local Address Routing Works", "status": "implemented", "outcome": "PASS. Success 0.986, 0.979, 1.000, 0.986 at N = 128, 256, 512, 1024 against the 0.38-0.50 collapse of frozen random labels under the identical rule. Coordinates derived FROM the substrate route; coordinates uncorrelated with it do not.", "route": "/lab/hierarchy" }, { "id": "AT-0550", "title": "Storage Debt — (log2 N)^2, Not O(log N)", "status": "implemented", "outcome": "FAIL ON THE STORAGE CLAUSE. Address bits per node 49, 64, 81, 100 — exactly the square of log2 N. The naive power fit of ~0.343 is explicitly disowned as what a squared logarithm looks like over three doublings. Median stretch climbs 1.50 → 2.88 (B101, B104).", "route": "/lab/hierarchy" }, { "id": "AT-0555", "title": "Debt Migration — Oracle → Beacon → Infrastructure", "status": "implemented", "outcome": "PROGRESS IN KIND, NOT A DISCHARGE. Per-trip endpoint-dependent computation, then per-trip endpoint-dependent flood, then a one-off endpoint-independent structure that can in principle amortise. Construction uncharged, maintenance untested, channel exposure unaudited (B102).", "route": "/lab/hierarchy" }, { "id": "AT-0556", "title": "Phase 60 Verdict", "status": "implemented", "outcome": "COMPACT ADDRESSABILITY FIRST PASS / STORAGE DEBT REMAINS. Addressability gate moves NOT ESTABLISHED → PARTIAL. Three of ten clauses met, two failed, four unmeasured. PHYSICAL EVIDENCE: NONE.", "route": "/lab/hierarchy" }, { "id": "AT-0533", "title": "The Oracle Is Gone — One-Hop Beacon Routing", "status": "implemented", "outcome": "PASS. Destination B emits a scalar field propagating one edge per tick; the payload compares only its immediate neighbours' beacon values and steps to the largest. No shortest-path call anywhere in the routing loop, no table, no graph knowledge beyond one hop. Twenty runs per size on fresh random connected cubic substrates, A and B chosen after the graph froze: success 1.0 at N = 128, 256, 512, 1024, 2048, 4096. Median full time (beacon setup included) 14.0, 17.0, 19.0, 20.5, 24.0, 25.0, fit z ~ 0.165. Q_time 4.571, 7.529, 13.474, 24.99, 42.667, 81.92. Not like-for-like with Phase 58's clock; the structural point is that removing the oracle did not destroy a growing advantage.", "route": "/lab/address" }, { "id": "AT-0534", "title": "Stretch Approximately One", "status": "implemented", "outcome": "PASS. Beacon-greedy paths are 5, 6, 8, 8, 10, 10 hops - at or extremely close to the true shortest path, so stretch ~ 1. This is what makes AT-0533 non-trivial: a random walk on an expander also arrives, after nothing like ten hops. It is also the direct contrast with AT-0537, where the identical greedy rule on random labels exceeds 100 hops.", "route": "/lab/address" }, { "id": "AT-0536", "title": "The Corridor — Sparse Activation At Last", "status": "implemented", "outcome": "PASS, MODEL-ASSISTED. Activation restricted to nodes near an A-B geodesic gives median active counts 21.5, 25, 52, 31, 47, 41.5 across N = 128 … 4096, fit ~ N^0.192 against Phase 58's N^1.031, with the activated fraction falling from ~17% to ~1%. First sublinear activation in the programme. Counts are non-monotone and under-sampled at twenty runs per size (B100), and the corridor condition uses global distances (B98).", "route": "/lab/address" }, { "id": "AT-0537", "title": "Random Label Routing Fail", "status": "implemented", "outcome": "FAIL, AND THE MOST INFORMATIVE FAILURE OF THE PHASE. Every node given a frozen random vector label BEFORE endpoint selection - genuinely endpoint-independent, genuinely pre-existing - with the payload seeing only neighbour labels and the destination label. Greedy descent collapses: success ~0.38-0.50 by N = 1024 depending on label dimension, greedy paths past 100 hops against a true 8-9, stretch above ten. Label proximity is uncorrelated with graph proximity on an expander, so greedy descent is a random walk with dead ends. Rules out the whole class of substrate-independent labels.", "route": "/lab/address" }, { "id": "AT-0538", "title": "Destination-Beacon Debt And Corridor-Construction Debt", "status": "implemented", "outcome": "FAIL, SELF-REPORTED BEFORE PUBLICATION. The beacon must reach A before local routing can work, and disseminating a local scalar over a low-diameter graph touches essentially every node, per trip; setup 8, 9, 10, 12, 13, 14 ticks tracking eccentricity - cheap in time, total in reach. The Phase 58 map debt is renamed, not paid. The corridor is defined by proximity to an A-B geodesic, a condition the substrate cannot evaluate, so the routing debt is NOT solved; marked yellow only because routing inside the corridor is genuinely local.", "route": "/lab/address" }, { "id": "AT-0541", "title": "The Real Problem Is Addressability", "status": "implemented", "outcome": "REFRAMING, NEW LADDER GATE. Pathfinding is already solved on these graphs - greedy descent on a good field gives stretch ~1. What a low-diameter substrate denies a traveller is somewhere to AIM: on a random cubic expander there is no geometry to read, so a destination is unaddressable unless the substrate carries structure encoding where things are relative to each other. That structure must be endpoint-independent, prepared before endpoint selection, compact at O(log N) bits per node, and charged. Nothing in the programme has produced one. ADDRESSABILITY is now a distinct gate because Phase 59 showed routing and addressability fail independently.", "route": "/lab/address" }, { "id": "AT-0544", "title": "Phase 59 Verdict", "status": "implemented", "outcome": "LOCAL ROUTING ACHIEVED, SPARSE CORRIDOR ACHIEVED - BOTH ON BORROWED GLOBAL INFORMATION. Autonomous routing PARTIAL, sparse activation PARTIAL, addressability NOT ESTABLISHED, energy/action still FAILED with the beacon flood replacing the extensive wake-up as the reason. PHYSICAL EVIDENCE: NONE.", "route": "/lab/address" }, { "id": "AT-0521", "title": "The Same Law, Thirty-Two Times Bigger", "status": "implemented", "outcome": "PASS. D = 0.6, a = 0.03, k = 4, eps = 0.03, beta = 0.8 carried unchanged from Phase 57 onto fresh random connected cubic substrates at N = 128 … 4096, three to four reps per size. Global activated fraction 1.0 at every size from a single one-node seed. Phase-on 8.76, 10.32, 12.18, 14.00, 15.68, 17.44 ticks against eccentricity 8, 9, 11, 12, 13, 14. Nothing retuned, which is what makes it evidence about the law rather than about one lucky graph.", "route": "/lab/payload" }, { "id": "AT-0522", "title": "z = 0.199 — Suggestive, Still Not A Law", "status": "implemented", "outcome": "INCONCLUSIVE, AND THE DROP IS THE FINDING. The global power fit falls from 0.317 over the Phase 57 window to about 0.199 over N = 128 … 4096, and the local interval exponent falls through the range instead of settling. An exponent that keeps shrinking as the window widens is what a logarithm looks like when a power is fitted to it. Strongly suggestive of logarithmic-like scaling; not an asymptotic proof. B89 stays open and B87 applies.", "route": "/lab/payload" }, { "id": "AT-0523", "title": "Restoration Duration Is Flat To N = 4096", "status": "implemented", "outcome": "PASS, FOR A REASON DERIVABLE FROM THE LAW. Duration from phase onset: 37.04, 36.64, 36.40, 36.02, 35.80, 35.72 - flat to slightly decreasing across a 32x range. The recovery timescale 1/eps is a constant that has no way of knowing N, so this gate passes by construction rather than by luck. Slight downward drift recorded, not smoothed away.", "route": "/lab/payload" }, { "id": "AT-0525", "title": "A Four-Component Payload Crossed The Phase", "status": "implemented", "outcome": "FIRST IDENTITY TRANSPORT IN THE PROGRAMME, IDEALISED. Exact invariant vector, A/B chosen after substrate freeze, B far in ordinary X labelling at ~N/2, one S edge per unit time, hops only across edges whose both endpoints exceed threshold, clock started at the trigger. Completion 9.20, 9.04, 11.12, 12.56, 16.60 against ordinary 64, 128, 256, 512, 1024, so Q_time = 6.96, 14.16, 23.02, 40.76, 61.69 - an advantage that GROWS with N, which no earlier mechanism here achieved. Completion fit z ~ 0.218. Identity error exactly 0, which in a noiseless carry-not-reconstruct toy means the rule is self-consistent, not that identity is robust (B96).", "route": "/lab/payload" }, { "id": "AT-0527", "title": "The Activity Debt — Collective Work Is Extensive", "status": "implemented", "outcome": "FAIL, AND THE MOST IMPORTANT NUMBER OF THE DAY. The dimensionless integrated |dc| + |dr| proxy reads 370.7, 761.0, 1602.2, 3261.2, 6496.4, 13189.7 at N = 128 … 4096, an exponent of about 1.031 with activity per node flat at 2.90-3.22. The TIME crack survives strongly in the toy; the COST crack is not established and cannot even be defined until a physical baseline with comparably extensive cost exists. Energy/action gate recorded as FAIL. The proxy is dimensionless and is NOT energy (B94).", "route": "/lab/payload" }, { "id": "AT-0529", "title": "The Routing Oracle Debt", "status": "implemented", "outcome": "FAIL, SELF-REPORTED BEFORE PUBLICATION. The phase opened the edges but the simulation chose them, computing a shortest path through S with global knowledge of the graph and of B's location. Every payload Q_time is therefore a best-case bound on what some unknown routing mechanism could achieve, not evidence that one exists. Identity transport capped at PARTIAL. Removal test: next hop from bounded-radius local state only, no address for B, no global table, and any destination tag's preparation and distribution charged to the ledger (B95).", "route": "/lab/payload" }, { "id": "AT-0532", "title": "Phase 58 Verdict", "status": "implemented", "outcome": "AUTONOMOUS TWO-PHASE TOY CANDIDATE / TIME CRACK STRENGTHENED, COST CRACK NOT ESTABLISHED. Time side upgraded to a strong toy lead; autonomous dynamics and restoration hold; identity transport records an idealised first pass; energy/action is a measured FAIL and routing is an acknowledged debt; causal consistency, physical mapping and laboratory evidence are untouched. PHYSICAL EVIDENCE: NONE.", "route": "/lab/payload" }, { "id": "AT-0509", "title": "One Cooperative Law, One Substrate, Two Phases", "status": "implemented", "outcome": "STRUCTURAL UPGRADE. Phase 56's excitable rule guaranteed its own front: a REST node beside an ACTIVE node always woke. Phase 57 replaces it with an activation/recovery pair on a connected random cubic substrate, dc/dt = D*mean_neighbour_difference + k*c(c-a)(1-c) - r and dr/dt = eps*(beta*c - r). The reaction term is NEGATIVE below a, so a weak lone excitation decays and recruitment becomes an outcome that can fail. Restoration is the recovery variable's own doing; there is no external reset, no endpoint input and no hand-switched Hamiltonian. Still stipulated rather than derived (B83).", "route": "/lab/spark" }, { "id": "AT-0510", "title": "Parameter Family Search — 39 of 54 Fail", "status": "implemented", "outcome": "COMPUTATIONAL RESULT AND THE REASON THE PASS COUNTS. Fifty-four frozen families over D in {0.6,1.0,1.5}, a in {0.03,0.07,0.12}, k in {2,4,7}, eps in {0.03,0.07}. Fifteen recruited globally at N = 32, 64, 128; thirty-nine did not. Best early finite-size phase-on exponent about 0.330. Selecting a survivor from a grid is a tuning step and is legitimate only because that set is then frozen and used unchanged everywhere afterwards.", "route": "/lab/spark" }, { "id": "AT-0511", "title": "The Spark Caught — Global Recruitment at Every Tested Size", "status": "implemented", "outcome": "FIRST AUTONOMOUS NUCLEATION PASS IN THE PROGRAMME. Survivor D=0.6, a=0.03, k=4, eps=0.03, beta=0.8, frozen; four runs per size at N = 32, 64, 128, 256, 512 from a single one-node seed. Global max activated fraction 1.0 at every size. Median phase-on 5.02, 6.80, 8.46, 10.46, 12.16 ticks against median graph eccentricity 5, 6.5, 8, 10, 10.5. Phase-on tracking eccentricity is a consistency check on a bounded-speed front, not an independent finding.", "route": "/lab/spark" }, { "id": "AT-0512", "title": "z = 0.317 Is a Finite-Size Fit and Nothing More", "status": "implemented", "outcome": "INCONCLUSIVE, DELIBERATELY. A power law, a logarithm and a log-power all fit the same five phase-on points; the local effective exponent does not converge and the sweep stops at N = 512. Under B87 the number may not be called sublinear and may not be cited in any advantage claim anywhere on the site. Blocker B89 raised.", "route": "/lab/spark" }, { "id": "AT-0513", "title": "Restoration, Measured From the Right Clock", "status": "implemented", "outcome": "PASS, AFTER CORRECTING OUR OWN MEASUREMENT. Absolute restoration timestamps 43.56 … 50.82 look weakly size-dependent only because they are measured from the seed and therefore contain the phase-on time. Measured as a DURATION from phase onset the values are 38.54, 38.68, 38.72, 38.72, 38.66 - essentially flat, as expected for a duration set by the recovery timescale 1/eps. Restoration succeeded at every size with no external reset. Blocker B91 raised: durations between defined model events, never timestamps.", "route": "/lab/spark" }, { "id": "AT-0514", "title": "Noise Gate — Zero Spontaneous Phases in 72 Runs", "status": "implemented", "outcome": "PASS AT ONE SIZE. At N = 128, twelve unseeded runs at each of sigma = 0, 0.001, 0.005, 0.01, 0.02, 0.04 produced zero spontaneous global phase events. With one intentional unit seed, recruitment succeeded 12 of 12 at every level and median phase time moved only 7.96 to 8.58. A promising toy stability window; 72 runs bound a rare-event rate only weakly and this is not physical robustness.", "route": "/lab/spark" }, { "id": "AT-0515", "title": "A Finite Trigger Threshold Separates C0 From C*", "status": "implemented", "outcome": "PASS, WITH THE WORD WITHHELD. At N = 128, amplitudes 0.05 to 0.40 recruited nothing in 8 runs each; 0.45 to 0.55 is inconsistent; 0.60 to 1.00 recruited every run. The toy therefore has a genuine finite trigger threshold, which is the structure a two-phase claim needs. It is NOT called a thermodynamic phase transition: order parameter, hysteresis loop and size-dependence of the threshold are all unmeasured. Blocker B92 raised.", "route": "/lab/spark" }, { "id": "AT-0518", "title": "Breakthrough Ladder After Phase 57", "status": "implemented", "outcome": "THREE FIRST PASSES, ONE PARTIAL, FOUR UNTOUCHED. Autonomous phase dynamics, autonomous restoration and trigger structure record first passes. Mathematical scaling is PARTIAL - promising and incomplete. Causal consistency, identity transport, energy/action scaling, physical mapping and laboratory evidence are all exactly where Phase 56 left them. Three passes on the medium say nothing about anything travelling through it.", "route": "/lab/spark" }, { "id": "AT-0520", "title": "Phase 57 Verdict", "status": "implemented", "outcome": "AUTONOMOUS TWO-PHASE TOY CANDIDATE / MATHEMATICAL LEAD. Exactly one rank above Phase 56 and no further. The medium is real as a mathematical object: two distinct states, a stable ordinary phase, a finite door between them, an autonomous return. Nothing has been carried through it, the action ledger has not been opened, and the cooperative potential may itself be an unpaid battery (B90). PHYSICAL EVIDENCE: NONE.", "route": "/lab/spark" }, { "id": "AT-0493", "title": "The Phase Speed Limit", "status": "implemented", "outcome": "MODEL THEOREM. With ordinary time T_X ~ N and T* = T_nucleate + T_transit + T_restore + T_prepare + T_debt where each component scales as N^z_k, the advantage ratio scales as N^(1 - z_max) up to logs. A finite sum is dominated by its worst term, so a single unavoidable component with z >= 1 caps Q at a constant fixed by coefficients. Consequence adopted as method: no headline ratio may be reported without a per-component exponent table beside it. Three illustrative constant-budget scenarios (3 log2 N + 2, 5.5 log2 N + 5, 12 log2 N + 10) all share one exponent and differ only in crossover size, which is exactly why constants are never the finding.", "route": "/lab/speed-limit" }, { "id": "AT-0494", "title": "One Frozen Local Law Replaces the Hand-Switched Rule", "status": "implemented", "outcome": "STRUCTURAL IMPROVEMENT, NOT EVIDENCE. The order field is now excitable and refractory: REST goes ACTIVE beside an ACTIVE neighbour, holds for k_E ticks, is REFRACTORY for k_R, returns to REST. The same law gates accessibility - a latent edge carries an interaction only where both endpoints are ACTIVE - and restoration is that law's own refractory tail. There is no external reset and no hand-switched Hamiltonian anywhere in the model. The law remains stipulated rather than derived (B83).", "route": "/lab/speed-limit" }, { "id": "AT-0495", "title": "A Genuinely Frozen Activation Window Kills Transit", "status": "implemented", "outcome": "FAIL, AND THE CLEANEST ILLUSTRATION OF THE GATE. A chord is open only while both endpoints are ACTIVE, so a payload gets at most k_E chord hops while the substrate needs about log2 N of them. With a fixed window, transit reverts to the ordinary Theta(N) route above a crossover size. Repair: one window law w(N) = ceil(2 log2 N), identical at every size and blind to the endpoints. It is scale-dependent and is declared as such - logarithmic, hence still z = 0 in the audit, but a parameter any realisation would have to explain (B88).", "route": "/lab/speed-limit" }, { "id": "AT-0496", "title": "Component-by-Component Exponents with Convergence and Lower Bounds", "status": "implemented", "outcome": "COMPUTATIONAL RESULT. Endpoint-blind medians over N = 512 … 65,536 under one frozen law. Fitted exponents: nucleation 0.101, transit 0.136, restoration 0.114, preparation 0, debt 0 - all with converged local exponents across the top half of the range. Worst time-side exponent 0.136, so the predicted time ratio grows as N^0.864. Activation action fits 1.118 and is charged at its argued Omega(N) bound. Method rule adopted: sublinearity requires BOTH a converged local exponent and an independent lower-bound argument (B87).", "route": "/lab/speed-limit" }, { "id": "AT-0498", "title": "Onset Is the Seed Event, Not the Threshold", "status": "implemented", "outcome": "ANSWERED AGAINST US AND RECORDED. The excitation front travels on the substrate from tick one, so the altered causal structure begins at the seed, before any corridor opens. The interval between seed and first open chord is therefore NOT ordinary-local and cannot be used to claim quiet locality. Every audit is timed from the seed tick (B86).", "route": "/lab/speed-limit" }, { "id": "AT-0499", "title": "Two Triggers, One Acyclic Event DAG in Fundamental Time", "status": "implemented", "outcome": "PASS WITH A DISTINCTION WORTH MORE THAN THE PASS. Two independent seeds were fired and their fronts allowed to interpenetrate; every arc advances the fundamental tick by one, so no closed causal loop exists regardless of the number of fronts. Thousands of arcs are forward in fundamental time and yet superluminal in the emergent cycle coordinate: fundamental order intact, emergent order violated. Still carried by one assumed global time orientation (B82).", "route": "/lab/speed-limit" }, { "id": "AT-0500", "title": "Structured Payload After Onset, Intact Through Restoration", "status": "implemented", "outcome": "PASS, WEAK BY CONSTRUCTION. An eight-component register cannot traverse a latent edge before both endpoints are ACTIVE, so nothing departs before onset; it arrives with every internal relation intact and the field returns to REST behind it. Preservation is structural because the toy applies no coupling map to the payload, so this clears an objection and establishes nothing positive (B72).", "route": "/lab/speed-limit" }, { "id": "AT-0501", "title": "The Energy Ledger Including Stored Background Free Energy", "status": "implemented", "outcome": "FAIL, AND THE PROGRAMME'S STANDING WALL. Gross activation is Theta(N log N) node-ticks under the window law. Amortising over the crossings one activation window can serve divides by a constant, because that count is k_E over the substrate diameter and does not grow with N. Pre-charged background energy is charged at the cost of having been placed, which is itself Theta(N). Net action per crossing scales as N^1.118 and the cost-ratio exponent is negative (B80, B84, B85).", "route": "/lab/speed-limit" }, { "id": "AT-0502", "title": "Robustness Across Independently Drawn Substrates", "status": "implemented", "outcome": "PASS. Eight independent generic matchings at N = 8,192 with identical endpoint draws on every graph. The time ratio varies by under one percent of its median, so the effect belongs to the bounded-degree ensemble rather than to one lucky graph.", "route": "/lab/speed-limit" }, { "id": "AT-0507", "title": "The Breakthrough Ladder", "status": "implemented", "outcome": "EIGHT INDEPENDENT GATES. Mathematical scaling PASSED; autonomous phase dynamics PASSED; causal consistency PARTIAL (global time orientation assumed); identity transport PARTIAL (structural only); energy and action scaling FAILED; robustness PASSED; physical mapping NOT ESTABLISHED; laboratory evidence NOT ESTABLISHED. A rung advances only on an actual result, and NOT ESTABLISHED is never counted as a pass.", "route": "/lab/speed-limit" }, { "id": "AT-0508", "title": "Phase 56 Verdict", "status": "implemented", "outcome": "MATHEMATICAL TWO-PHASE CRACK, HELD AT THE SAME RANK AS PHASE 55 AND ON BETTER FOUNDATIONS. The hand-switched rule is gone, the advantage is decomposed rather than announced, the onset question is answered against us, and the time side survives a component audit with converged exponents and lower bounds. The action side still fails, and it fails for a reason argued from the accessibility rule itself rather than measured: exposing a corridor to an endpoint drawn anywhere requires exciting a constant fraction of the substrate. PHYSICAL EVIDENCE: NONE.", "route": "/lab/speed-limit" }, { "id": "AT-0479", "title": "TRANSPORT-IMPLIES-SIGNALLING - The Gate We Had Was Self-Contradictory", "status": "implemented", "outcome": "MODEL THEOREM, AND A CORRECTION TO OUR OWN METHOD. Any channel carrying two distinguishable A-preparations to B-outputs with distinguishability delta > 0 in time shorter than ordinary X signalling has positive classical signalling capacity, because repetition drives discrimination error below exp(-m delta^2 / 2) at about 1/delta^2 uses - a finite, N-independent cost against an ordinary Theta(N) per bit. If delta = 0 nothing was transported. Therefore 'operational shortcut plus no signalling during the transition' is unsatisfiable by definition, and it is retired. Replacement: PHASE-SELECTIVE CAUSALITY.", "route": "/lab/causal-phase" }, { "id": "AT-0480", "title": "The Replacement Taxonomy - Five Stages, One Audit", "status": "implemented", "outcome": "FRAMEWORK. C0 ordinary phase must carry an exact X-local operational cone; initiation is a local or fully accounted event; in C* the allowed-transition graph changes and a new causal cone is permitted; restoration returns C0; the causality audit targets closed causal loops and consistency, NOT preservation of the old cone during C*. Eight failure conditions pre-registered before the toy was run.", "route": "/lab/causal-phase" }, { "id": "AT-0481", "title": "The Construction - Cubic Substrate, One Local Order Variable, Two Phases", "status": "implemented", "outcome": "TOY MODEL. One bounded-degree substrate: Hamiltonian cycle of ordinary access edges plus a generic perfect matching of latent relational edges, maximum degree 3, no destination field anywhere in the state. A local order variable c_i with one translation-invariant two-phase rule decides which incident interactions are accessible.", "route": "/lab/causal-phase" }, { "id": "AT-0482", "title": "Nucleation - Generic Local Trigger Forms C* in O(log N)", "status": "implemented", "outcome": "COMPUTATIONAL RESULT. The c-front covers the substrate in the trigger eccentricity on S, which is logarithmic across N = 64 … 8192 under one frozen rule. During nucleation the front IS the new causal relation, admissible only after the local initiating event and never before it.", "route": "/lab/causal-phase" }, { "id": "AT-0483", "title": "End-to-End Time - Trigger, Cross, Restore, All Charged", "status": "implemented", "outcome": "COMPUTATIONAL RESULT. Total completion time stays logarithmic while the ordinary cycle time grows linearly, so the time ratio grows parametrically with N under one frozen parameter set with endpoints drawn only after freezing. Second quantity in the programme that grows rather than fades, and the first measured end to end with the phase change charged in time.", "route": "/lab/causal-phase" }, { "id": "AT-0484", "title": "Action Ledger - What the Phase Change Actually Costs", "status": "implemented", "outcome": "FAIL. Forming and restoring C* flips 2N order variables. Q_cost never exceeds one at any size and does not grow. The construction buys logarithmic time by spending linear action over the whole substrate (B80).", "route": "/lab/causal-phase" }, { "id": "AT-0485", "title": "Controls (a) to (j)", "status": "implemented", "outcome": "NINE OF TEN AS REQUIRED. Strip the latent matching and the advantage vanishes; freeze c = 0 and it vanishes, which is the operational statement that the latent sector is invisible in C0; re-embed the cycle and it survives; draw endpoints after freezing and it survives; move the trigger and total time barely moves; kill 1-10 percent of sites and the front routes around them; ten repeated cycles restore c exactly. The single failure is (j), the action ledger.", "route": "/lab/causal-phase" }, { "id": "AT-0486", "title": "Structured-Object Transport", "status": "implemented", "outcome": "PASS, WEAK BY CONSTRUCTION. An eight-component register is carried as one unit and all internal relations survive. Preservation is structural rather than dynamical - the toy applies no coupling map - so this removes an objection and establishes nothing positive.", "route": "/lab/causal-phase" }, { "id": "AT-0487", "title": "Causal-Loop Audit", "status": "implemented", "outcome": "ACYCLIC, CARRIED BY AN ASSUMPTION. The event digraph over (site, tick) mixing ordinary and anomalous transitions is acyclic: every admissible arc strictly advances the global tick, so no combination of C0 and C* transitions closes a causal loop. The result rests on one assumed global time orientation; observer-dependent ordering of two independent triggers is NOT MODELED and is where a genuine paradox would live (B82).", "route": "/lab/causal-phase" }, { "id": "AT-0488", "title": "Onset Boundary - Nothing Crosses Before the Initiating Event", "status": "implemented", "outcome": "MODEL PROPERTY. Before initiation every matching edge is inaccessible and contributes no arc, so C0 influence is exactly the cycle cone. After initiation the cone is defined on the fundamental substrate. At every instant influence respects the cone of the phase in force, so this is a causal-phase transition in the model's own bookkeeping and carries no relativistic content.", "route": "/lab/causal-phase" }, { "id": "AT-0489", "title": "Restoration Cost - Where the Advantage Can Still Die", "status": "implemented", "outcome": "INCONCLUSIVE, BOTH BRANCHES REPORTED. Restoration while C* is active sweeps on S in O(log N) and preserves the ratio. Restoration forced onto ordinary couplings costs Theta(N) and collapses the ratio toward one. Which applies is a property of a generator that has not been written (B81, B83).", "route": "/lab/causal-phase" }, { "id": "AT-0490", "title": "Gate Sheet", "status": "implemented", "outcome": "SEVEN PASS, ONE FAIL, TWO NOT MODELED. Ordinary-phase locality, lawful initiation, endpoint blindness, parametric time advantage, restoration, consistency and identity all pass. The action ledger fails. Generator and physical evidence are NOT MODELED, and NOT MODELED is never counted as a pass.", "route": "/lab/causal-phase" }, { "id": "AT-0491", "title": "Blockers Raised", "status": "implemented", "outcome": "B80 unpaid Theta(N) action bill; B81 restoration under ordinary couplings costs Theta(N); B82 one global time orientation is doing the anti-paradox work; B83 no generator produces the two-phase rule.", "route": "/lab/causal-phase" }, { "id": "AT-0492", "title": "Phase 55 Verdict", "status": "implemented", "outcome": "MATHEMATICAL TWO-PHASE CRACK. A self-contradictory gate was replaced with a coherent one, and the strongest toy the corrected gate allows shows a time ratio that grows with N under frozen parameters, an acyclic event order and a structurally intact payload - and an action bill that does not scale. A causal-phase transition candidate must pay for its own phase; this one does not, so it is awarded the second rank and no higher. PHYSICAL EVIDENCE: NONE.", "route": "/lab/causal-phase" }, { "id": "AT-0454", "title": "Lieb-Robinson Quasi-Locality as the Formal Ordinary-Locality Gate", "status": "implemented", "outcome": "EXTERNAL CONSTRAINT IMPORTED, NOT SUPPORT. Local lattice Hamiltonians with bounded short-ranged interactions obey a Lieb-Robinson-type bound: information propagates inside an effective cone up to exponentially small tails. This established result now plays the role of our hand-written ordinary X-locality gate, and it is an obstruction to this programme rather than evidence for it. Consequence: any proposed realisation with a genuinely local Hamiltonian must name WHICH object underlying the cone changes - interaction graph, interaction norms, or generator. Naming none is NOT MODELED (B73).", "route": "/lab/external" }, { "id": "AT-0455", "title": "Code Subspaces and Holographic Reconstruction as Precedent for Access Language", "status": "implemented", "outcome": "LANGUAGE PRECEDENT GRANTED, TRANSPORT PRECEDENT REFUSED. Operator-algebra quantum error correction and holographic tensor-network codes establish that operator accessibility can depend on a code subspace and on the region considered, which is genuine precedent for writing accessibility as a sector property rather than a distance property. They supply no transport and no superluminal signalling, and they are explicitly consistent with no-signalling. Statistical-mechanics mappings of code thresholds add precedent that accessibility can be a sharp phase, and demand of us an order parameter, a transition point and a finite-size collapse. ANALOGY ONLY.", "route": "/lab/external" }, { "id": "AT-0456", "title": "The Operational Locality Bound", "status": "implemented", "outcome": "MODEL THEOREM. Under H1 all controllable observables lie in an algebra A_X, H2 the generator is local and bounded on the interaction graph, H3 a Lieb-Robinson-type bound holds, and H4 the structure is fixed throughout, hidden substrate connectivity outside A_X cannot produce controllable faster-than-X signalling. Any correlation carried by the hidden sector is either uncontrollable, undetectable, or already inside the cone. A controllable shortcut therefore REQUIRES failure of H1, H2 or H4: the accessible algebra, the interaction graph, or the generator must change (B73).", "route": "/lab/external" }, { "id": "AT-0457", "title": "Corollary - The Access-Channel Paradox Returns on the Structure Change", "status": "implemented", "outcome": "FAIL FOR THE OBVIOUS ESCAPE. If the required structure change is itself locally controllable and remotely detectable through the hidden substrate, it is an operation that is faster through S than through X, so AT-0443 applies to the change rather than to the transition. Five loopholes enumerated, one per hypothesis: L1 accessible algebra changes OPEN; L2 interaction graph changes CLOSED BY COST; L3 norms diverge CLOSED BY COST; L4 generator switched mid-protocol CLOSED BY PARADOX; L5 algebra changes via a global compatibility condition with no local selector OPEN. The loophole must be a lawful structure change that is not locally selectable or not remotely readable (B74).", "route": "/lab/external" }, { "id": "AT-0458", "title": "Programmable Lattice Experiments as a Contingent Testbed", "status": "implemented", "outcome": "NOTED, NOT ACTED ON. Superconducting-circuit and comparable programmable simulators already measure information spreading, correlation cones and localisation transitions on interaction graphs chosen by the experimenter. This licenses an eventual analogue-engineering testbed for an allowed-transition switch and nothing about spacetime: a result there would be a result about a programmed circuit whose distance is a coupling graph we selected.", "route": "/lab/external" }, { "id": "AT-0459", "title": "TOY INFORMATION AUDIT - A Constant Remote Trace Is Not Hidden", "status": "implemented", "outcome": "FAIL. A weak but CONSTANT latent remote distinguishability delta does not solve no-signalling asymptotically. Resolving a bias delta takes about k/delta^2 repetitions at one activation sweep each, so a constant delta costs a constant number of repetitions while the ordinary route costs Theta(N); beyond a crossover size the latent route is the cheaper way to move a bit and the construction is a channel. Illustrative delta scalings tested: constant LEAKS, 1/sqrt(N) stays hidden with detection time growing like N log N, 1/N comfortably hidden, zero exactly forbidden. The statistical detection-time model is ILLUSTRATIVE, NOT A THEOREM (B75).", "route": "/lab/external" }, { "id": "AT-0460", "title": "Suppression Requirement Extracted", "status": "implemented", "outcome": "REQUIREMENT STATED. To keep a latent channel operationally hidden as scale grows, remote distinguishability and control must vanish with N at least about as fast as 1/sqrt(N), or be exactly forbidden by the ordinary-phase observable algebra or constraint. Both surviving branches are self-defeating in the same way: a trace that cannot be read also cannot confirm or exploit any transport. Safety and usefulness are in direct opposition, which is the sharpest form the Access-Channel Paradox has taken (B75).", "route": "/lab/external" }, { "id": "AT-0461", "title": "Connections Panel - Established Work as Constraint, Not Support", "status": "implemented", "outcome": "Four connections recorded with an explicit 'what it does not give us' and 'demand it places on us' field each: quasi-locality bounds as the formal locality gate, code-subspace and holographic reconstruction as precedent for access language, statistical-mechanics mappings of code thresholds as precedent for accessibility-as-phase, and programmable lattice experiments as a contingent testbed. Every one tightens a test. NONE of them supports Adjacency Theory, and no endorsement by their authors is implied or claimed.", "route": "/lab/external" }, { "id": "AT-0462", "title": "Staged Analogue Test Plan - Written and Locked", "status": "implemented", "outcome": "CONTINGENT AND CURRENTLY UNREACHED. Four stages specified - M0 classical coupled oscillators or a passive electrical board, M1 a programmable constraint layer with a full energy ledger, M2 a photonic or phononic lattice with an imageable cone, M3 a superconducting-circuit or comparable simulator. Milestone zero is to reproduce the abstract allowed-transition phase switch and the five-ruler diagnostics in hardware. Every stage carries preregistered observables, null controls, an energy and cost ledger, and a mandatory comparison against the conventional causal explanation. The plan is locked behind the no-signalling gate (AT-0451 FAIL), the cost gate (AT-0450 FAIL) and the identity gate (AT-0452 NOT MODELED). No claim of moving matter and no claim of faster-than-light anything.", "route": "/lab/external" }, { "id": "AT-0463", "title": "Phase 53 Verdict", "status": "implemented", "outcome": "EXTERNAL CROSS-CHECK COMPLETED / CANDIDATE STILL REJECTED. THE REAL PHYSICS MAKES OUR TEST HARDER, AND OUR OWN AUDIT SAYS A SMALL LEAK IS STILL A LEAK. Established quasi-locality gives the ordinary-locality gate a rigorous form and names the three objects a realisation would have to change; code-subspace results license the constraint language and refuse the transport; the information audit removes the last comfortable escape. Verdict taxonomy awards neither NON-SIGNALLING TRANSITION CANDIDATE nor OPERATIONAL CRACK CANDIDATE. NO PHYSICAL MECHANISM / NO PHYSICAL EVIDENCE.", "route": "/lab/external" }, { "id": "AT-0439", "title": "One Substrate, Two Access States — Construction", "status": "implemented", "outcome": "A single bounded-degree substrate S = (V, E_X ∪ E_latent) on N sites: a cycle of ordinary couplings plus latent generic edges i <-> i + 2^r(i), where r(i) is the trailing-zero rank of the site index. Maximum degree stays bounded, no edge is created at run time, and the latent rule is a function of the index alone with zero destination bits. The ordinary phase exposes only the cycle; the open phase exposes all of S. TOY MODEL / CONSTRUCTED MATHEMATICAL SYSTEM.", "route": "/lab/access" }, { "id": "AT-0440", "title": "Measured Scaling of the Structural Ratio Q", "status": "implemented", "outcome": "FIRST POSITIVE SCALING EXPONENT IN THE PROGRAMME. Ordinary X distance scales O(N) while both open-phase distance and the local activation flood scale O(log N). Recorded median toy values — N=32: 16 / 4 / 5.5 / 9, Q=1.778; 64: 32 / 5 / 7 / 11, Q=2.909; 128: 64 / 6 / 8 / 14, Q=4.571; 256: 128 / 6.5 / 9 / 16, Q=8.0; 512: 256 / 7 / 11 / 18, Q=14.222; 1024: 512 / 9 / 12 / 20.5, Q=24.99 — give a finite-size fitted exponent of approximately 0.764 against a structural target of N / log N. Live breadth-first recomputation reproduces the growth. COMPUTATIONAL RESULT inside a system we constructed (B69).", "route": "/lab/access" }, { "id": "AT-0441", "title": "Interactive Access-State Diagram", "status": "implemented", "outcome": "Same nodes, same edges, two access states, rendered and switchable at N = 32, 64 and 128. In C_0 the pair reads N/2 apart; in C* the shortest lawful path collapses to about log_2 N hops. The diagram raises an explicit warning whenever the unlock front is set to controllable and detectable, because that configuration is a channel rather than a shortcut.", "route": "/lab/access" }, { "id": "AT-0442", "title": "Constraint-Structure Hypothesis — G_allowed(Psi, C)", "status": "implemented", "outcome": "MODEL HYPOTHESIS, NOT A CLAIM. Distance is demoted from primitive and replaced by an allowed-transition graph: the substrate may carry rich relations while a constraint layer C decides which transitions are accessible. C_0 yields X-local transitions, a hypothetical lawful phase C* admits latent transitions, and the cycle must return to C_0 with bounded residual debt. Gauge-like and code-like structures are named as ANALOGIES AND CLASSES TO TEST; nothing is derived from established physics.", "route": "/lab/access" }, { "id": "AT-0443", "title": "The Access-Channel Paradox", "status": "implemented", "outcome": "FATAL AUDIT OF THE OPERATIONAL READING. Trilemma, stated precisely: a latent sector cannot simultaneously be (1) faster through S than ordinary X, (2) locally controllable and (3) remotely detectable, while still claiming ordinary operational X-locality. If all three hold, the unlock front is itself the shortcut communication channel and the construction describes a world whose causal structure is S, not X. The featured construction holds all three. At least one property must be unavailable in the ordinary phase (B69).", "route": "/lab/access" }, { "id": "AT-0444", "title": "A — Non-Signalling Latent-Sector Theorem Search", "status": "implemented", "outcome": "OBSTRUCTION RECORDED. No construction was found in which S has O(log N) diameter while every ordinary-phase controllable observable retains an O(N) influence cone in X. The obstruction is structural: whatever local operation switches the constraint sector propagates through S, and its arrival is the fast influence. Non-signalling requires that the switch be either non-local to prepare or invisible at B.", "route": "/lab/access" }, { "id": "AT-0445", "title": "B — Control-vs-Detectability Matrix", "status": "implemented", "outcome": "Four cases tested. Controllable and detectable: HIDDEN CHANNEL, rejected. Controllable and undetectable: no signal, but also no confirmable transport. Uncontrollable and detectable: nothing can be decided to be used. Neither: operationally vacuous. Only the uncontrollable branch survives without smuggling a preexisting channel, and it survives precisely by being unusable (B71).", "route": "/lab/access" }, { "id": "AT-0446", "title": "C — Global-Compatibility Test", "status": "implemented", "outcome": "FAIL ON COST. A transition enabled by a conserved global constraint-satisfaction condition genuinely avoids an A->B signal, but preparing that global state under the same local rules costs a Theta(N) pass over the substrate. Charged in full, Q_cost falls below one. The signal was not eliminated, it was paid for in advance (B70).", "route": "/lab/access" }, { "id": "AT-0447", "title": "D — Code-Subspace Toy", "status": "implemented", "outcome": "MATHEMATICAL ANALOGY ONLY. Ordinary observables restricted to a subspace in which latent edges act as unobservable equivalences. Explicit no-signalling checks were run over the restricted observable algebra: no arbitrary bit crosses. The collective operation also fails to move a composite identity between logical sectors, so the construction is non-signalling and inert at the same time. No quantum-mechanical claim is made anywhere in this experiment.", "route": "/lab/access" }, { "id": "AT-0448", "title": "E — Reversibility and Adjacency Debt", "status": "implemented", "outcome": "PASS, BUT UNINFORMATIVE. The cycle C_0 -> C* -> C_0 restores every ordinary observable and constraint exactly, with zero residual debt. The restoration is perfect because the constraint layer never modified the substrate state: a costless mask does no work, so this pass carries no evidential weight (B72).", "route": "/lab/access" }, { "id": "AT-0449", "title": "F — Endpoint Blindness", "status": "implemented", "outcome": "PASS. The substrate, the latent rule, the constraint layer and the initial state are frozen before A and B are named. The latent rule depends on the site index only; destination bits used: zero. Whatever this construction is, it was not tuned toward its endpoints.", "route": "/lab/access" }, { "id": "AT-0450", "title": "G — Full Parametric Cost Accounting", "status": "implemented", "outcome": "SPLIT VERDICT. Q_time grows with N — the first time in this programme — while Q_cost, once preparation, constraint transition, operational transition and restoration are all charged, falls below one and continues to fall. The time ratio is real and the cost ratio kills it. Both are reported (B70).", "route": "/lab/access" }, { "id": "AT-0451", "title": "H — Information-Theoretic Kill Test", "status": "implemented", "outcome": "FAIL. One classical bit was encoded in the supposedly innocent control: open the sector, or do not. B distinguishes the two in O(log N) steps against an ordinary-causality bound of Theta(N). Classification: HIDDEN CHANNEL. This single test is sufficient to refuse the operational reading of AT-0440 regardless of every other result on this page (B69).", "route": "/lab/access" }, { "id": "AT-0452", "title": "I / J — Identity Transport and Robustness", "status": "implemented", "outcome": "MIXED. Robustness PASS: zero tuned parameters, and the scaling survives latent-edge rewiring and noise without fine tuning. Identity transport NOT MODELED under the constraint formulation — a structured multi-component state with relational and internal invariants has not been carried through a C_0 -> C* -> C_0 cycle. An unrun test is not a pass (B72).", "route": "/lab/access" }, { "id": "AT-0453", "title": "Phase 52 Verdict", "status": "implemented", "outcome": "MATHEMATICAL CONSTRAINT CRACK. THE ROAD REALLY GETS BETTER WITH SCALE — AND THE KEY THAT OPENS IT IS ITSELF A MESSAGE. Gates: one bounded-degree substrate PASS, endpoint blindness PASS, parametric growth of Q_time PASS, full cost accounting FAIL, no-signalling FAIL, identity transport OPEN, robustness PASS, no physical claim PASS. This is NOT an OPERATIONAL CRACK CANDIDATE and NOT a physical breakthrough. NO PHYSICAL MECHANISM / NO PHYSICAL EVIDENCE.", "route": "/lab/access" }, { "id": "AT-0431", "title": "Local Conductance Phase — Construction and Locality Audit", "status": "implemented", "outcome": "A weighted ring whose edge conductances are set by a strictly local field g_i(t+1) = g_i + kappa (g_{i-1} - 2 g_i + g_{i+1}) + alpha (g_i - g_i^3), with w_i = clip(1 + beta max(0, g_i), 1, w_max) under a FROZEN total budget sum(w_i - 1) <= E. Zero long-range A-B edges are ever created, the ring keeps exactly N edges before and after, the rule is translation invariant and carries zero destination bits, and the pair A = 0, B = floor(N/2) is fixed before any run.", "route": "/lab/rulers" }, { "id": "AT-0432", "title": "Four Rulers — Geometry, Resistance, Spectrum, Causal Time", "status": "implemented", "outcome": "POSITIVE, AND STRICTLY STRONGER THAN A COORDINATE TRICK. The pair is measured by weighted geodesic d_geo, effective resistance R_eff, spectral gap lambda_2 of the weighted Laplacian, and operational causal arrival time T_causal. Three of the four are chart-invariant and one is the arrival time of a real disturbance, so none of them can be produced by redrawing the map as in AT-0425. In the same locally generated phase all four move coherently in the same direction.", "route": "/lab/rulers" }, { "id": "AT-0433", "title": "Small-System Trial Search — 144 Trials", "status": "implemented", "outcome": "At N = 24, sweeping twelve amplitudes by twelve seeds, coherent four-ruler movement occurs in a minority of trials with end-to-end ordinary-time advantage after setup in the range of roughly 1.19x to 1.62x depending on the coherence threshold. The originating exploratory sweep recorded 12/144 coherent trials in a 1.19x-1.30x band. Coherence at small N is real; it is not evidence of anything that survives scale.", "route": "/lab/rulers" }, { "id": "AT-0434", "title": "Scaling Audit — Best-Case Advantage Against N", "status": "implemented", "outcome": "NEGATIVE, AND DECISIVE. One frozen parameter set across N = 24 … 256. Best-case end-to-end advantage after setup falls monotonically — originating sweep N=24: 1.564, N=32: 1.377, N=48: 1.223, N=64: 1.159, N=96: 1.100 — and the live recomputation reproduces the same decay. The fitted exponent of (A - 1) against N is approximately -1.0 with R^2 above 0.98. The absolute time saving is a constant set by the fixed conductance budget; the distance it must beat grows like N. Classification: FINITE-SCALE FOUR-RULER EFFECT / NO PARAMETRIC CRACK (B66).", "route": "/lab/rulers" }, { "id": "AT-0435", "title": "Ruler Weakening Under Scale", "status": "implemented", "outcome": "The geodesic, resistance and spectral shifts themselves weaken as N grows: the fixed budget is simply spread thinner across a larger system. The rulers do not merely stop paying off, they stop moving. Weakening rulers and a decaying advantage are one phenomenon seen twice (B66, B68).", "route": "/lab/rulers" }, { "id": "AT-0436", "title": "Frozen-Parameter Guard", "status": "implemented", "outcome": "PASS. kappa, alpha, the conductance budget E, the cap w_max and the endpoint pair are identical at every system size, and the amplitude sweep is identical at every size. Re-choosing kappa and alpha per N was measured rather than merely prohibited: it would have inflated the reported advantage and flattened the apparent decay. Per-size tuning is the standard way a dying effect is made to look like a law.", "route": "/lab/rulers" }, { "id": "AT-0437", "title": "Critical-Regime Probe", "status": "implemented", "outcome": "OPEN QUESTION, STATED PRECISELY. Dynamic exponent measured from T_phase ~ N^z alongside correlation-length scaling xi ~ N^a under the frozen rule. Off criticality xi is finite, which is exactly why the saving is a constant. The next hypothesis is a genuine collective critical regime in which correlation length and susceptibility grow with N under fixed local equations, with z < 1 AND all four rulers still changing by O(1), so that total completion time scales sublinearly. No endpoint-specific shortcut may be used to reach it (B68).", "route": "/lab/rulers" }, { "id": "AT-0438", "title": "Four-Ruler Verdict", "status": "implemented", "outcome": "THE RULERS AGREED — BUT THE CRACK CLOSED AS THE UNIVERSE GOT BIGGER. Eight gates: strict locality PASS, no endpoint encoding PASS, four-ruler coherence PASS, operational advantage PASS at small N, parametric growth FAIL, frozen parameters PASS, critical regime FAIL, no physical claim PASS. Final classification FINITE-SCALE FOUR-RULER EFFECT / NO PARAMETRIC CRACK. NO PHYSICAL MECHANISM / NO PHYSICAL EVIDENCE.", "route": "/lab/rulers" }, { "id": "AT-0425", "title": "Explicit E1 Countermodel — Folded / Unwrapped Emergence", "status": "implemented", "outcome": "MATHEMATICAL CRACK OF HYPOTHESIS E1. Microphysics is an N-site ring with nearest-neighbour propagation at one edge per step. The observation map cuts the ring and unrolls it: F_N(i) = i. The pair A = 0, B = N-1 are microscopic neighbours, d_S = 1 and local transport time 1, yet emergently separated by D_X = N-1, so Q = (N-1)/1 ~ N. Numerical scaling over N = 16 … 2048 fits Q ~ N^1.0111. The minimum global Lipschitz constant satisfies L_N >= N-1, so the leverage exists exactly because there is no uniform finite Lipschitz bound. Labelled MATHEMATICAL PROPERTY / OBSERVATIONAL GEOMETRY ARTIFACT; no transport, no mechanism (B63).", "route": "/lab/fold" }, { "id": "AT-0426", "title": "Seam / Coordinate Artifact Test", "status": "implemented", "outcome": "The anomalous pair is tied to the cut. Sweeping the seam over all N placements moves the high-Q pair with it, one anomalous adjacent pair per seam, and every adjacent pair in the ring can be made to look maximally distant by choosing the seam. Random pairs away from the seam show Q of order 1. A property that can be relocated onto any pair by relabelling is a property of the labels (B63).", "route": "/lab/fold" }, { "id": "AT-0427", "title": "Seam-Free Invariant Metric Test", "status": "implemented", "outcome": "MANDATORY NEGATIVE CONTROL, PASSED. Replacing the unwrapped line metric with the intrinsic ring metric min(|i-j|, N-|i-j|) collapses Q to exactly 1 at every scale, exponent 0. Large Q alone is therefore insufficient evidence of anything: the same microstate yields Q ~ N or Q = 1 depending only on which chart is used to read it (B64).", "route": "/lab/fold" }, { "id": "AT-0428", "title": "Generic Fold Test", "status": "implemented", "outcome": "Observation maps generated from translation-invariant local dynamics that can spontaneously form folds, with the rule frozen before A and B are selected. Folds do form, and high-Q pairs do appear without endpoint targeting, at low density and always co-located with a fold or branch. Crucially the folds are detectable by invariant local observables — the winding or branch index of the map is readable without knowing the pair — so the anomaly is announced by the chart rather than hidden in the physics (B65).", "route": "/lab/fold" }, { "id": "AT-0429", "title": "Operational Equivalence Test", "status": "implemented", "outcome": "For every high-Q pair found: microscopic communication time 1 step, local neighbourhood structure adjacent, clock synchronisation immediate, observer-invariant event relations near. Only the chart-dependent emergent geodesic reads far. Not a single invariant observable treats the pair as distant. Label: RELABELING CRACK ONLY. The CAUSAL/GEOMETRIC MISMATCH CANDIDATE branch was available and was not reached.", "route": "/lab/fold" }, { "id": "AT-0430", "title": "First Crack Gate", "status": "implemented", "outcome": "OUTCOME (A) COORDINATE ARTIFACT, with outcome (B) MATHEMATICAL E1 CRACK granted on the narrow mathematical point that the theorem's uniform-Lipschitz hypothesis is genuinely and explicitly violated. Outcome (C) refused. No physical breakthrough is claimed. Same-equations, identity, information-debt, preparation and operational-signal gates all preserved and all reported. NO PHYSICAL MECHANISM / NO PHYSICAL EVIDENCE.", "route": "/lab/fold" }, { "id": "AT-0415", "title": "Candidate Family: Dynamical Quotient Geometry", "status": "implemented", "outcome": "A ring of N sites of degree 2 with no long-range edge at any time. Auxiliary field r_i(t+1) = clip(r_i + kappa (r_{i-1} - 2 r_i + r_{i+1}) + u_i), with a translation-invariant drive u_i that fires only when the site sits on a boundary and reads only its own two neighbours. Two tagged objects A and B are never written by the update. The observable space is the quotient this field induces, and it reorganises under the same equations.", "route": "/lab/crack" }, { "id": "AT-0416", "title": "Observable Metric Construction", "status": "implemented", "outcome": "Three lawful observables defined from the microstate: (A) quotient class metric, (B) state-dependent weighted path metric that reprices existing physical edges, (C) dynamically rewired observation graph. A and C are OBSERVATIONAL adjacency and carry nothing; B is TRANSPORT-COMPATIBLE and adds no edge. The distinction is recorded per construction and is what AT-0422 then tests.", "route": "/lab/crack" }, { "id": "AT-0417", "title": "Identity-Preserving Pair Protocol", "status": "implemented", "outcome": "Identity intact in every run: the tags are never touched by the update, and nothing is transported. Cost C_S = sum over t and i of |dr_i| + |u_i|, so all auxiliary-field evolution needed to create the geometry is charged, with the preparation ledger shown as its own line and then included in the total. No free background.", "route": "/lab/crack" }, { "id": "AT-0418", "title": "Scaling Search", "status": "implemented", "outcome": "NEGATIVE. Scales 32, 64, 128, 256, 512 with frozen parameters. Fitted exponents: quotient -1.19 +/- 0.77, weighted path +0.21 +/- 0.33, observation graph -1.15 +/- 0.69. No construction has an exponent above zero outside its interval, so none shows leverage that grows with system size. At the two largest scales the quotient and observation metrics record exactly zero leverage because the coarsening pins before it reaches the pair; those points are reported and excluded from the fit (B60, B62).", "route": "/lab/crack" }, { "id": "AT-0419", "title": "Local-Cone Audit", "status": "implemented", "outcome": "PASS. Two copies differing in one site by 0.2 were evolved side by side at N = 128. The maximum excess of the divergence radius over v.t is 0, so the microscopic cone is exactly one site per step and never wider. Any change in the observable metric outside the cone is produced by evolution that already happened locally everywhere, not by instantaneous remote dependence.", "route": "/lab/crack" }, { "id": "AT-0420", "title": "Information-Debt Test", "status": "implemented", "outcome": "The clean candidate and the hierarchical family use translation-invariant rules and generic initial conditions with zero destination bits. The two high-leverage variants are disqualified before their numbers are read: the endpoint-addressed drive needs ceil(log2 N) bits of destination address, and the preloaded class field needs Theta(N) bits, which is the whole answer written into the setup (B61).", "route": "/lab/crack" }, { "id": "AT-0421", "title": "Preparation-Amortization Audit", "status": "implemented", "outcome": "Preparation is never hidden. Single-use exponent -1.15 against amortized exponent -1.09 over M = 32 reuses: amortization moves the constant and leaves the law alone, because maintaining the prepared field against diffusion is itself an ongoing local cost. Reusable-background accounting remains an assumption, and prior work already found prepared geometry to be route-specific (B48).", "route": "/lab/crack" }, { "id": "AT-0422", "title": "No-Signalling-via-Metric Trap", "status": "implemented", "outcome": "DECISIVE CONTROL. A acts locally at its own site to encode one controllable bit. At N = 128 the observable separation after preparation is 9 hops while the physical distance is 64 sites, and the far site first shows any dependence at step 188 against a cone bound of 64. Label: OBSERVATIONAL SHORTCUT ONLY. Closeness in an observable metric delivers no operational reach whatsoever (B59).", "route": "/lab/crack" }, { "id": "AT-0423", "title": "Candidate Kill Matrix", "status": "implemented", "outcome": "Six candidates scored against ten survival rows, zero survivors. All three quotient-geometry observables and the second family die on parametric Q and on survival to large N; the two controls die additionally on same-equations and endpoint encoding. The locally grown hierarchy is BOUNDED at exponent -0.09: every local merge round rewrites Theta(N) sites to remove Theta(N) of separation, so the geometry costs exactly what it buys (B60).", "route": "/lab/crack" }, { "id": "AT-0424", "title": "Wall-Crack Verdict", "status": "implemented", "outcome": "NO CRACK. Every candidate reduced to bounded leverage, hidden preparation or pure relabelling. Outcome 2 (mathematical crack only) was available and was not reached; outcome 3 (operational crack candidate) was never in question, since no controllable influence ever arrived before the cone. NO PHYSICAL MECHANISM / NO PHYSICAL EVIDENCE. No relativity violation, wormhole, transport or signalling claim appears anywhere in this package.", "route": "/lab/crack" }, { "id": "AT-0407", "title": "Necessary Escape Theorem", "status": "implemented", "outcome": "Leverage redefined as observable separation per unit of fully accounted lawful completion cost, Q = D_X / C_S. Theorem: if F is fixed, single-valued and globally L-Lipschitz with finite L, and every lawful path satisfies C_S >= c d_S with c > 0, then Q <= L/c. A seed-407 sweep at scales 8, 16, 32, 64 and 128 found no lawful pair above the ceiling. The theorem establishes at-least-one-door necessity; it does not select a door and prices nothing physically (B55).", "route": "/lab/sharpened" }, { "id": "AT-0408", "title": "Door Minimality Audit", "status": "implemented", "outcome": "The three hypotheses are mapped to four doors — no uniform finite Lipschitz bound, dynamical map or metric, lawful cost not floored by the static state distance, and emergence that is not single-valued on a fixed topology. Logical independence tested with single-removal countermodels in which exactly one hypothesis is dropped. Correction on the record: the doors exhaust the hypotheses of this theorem only, not conceivable physics, and no door is physically priced (B57).", "route": "/lab/sharpened" }, { "id": "AT-0409", "title": "Bounded-Leverage Theorem", "status": "implemented", "outcome": "Generalised from the L = 1, c = 1 normalisation of Phase 47 to arbitrary finite L and c. Any finite ceiling, up to 100,000 in the recorded table, is purchasable by inflating L or shrinking c, and every such ceiling has exponent zero against system scale. Parametric leverage — growth of Q with scale under frozen dynamics and frozen accounting — is the only admissible target from here (B56).", "route": "/lab/sharpened" }, { "id": "AT-0410", "title": "Same-Equations Requirement", "status": "implemented", "outcome": "Formalised: one frozen dynamics D_theta must show an ordinary regime with a finite emergent cone AND an anomalous regime with parametrically growing Q, with no second transport or control channel, no per-destination parameter reset and no prewritten endpoint data. Every setting reproduced the ordinary regime; none produced the anomalous one. The parameter that would buy leverage is the parameter that destroys the finite cone (B58, B54).", "route": "/lab/sharpened" }, { "id": "AT-0411", "title": "Blind Counterexample Search", "status": "implemented", "outcome": "Systems generated and frozen with the leverage objective never consulted, across nonlinear maps, graphs, quotient-like observation relations, state-dependent metrics and constrained lawful dynamics. Every high-Q survivor was classifiable by which hypothesis it broke, and no frozen system produced a positive scaling exponent. Zero theorem contradictions, so no re-derivation was required. NOT EXPECTED BY CONSTRUCTION, and still negative (B58).", "route": "/lab/sharpened" }, { "id": "AT-0412", "title": "Finite-Scale Mirage Audit", "status": "implemented", "outcome": "Controls built deliberately to produce a huge Q at one finite scale — normalisation choice, near-singular Jacobian, tuned tiny cost floor, preloaded edges and endpoint encoding — every one saturated as the system grew and is labelled FINITE-SCALE MIRAGE. A hand-written parametric control confirms the classifier fires when growth is real (B56).", "route": "/lab/sharpened" }, { "id": "AT-0413", "title": "Einstein-Emergent Benchmark", "status": "implemented", "outcome": "In the same candidate equations, small perturbations propagate with a finite measured front speed and local causal ordering is respected with zero violations. 'Einstein-like' is used strictly in the limited sense of finite local causal propagation: no Einstein field equation is derived, recovered or approximated. This is a precondition of the programme, never an achievement.", "route": "/lab/sharpened" }, { "id": "AT-0414", "title": "Foundational Gate v2", "status": "implemented", "outcome": "NO PHYSICAL MECHANISM / NO PHYSICAL EVIDENCE. The theorem, the necessity claim, the independence audit, the definition of parametric leverage, the mirage audit and the ordinary finite-speed regime all pass. The gate fails where it should: no blind candidate survives the scaling test and no single dynamics shows both regimes. NOT MODELED is never counted as a pass.", "route": "/lab/sharpened" }, { "id": "AT-0401 (req. AT-0373)", "title": "Lipschitz No-Go", "status": "implemented", "outcome": "For a fixed globally L-Lipschitz map F: S -> X, d_X <= L d_S by definition of the Lipschitz constant. A seeded sweep at seed 373 over random normalised linear maps in dimensions 3, 5, 8 and 12 tested 9,600 state pairs; the largest observed ratio was 0.99982 and there were no violations. MATHEMATICAL PROPERTY plus toy numerical check (B52).", "route": "/lab/foundation" }, { "id": "AT-0402 (req. AT-0374)", "title": "Escape-Condition Audit", "status": "implemented", "outcome": "Exactly four escape classes, one per hypothesis of the theorem: non-Lipschitz or critical regions, dynamical map or metric, lawful path metric different from the static state metric, and quotient / branching / topology change. No speculative fifth branch admitted (B53).", "route": "/lab/foundation" }, { "id": "AT-0403 (req. AT-0375)", "title": "Cost of Escape", "status": "implemented", "outcome": "Each escape class carries named debts already in this ledger: singular Jacobian and identity amplification, map-edit action and front precedence, pathwise causality and route specificity, topology bookkeeping and gauge discipline. Three of four are priced and all cost more than ordinary traversal; topology change is NOT MODELED and therefore unavailable (B53).", "route": "/lab/foundation" }, { "id": "AT-0404 (req. AT-0376)", "title": "Same-Equations Dual-Regime Test", "status": "implemented", "outcome": "One minimal family f_a(x) = x + (a/k) sin(kx), one parameter, no hand-added channel. Ordinary finite-speed emergent behaviour appears at every setting; the apparent leverage at high sharpness is entirely growth of the global Lipschitz constant and the L-normalised stretch never exceeds 1. No setting gives both regimes (B54).", "route": "/lab/foundation" }, { "id": "AT-0405 (req. AT-0377)", "title": "Blind Emergence Search", "status": "implemented", "outcome": "Generate, freeze, then search, in that order in code, with the shortcut objective never consulted during generation. Across 24 frozen models and 5,760 endpoint probes the best straight-line leverage was 0.962 and the best lawful leverage 0.954. Nothing above the bound occurs naturally. NOT EXPECTED BY CONSTRUCTION, and still negative.", "route": "/lab/foundation" }, { "id": "AT-0406 (req. AT-0378)", "title": "Foundational Gate", "status": "implemented", "outcome": "FIXED SMOOTH EMERGENCE INSUFFICIENT. Five of ten criteria pass; every failing criterion is substantive. Next work must identify which escape condition is mathematically necessary and whether it can arise from the SAME underlying equations without hand insertion. No new mechanism family may be opened until that question is posed as a theorem.", "route": "/lab/foundation" }, { "id": "AT-0391 (req. AT-0363)", "title": "Adjacency-as-Primitive Baseline", "status": "implemented", "outcome": "Bond A_ij(t) treated as the primitive dynamical variable with distance derived only afterwards. The seed-363 null reproduces the recorded statistics and is kept as a control, never a finding: the compatibility that drives the bond was inserted into its own equation (B49).", "route": "/lab/resonance" }, { "id": "AT-0400 (req. AT-0372)", "title": "Resonant Adjacency Gate", "status": "implemented", "outcome": "Gate not cleared. Bonds with no similarity hand-off grow everywhere at once, tuned bonds need continual retuning and do not transfer, addressing costs about ten bits against one bit of payload, and the full activation ledger costs more than ordinary traversal (B50, B51).", "route": "/lab/resonance" }, { "id": "AT-0381 (req. AT-0353)", "title": "Local Reservoir Ledger", "status": "implemented", "outcome": "Every edge of a 60-edge route holds a stored resource; each transit draws 0.8 per edge and bounded local recharge puts a little back between trips. Eight trips complete on a loading of 360 units, and the reservoir balance closes to numerical zero — nothing appears without a source.", "route": "/lab/infrastructure" }, { "id": "AT-0382 (req. AT-0354)", "title": "Full Amortized Cost", "status": "implemented", "outcome": "Marginal external input after preload is 4.40 per trip. Fully amortized — preload, recharge, triggers, maintenance, less what is left in the route — it is 49.40 per trip, against 48.00 for ordinary traversal. An eleven-fold understatement (B46).", "route": "/lab/infrastructure" }, { "id": "AT-0383 (req. AT-0355)", "title": "Route-Length Scaling", "status": "implemented", "outcome": "Preload grows at 6.00 units per edge with R² above 0.999 and per-trip cost tracks it, while the trigger stays flat in length. Infrastructure energy is linear in route length; there is no length at which preparing the route becomes cheap (B47).", "route": "/lab/infrastructure" }, { "id": "AT-0384 (req. AT-0356)", "title": "Utilization Break-Even", "status": "implemented", "outcome": "A one-off dynamic corridor never amortizes; the preconditioned route beats it quickly but edge capacity caps a loading at eight completed trips, so it does not cross ordinary traversal in the tested range. Any crossover exists only inside these toy assumptions.", "route": "/lab/infrastructure" }, { "id": "AT-0385 (req. AT-0357)", "title": "Reservoir Propagation", "status": "implemented", "outcome": "Delivering the loading locally from a depot costs transport overhead that grows with distance, plus charged setup time. Instantaneous placement everywhere is priced and then rejected as a forbidden control — it is the assumption that preparation is free.", "route": "/lab/infrastructure" }, { "id": "AT-0386 (req. AT-0358)", "title": "Destination Independence", "status": "implemented", "outcome": "A corridor prepared between two sites is reused by only a small fraction of a randomly requested journey, and most journeys get nothing from it. Classified ROUTE-SPECIFIC INFRASTRUCTURE, not universal adjacency (B48).", "route": "/lab/infrastructure" }, { "id": "AT-0387 (req. AT-0359)", "title": "Network Geometry", "status": "implemented", "outcome": "Prepared chords on a ring cut the mean pairwise cost and produce a real effective-adjacency gain, entirely by graph routing over links somebody paid for. Energy per unit of gain rises as chords are added.", "route": "/lab/infrastructure" }, { "id": "AT-0388 (req. AT-0360)", "title": "Hub Hypothesis", "status": "implemented", "outcome": "Preparing every pair is O(N²) and gives the shortest journeys; hub-and-spoke costs far less and stretches every journey through one node; the hierarchy sits between. The standard cost-versus-stretch tradeoff of any transport network, with no physical content.", "route": "/lab/infrastructure" }, { "id": "AT-0389 (req. AT-0361)", "title": "Universal-Medium Challenge", "status": "implemented", "outcome": "A medium homogeneous enough to serve arbitrary endpoints costs with the area it covers rather than the journey it saves, many times a single corridor. All negative controls fail as required: unprepared carries nothing, and the same energy spread below the activation draw is stranded.", "route": "/lab/infrastructure" }, { "id": "AT-0390 (req. AT-0362)", "title": "Infrastructure Gate", "status": "implemented", "outcome": "Recorded status: GATE NOT CLEARED, classified ROUTE-SPECIFIC INFRASTRUCTURE. Maximum award available remains STORED-ENERGY INFRASTRUCTURE TOY / PHYSICAL EVIDENCE NONE.", "route": "/lab/infrastructure" }, { "id": "AT-0371 (req. AT-0343)", "title": "Phase-Switch Amplification Audit", "status": "implemented", "outcome": "A tiny trigger in a single-field bistable medium produces an integrated response several hundred times its own energy, but the field settles into a persistent alternate state and no candidate restores near baseline. Classified PHASE-SWITCH AMPLIFICATION WITH STATE DEBT (B43).", "route": "/lab/stored-medium" }, { "id": "AT-0372 (req. AT-0344)", "title": "Recovery-Field Baseline", "status": "implemented", "outcome": "With an explicit recovery field the medium restores to between about 1e-8 and 1e-4, and the excitation never leaves the trigger neighbourhood — a front of only a few cells. TRANSIENT LOCAL AMPLIFICATION / NO LONG-RANGE PROPAGATION (B44).", "route": "/lab/stored-medium" }, { "id": "AT-0373 (req. AT-0345)", "title": "Propagation-vs-Restoration Tradeoff", "status": "implemented", "outcome": "Across the excitability-recovery plane the regions are disjoint: cells either restore and stay local, or propagate and leave the medium switched. Zero cells did both (B44).", "route": "/lab/stored-medium" }, { "id": "AT-0374 (req. AT-0346)", "title": "Stored-Medium Energy Ledger", "status": "implemented", "outcome": "Every cell carries an explicit free-energy reservoir; positive reaction work is only permitted where the reservoir can pay. Reach scales with stored energy and the debit matches the work to numerical tolerance (B45).", "route": "/lab/stored-medium" }, { "id": "AT-0375 (req. AT-0347)", "title": "Trigger-vs-Reservoir Scaling", "status": "implemented", "outcome": "Trigger cost is flat in route length; preloaded infrastructure energy and per-transit depletion are linear in it. A finite trigger covering a long route means a long route was charged in advance (B45).", "route": "/lab/stored-medium" }, { "id": "AT-0376 (req. AT-0348)", "title": "Preconditioned Medium Test", "status": "implemented", "outcome": "Prepositioned infrastructure is admitted as its own mechanism class. Amortised cost per trip falls with reuse but the setup energy is never dropped, and in the tested range it does not undercut ordinary traversal.", "route": "/lab/stored-medium" }, { "id": "AT-0377 (req. AT-0349)", "title": "Self-Recharging Medium Challenge", "status": "implemented", "outcome": "Closing the cycle requires explicitly accounted external recharge at bounded local rate, plus waiting time. Nothing in this family recharges itself.", "route": "/lab/stored-medium" }, { "id": "AT-0378 (req. AT-0350)", "title": "No-Free-Amplification Control", "status": "implemented", "outcome": "Under the declared energy functional, response work never exceeds trigger plus reservoir debit plus external input in any sampled configuration. Any positive residual is reported as a model bug, not a discovery.", "route": "/lab/stored-medium" }, { "id": "AT-0379 (req. AT-0351)", "title": "Infrastructure-vs-Vehicle Split", "status": "implemented", "outcome": "Three accounting models — stored along the route, carried by the traveller, supplied from origin — are reported separately and never summed. Switching between them silently is how a shortcut gets manufactured.", "route": "/lab/stored-medium" }, { "id": "AT-0380 (req. AT-0352)", "title": "Stored-Medium Gate", "status": "implemented", "outcome": "Recorded status: GATE NOT CLEARED. Maximum award available remains STORED-MEDIUM CORRIDOR IN TOY MODEL / PHYSICAL EVIDENCE NONE.", "route": "/lab/stored-medium" }, { "id": "AT-0361 (req. AT-0343)", "title": "Multi-Observer Invariant Audit", "status": "implemented", "outcome": "Independent charts of the same run agree on event order and on normalised displacement to machine precision (~1e-14). Hygiene met, no evidential weight (B42).", "route": "/lab/scale-power" }, { "id": "AT-0362 (req. AT-0344)", "title": "Local-Scale Power Ceiling", "status": "implemented", "outcome": "Under bounded amplitude, |dλ/dt| < 3, a gradient bound and enforced restoration, best gated leverage is about 1.5 at a large accounted action; most gated candidates sit between 1.3 and 1.5 (B40).", "route": "/lab/scale-power" }, { "id": "AT-0363 (req. AT-0345)", "title": "Nonlinear Scale Interaction Search", "status": "implemented", "outcome": "A bounded local self-interaction is necessary for the gain — the linear ablation is measurably weaker — and the Jacobian guard confirms no gain was manufactured near singularity.", "route": "/lab/scale-power" }, { "id": "AT-0364 (req. AT-0346)", "title": "Critical Scale Response", "status": "implemented", "outcome": "No phase-transition-like response found: the reorganised region grows in proportion to the trigger, with denominator guards active near zero baseline.", "route": "/lab/scale-power" }, { "id": "AT-0365 (req. AT-0347)", "title": "Self-Amplifying Scale Pulse", "status": "implemented", "outcome": "A finite local trigger spreads by diffusion and decays, retaining only a few percent of its amplitude. Bounded self-propagation NOT demonstrated; never called a soliton.", "route": "/lab/scale-power" }, { "id": "AT-0366 (req. AT-0348)", "title": "Scale-Pulse Backreaction", "status": "implemented", "outcome": "With the traveller pushing back on the field the leverage degrades slightly. The free-ride figure is retained as a control and never reported as the result.", "route": "/lab/scale-power" }, { "id": "AT-0367 (req. AT-0349)", "title": "Action-vs-Leverage Law", "status": "implemented", "outcome": "Action grows superlinearly with leverage across the gated set. Recorded as ENGINEERINGLY UNFAVOURABLE IN TOY MODEL; no cheap regime exists in the sampled family (B41).", "route": "/lab/scale-power" }, { "id": "AT-0368 (req. AT-0350)", "title": "Observer-Causal Consistency", "status": "implemented", "outcome": "No ordering contradictions. Chart-specific apparent superluminality is a bookkeeping artefact and is rejected as a claim.", "route": "/lab/scale-power" }, { "id": "AT-0369 (req. AT-0351)", "title": "Emergent-Limit Recovery v2", "status": "implemented", "outcome": "At baseline λ the branch reduces to the ordinary finite-speed emergent behaviour, and the field restores inside the debt tolerance. Necessary condition, not an achievement.", "route": "/lab/scale-power" }, { "id": "AT-0370 (req. AT-0352)", "title": "Scale-Field Gate v2", "status": "implemented", "outcome": "Recorded status: GATE NOT CLEARED. Maximum award available remains LOCAL-SCALE LEVERAGE IN TOY MODEL / PHYSICAL EVIDENCE NONE.", "route": "/lab/scale-power" }, { "id": "AT-0331", "title": "Identity Through the Travelling Corridor", "status": "implemented", "outcome": "G10 closed by measurement. The traveller now has an internal identity vector; riding the corridor peaks at about twice the identity disturbance of walking the same route.", "route": "/lab/carrier" }, { "id": "AT-0332", "title": "Front-Precedence Bound", "status": "implemented", "outcome": "Causal cutoff enforced: the traveller is never helped by a corridor that has not reached it. Any net advantage is bounded below by the front's own crossing time (B28).", "route": "/lab/carrier" }, { "id": "AT-0333", "title": "Matched-Progress Identity Comparison", "status": "implemented", "outcome": "The ride is worse than the walk at every matched fraction of the route. Median ratio about 2x. Matched progress does not rescue it.", "route": "/lab/carrier" }, { "id": "AT-0334", "title": "Smoothness / Affordability Frontier", "status": "implemented", "outcome": "Peak identity disturbance and accounted action are anti-correlated across corridor width. Gentleness is purchased, never given (B35).", "route": "/lab/carrier" }, { "id": "AT-0335", "title": "Synchronisation-Free Corridor Search", "status": "implemented", "outcome": "Launch-offset sweep. The tolerant window is only a few model time units wide, so the arrangement still needs an unmodelled coordinating agent (B26).", "route": "/lab/carrier" }, { "id": "AT-0336", "title": "Standing-Medium Legitimacy Audit", "status": "implemented", "outcome": "Setup and maintenance are charged separately from the per-trip cost. The standing corridor is classified PREPOSITIONED INFRASTRUCTURE and never wins on time for one trip (B30, B33).", "route": "/lab/carrier" }, { "id": "AT-0337", "title": "Geometry Price Derivation Attempt", "status": "implemented", "outcome": "Four pricings, and the verdict moves. The cost of a geometry edit is declared by us, not derived from the model's own dynamics (B25).", "route": "/lab/carrier" }, { "id": "AT-0338", "title": "Closed-Cycle Identity Debt", "status": "implemented", "outcome": "MATHEMATICAL PROPERTY of the coupling law: the identity drive is sign-blind in the gradient, so an out-and-back cycle accumulates residue instead of cancelling it (B36).", "route": "/lab/carrier" }, { "id": "AT-0339", "title": "Carrier Nontriviality Control", "status": "implemented", "outcome": "A sham corridor with identical field and identical charge but no coupling produces neither the benefit nor the damage. The result is structural in the model, not a bookkeeping artefact.", "route": "/lab/carrier" }, { "id": "AT-0340", "title": "Carried-Traveller Gate v1", "status": "implemented", "outcome": "3 of 13 requirements met, 2 NOT MODELED. Recorded status: GATE NOT CLEARED, NEGATIVE RESULT / DAMAGE RIDES WITH THE CORRIDOR.", "route": "/lab/carrier" }, { "id": "AT-0255", "title": "Constrained Schedule Search", "status": "implemented", "outcome": "RETUNED TOY IMPROVEMENT — median peak identity disturbance falls roughly a fifth, but every schedule is re-tuned per system.", "route": "/lab/schedules" }, { "id": "AT-0256", "title": "Frozen Schedule Transfer", "status": "implemented", "outcome": "One schedule discovered on a training ensemble, frozen, and carried to unseen systems, higher dimension, sparser topology, larger displacement and heavier drift.", "route": "/lab/schedules" }, { "id": "AT-0257", "title": "Universal Schedule No-Go / Survival", "status": "implemented", "outcome": "Compact fixed schedules compared against fixed coupling and an adaptive gate on identical cases with no retuning.", "route": "/lab/schedules" }, { "id": "AT-0258", "title": "Peak-Damage Floor", "status": "implemented", "outcome": "A positive lower bound on achievable worst-case identity disturbance persists at matched destination error and enforced coupling floor. This is the most restrictive negative result currently standing.", "route": "/lab/schedules" }, { "id": "AT-0259", "title": "Moving-Invariant Candidate", "status": "implemented", "outcome": "Redefining identity as a dynamical equivalence class lowers the score only when observable completeness falls; negative controls catch the vacuous quotients.", "route": "/lab/schedules" }, { "id": "AT-0260", "title": "Counterdiabatic-Like Toy Control", "status": "implemented", "outcome": "A purely mathematical local auxiliary term reduces transient excitation with its full action charged. Toy control analogy only; no connection to physical driving protocols is claimed.", "route": "/lab/schedules" }, { "id": "AT-0261", "title": "Control Necessity and Locality Audit", "status": "implemented", "outcome": "Locality, boundedness, freezing, ablation necessity and a generic-feedforward comparison are all required; direct identity freezing is forbidden.", "route": "/lab/schedules" }, { "id": "AT-0262", "title": "End-of-Day Gate", "status": "implemented", "outcome": "Full blocker vector rerun with an explicit resume state. Recorded status: NONE PASSED.", "route": "/lab/schedules" }, { "id": "AT-0263", "title": "Two-Layer State Model", "status": "implemented", "outcome": "Y, pi, X, O, I and T formalised. Einstein-like local behaviour is kept as an emergent benchmark, not adopted as an axiom.", "route": "/lab/deeper" }, { "id": "AT-0264", "title": "Projection Leverage Null", "status": "implemented", "outcome": "Generic Gaussian maps already amplify by their largest singular value. Raw leverage is labelled EXPECTED BY MAP GEOMETRY; normalised leverage cannot exceed 1 for a linear map.", "route": "/lab/deeper" }, { "id": "AT-0265", "title": "Nonlinear Projection Leverage", "status": "implemented", "outcome": "Smooth nonlinear projections relabel amplification rather than creating leverage once the peak local Jacobian is charged.", "route": "/lab/deeper" }, { "id": "AT-0266", "title": "Short-Y / Far-X Search", "status": "implemented", "outcome": "Lawful bounded local Y paths searched against a matched random-map control on the identical path family.", "route": "/lab/deeper" }, { "id": "AT-0267", "title": "Projected-Path Audit", "status": "implemented", "outcome": "The projected trajectory is sampled throughout. Candidates that sweep the ordinary intermediate region are rejected as traversal, not leverage.", "route": "/lab/deeper" }, { "id": "AT-0268", "title": "Emergent Locality Test", "status": "implemented", "outcome": "POSITIVE: a finite propagation cone emerges from purely local Y interactions with no speed inserted. Reported dimensionlessly, in sites per integration step.", "route": "/lab/deeper" }, { "id": "AT-0269", "title": "Dual-Channel Challenge", "status": "implemented", "outcome": "The ordinary channel exists; no distinct lawful high-leverage transition class survives the audits. The dual-channel question is unanswered, not answered.", "route": "/lab/deeper" }, { "id": "AT-0270", "title": "Identity Across Projection", "status": "implemented", "outcome": "Identity is read only through O ∘ pi with the definition fixed before the search; the unmeasured fraction of Y is reported alongside every deviation.", "route": "/lab/deeper" }, { "id": "AT-0271", "title": "Causal-Consistency and Signalling Audit", "status": "implemented", "outcome": "Toy signalling protocols constructed. No contradiction arises only because no channel outran the emergent cone; that is an absence of a candidate, not causal safety.", "route": "/lab/deeper" }, { "id": "AT-0272", "title": "Deeper-Layer Gate", "status": "implemented", "outcome": "Full blocker stack plus projection-specific blockers. Recorded status: NONE PASSED.", "route": "/lab/deeper" }, { "id": "AT-0273", "title": "Fixed-Projection Continuity No-Go", "status": "implemented", "outcome": "MODEL THEOREM. A fixed smooth projection maps continuous paths to continuous paths, so it cannot produce skip-the-middle relocation. Only Jacobian stretch, singularity, or a dynamical map remain.", "route": "/lab/geometry" }, { "id": "AT-0274", "title": "Lipschitz Bound Audit", "status": "implemented", "outcome": "Normalised random maps at seed 273 never exceed leverage 1, and the sampled maximum falls with dimension. Leverage at or below the bound is EXPECTED BY PROJECTION STRETCH.", "route": "/lab/geometry" }, { "id": "AT-0275", "title": "Singular-Map Trap", "status": "implemented", "outcome": "Near-singular and discontinuous projections built deliberately as positive controls for fakery. All rejected: leverage collapses after normalisation and sensitivity explodes.", "route": "/lab/geometry" }, { "id": "AT-0276", "title": "Dynamic Projection Hypothesis", "status": "implemented", "outcome": "pi promoted to pi_lambda with lambda tracked: rate cap, propagation frontier, declared price, mandatory restoration. The only route the AT-0273 theorem leaves open.", "route": "/lab/geometry" }, { "id": "AT-0277", "title": "Dynamic Metric Hypothesis", "status": "implemented", "outcome": "Object motion in fixed geometry separated from geometry change around a nearly static object. The distinction is now measurable, and the cost visibly migrates between sectors.", "route": "/lab/geometry" }, { "id": "AT-0278", "title": "Metric-Change Cost", "status": "implemented", "outcome": "Geometry edits are charged and closure is enforced. At the declared price the dynamic arm costs more total action than ordinary traversal.", "route": "/lab/geometry" }, { "id": "AT-0279", "title": "Adjacency-Without-Object-Traversal Toy", "status": "implemented", "outcome": "The traveller's own arc collapses and peak identity disturbance falls sharply, but the geometry edit crosses the region instead. Classified COST MIGRATION, NOT NON-TRAVERSAL.", "route": "/lab/geometry" }, { "id": "AT-0280", "title": "Geometry-Restoration Cycle", "status": "implemented", "outcome": "Full cycle closes: geometry returns to baseline, ordering stays consistent, residue is read only after closure.", "route": "/lab/geometry" }, { "id": "AT-0281", "title": "Emergent-Einstein Benchmark", "status": "implemented", "outcome": "POSITIVE: ordinary perturbations in the restored geometry still propagate with the same finite dimensionless front speed as before the cycle. Toy benchmark, no GR derivation claimed.", "route": "/lab/geometry" }, { "id": "AT-0282", "title": "Dynamic-Geometry Gate", "status": "implemented", "outcome": "Strict stack including stretch, singularity, coordinate, cost, debt, restoration, locality and nontriviality. Recorded status: NONE PASSED.", "route": "/lab/geometry" }, { "id": "AT-0283", "title": "Geometry Compression Cost Curve", "status": "implemented", "outcome": "TOY COST BENCHMARK at seed 283. Compression is easy while geometry edits are free; once manipulation, equal restoration and roughness are charged the cost-versus-shrink curve turns sharply upward.", "route": "/lab/compression" }, { "id": "AT-0284", "title": "Matched-Compression Efficiency", "status": "implemented", "outcome": "Every control law bisected onto the same shrink ratio and the same restoration accuracy. The cheapest law still costs multiples of ordinary traversal of the same chain (B22).", "route": "/lab/compression" }, { "id": "AT-0285", "title": "Smooth-vs-Localized Deformation", "status": "implemented", "outcome": "Broad smooth deformation is far cheaper in action than concentrated deformation at equal compression — but it is cheap precisely because it moves everything, which is what AT-0290 then charges for.", "route": "/lab/compression" }, { "id": "AT-0286", "title": "Critical Geometry Response", "status": "implemented", "outcome": "Apparent threshold-like gain in the nonlinear control law is a DENOMINATOR ARTEFACT NEAR THRESHOLD. Guarded, the marginal return on extra action does not spike.", "route": "/lab/compression" }, { "id": "AT-0287", "title": "Geometry Soft-Mode Search", "status": "implemented", "outcome": "Hessian eigen-decomposition with full-rank and nullspace audits. The efficiency of the softest collective mode tracks the dimension count and is EXPECTED BY DIMENSION COUNT, not emergent physics.", "route": "/lab/compression" }, { "id": "AT-0288", "title": "Traveling Geometry Pulse", "status": "implemented", "outcome": "A rate-capped deformation front shortens each link just ahead of the traveller while obeying the emergent finite speed. Local crossing is short; the control front still sweeps the region (B21). No superluminal behaviour claimed.", "route": "/lab/compression" }, { "id": "AT-0289", "title": "Geometry Restore Closure", "status": "implemented", "outcome": "After crossing, every control variable and every operational distance away from the destination must return within tolerance. Residue is recorded as debt rather than discarded.", "route": "/lab/compression" }, { "id": "AT-0290", "title": "Background-Disturbance Audit", "status": "implemented", "outcome": "New metric Collateral Geometry Distortion. Unconstrained compression moves a large fraction of unrelated pairwise distances at peak (B23).", "route": "/lab/compression" }, { "id": "AT-0291", "title": "Localized Corridor Challenge", "status": "implemented", "outcome": "Key score: useful compression divided by action plus collateral distortion plus debt. Bounded corridors suppress the background disturbance but pay a sharp premium, and narrow corridors are infeasible under the deformation cap (B24).", "route": "/lab/compression" }, { "id": "AT-0292", "title": "Dynamic-Geometry Gate v1", "status": "implemented", "outcome": "Thirteen requirements spanning genuine distance reduction, bounded local dynamics, matched efficiency, collateral distortion, pathwise identity, short local crossing, exact restoration, debt, robustness, scale, nontriviality and emergent locality before and after. Recorded status: NONE PASSED. Maximum available award ROBUST IN TOY MODEL / REQUIRES PHYSICAL THEORY; physical evidence NONE.", "route": "/lab/compression" }, { "id": "AT-0293", "title": "Localized vs Global Geometry Control", "status": "implemented", "outcome": "COMPUTATIONAL RESULT / MODEL-DEPENDENT at seed 293. At matched compression the localized corridor reproduces the recorded benchmark (Gaussian action ~36.4, collateral ~7.7%) against a global rewrite at ~101 action and ~55% collateral.", "route": "/lab/corridor" }, { "id": "AT-0294", "title": "Corridor Width Optimization", "status": "implemented", "outcome": "A Pareto frontier rather than an optimum: narrow corridors keep the background still but cost more action and grow sharp shoulders; wide ones smooth the shoulders and leak into unrelated distances.", "route": "/lab/corridor" }, { "id": "AT-0295", "title": "Boundary / Gradient Debt", "status": "implemented", "outcome": "The localized advantage survives a sixty-four-fold escalation of the gradient price, but only because the corridor widens to pay the boundary debt with breadth.", "route": "/lab/corridor" }, { "id": "AT-0296", "title": "Traveling Pulse Dynamics", "status": "implemented", "outcome": "The corridor is grown by rate-capped nearest-neighbour updates at a bounded front speed. No remote or instantaneous geometry edits are permitted anywhere in the run.", "route": "/lab/corridor" }, { "id": "AT-0297", "title": "Pulse-Crossing Synchronization", "status": "implemented", "outcome": "The traveller may cross only while the corridor is compressed. The window is finite and mistiming destroys the advantage, so the mechanism depends on coordination it cannot explain (B26).", "route": "/lab/corridor" }, { "id": "AT-0298", "title": "Pulse Restoration", "status": "implemented", "outcome": "The field relaxes back within tolerance and the cycle closes, but the disturbance emitted outside the corridor during the cycle is recorded rather than forgiven.", "route": "/lab/corridor" }, { "id": "AT-0299", "title": "Collateral Causality Audit", "status": "implemented", "outcome": "Local propagation reach outside the corridor changes by well under a percent and no distance ordering flips. A rejection filter passed, not a positive result.", "route": "/lab/corridor" }, { "id": "AT-0300", "title": "Multi-Dimensional Corridor", "status": "implemented", "outcome": "On a square lattice the action advantage survives and grows, but the corridor becomes a tube and collateral distortion among unrelated pairs rises by more than an order of magnitude (B27).", "route": "/lab/corridor" }, { "id": "AT-0301", "title": "Frozen Corridor Law Transfer", "status": "implemented", "outcome": "POSITIVE within the toy: a single scale-relative rule — corridor width about 0.40 of target separation — transfers to unseen sizes, separations, backgrounds and noise with negligible penalty and no retuning.", "route": "/lab/corridor" }, { "id": "AT-0302", "title": "Dynamic-Geometry Gate v2", "status": "implemented", "outcome": "Fourteen requirements. Recorded status: 12 of 14 passed — identity coupling is NOT MODELED in this phase, and the full cycle still costs more than covering the distance outright. GATE NOT CLEARED. Physical evidence NONE.", "route": "/lab/corridor" }, { "id": "AT-0303", "title": "Control-Front Speed Tradeoff", "status": "implemented", "outcome": "Sweeping the driven front speed at seed 303: faster fronts complete sooner but action rises superlinearly and collateral distortion widens. No free speed anywhere in the swept range (B29).", "route": "/lab/pulse" }, { "id": "AT-0304", "title": "No-Problem-Transfer Audit", "status": "implemented", "outcome": "DECISIVE NEGATIVE. The traveller walks about 45% of the baseline distance, but the control front must reach the far target first and net completion including restoration is about 1.8x ordinary traversal. PROBLEM TRANSFERRED TO CONTROL FIELD (B28).", "route": "/lab/pulse" }, { "id": "AT-0305", "title": "Self-Propagating Pulse", "status": "implemented", "outcome": "A bistable excitable medium with refractory recovery sustains a front after finite local initiation at about 0.67 links per step. Self-sustaining, still finite-speed, still dissipative.", "route": "/lab/pulse" }, { "id": "AT-0306", "title": "Pulse Soliton-Like Stability Toy", "status": "implemented", "outcome": "Six of nine amplitude-width profiles survive perturbation with near shape preservation. Stability is a property of the medium, not evidence of a shortcut.", "route": "/lab/pulse" }, { "id": "AT-0307", "title": "Pre-Existing Medium vs On-Demand Corridor", "status": "implemented", "outcome": "A standing medium costs about 61.5 per crossing against about 110 on demand, but only after preparing the entire chain and paying maintenance forever. Completion is still slower than ordinary traversal.", "route": "/lab/pulse" }, { "id": "AT-0308", "title": "Bidirectional Restoration Wave", "status": "implemented", "outcome": "The trailing restoration wave closes the cycle within tolerance, but restoration is charged at the same rate as construction and the residue is recorded rather than forgiven.", "route": "/lab/pulse" }, { "id": "AT-0309", "title": "Traveller-Pulse Synchronization", "status": "implemented", "outcome": "The crossing window is narrow: delays beyond a few steps miss the corridor entirely and the traveller never completes. The advantage is conditional on coordination that has no mechanism (B26).", "route": "/lab/pulse" }, { "id": "AT-0310", "title": "Net Time-to-Destination", "status": "implemented", "outcome": "Net completion including front propagation and restoration is about 43.2 model time units against about 24.0 for ordinary local traversal — a ratio of about 1.80. The shortcut is slower than walking.", "route": "/lab/pulse" }, { "id": "AT-0311", "title": "Infrastructure-Amortized Test", "status": "implemented", "outcome": "INFRASTRUCTURE-ONLY BENEFIT. Amortized over repeated crossings the medium wins on action after roughly nine crossings, but never on time, and it is a prepared channel between two prepared places (B30).", "route": "/lab/pulse" }, { "id": "AT-0312", "title": "Travelling-Corridor Gate", "status": "implemented", "outcome": "Fifteen requirements. Recorded status: 10 of 15 passed. Decisive failures on net completion time and on problem transfer to the control field. GATE NOT CLEARED. Physical evidence NONE.", "route": "/lab/pulse" }, { "id": "AT-0313", "title": "One-Shot Trigger Baseline", "status": "implemented", "outcome": "NEGATIVE RESULT: SIMPLE EXCITABLE MEDIUM INSUFFICIENT. A single bounded local trigger in a one-dimensional excitable reaction-diffusion geometry medium opened roughly a third of the sixty-nine-edge route and then collapsed. Zero full crossings (B31).", "route": "/lab/self-pulse" }, { "id": "AT-0314", "title": "Excitability Threshold Map", "status": "implemented", "outcome": "Threshold, diffusion, damping, trigger width and trigger amplitude swept and classified as decay, pinned front, partial propagation, full propagation or blow-up. No full propagation anywhere in the swept box; past the boundary the medium diverges instead.", "route": "/lab/self-pulse" }, { "id": "AT-0315", "title": "Soliton-Like Pulse Search", "status": "implemented", "outcome": "A conservative dispersive toy medium does produce localized structures that travel with no drive and restore the background after passage — and none of them carries enough compression to help a traveller. Self-propagation is necessary, not sufficient (B32). Pure mathematics, no physical claim.", "route": "/lab/self-pulse" }, { "id": "AT-0316", "title": "Pulse Energy/Action Accounting", "status": "implemented", "outcome": "Trigger action, carried-field action and residual background distortion accounted separately and compared against the continuously driven corridor. The cheap arm is only cheap because it never arrives.", "route": "/lab/self-pulse" }, { "id": "AT-0317", "title": "Traveller-Pulse Synchronization", "status": "implemented", "outcome": "The traveller may only move through currently compressed links. On the self-propagating arm there was nothing to walk through; the driven arm completes only under continuous remote actuation and still not faster than ordinary traversal.", "route": "/lab/self-pulse" }, { "id": "AT-0318", "title": "Medium Preconditioning", "status": "implemented", "outcome": "One-time preparation cost is reported separately from per-trip trigger and maintenance cost, so setup debt can never be hidden inside an attractive per-trip figure (B33).", "route": "/lab/self-pulse" }, { "id": "AT-0319", "title": "Reusability and Degradation", "status": "implemented", "outcome": "Repeated pulses through the same medium with the recovery field carried forward. Reach drift is recorded; repeatability of a failure is not counted as support.", "route": "/lab/self-pulse" }, { "id": "AT-0320", "title": "Bidirectional / Reversal Test", "status": "implemented", "outcome": "A to B and B to A under the same frozen medium and rule give comparable reach and comparable restoration, confirming the rule is directionally symmetric rather than confirming the hypothesis.", "route": "/lab/self-pulse" }, { "id": "AT-0321", "title": "Causal-Front Audit", "status": "implemented", "outcome": "The traveller never advances beyond the furthest point the front has reached. Any surviving net advantage traces to a medium prepared along the whole route in advance and is classified PREPOSITIONED INFRASTRUCTURE (B33).", "route": "/lab/self-pulse" }, { "id": "AT-0322", "title": "Self-Propagating Corridor Gate", "status": "implemented", "outcome": "Thirteen requirements covering one-time triggering, finite front speed, full-route propagation, collateral, restoration, repeatability, reversal, setup debt, identity, action, net time and prepositioning. GATE NOT CLEARED, decisive failure on full-route propagation. Physical evidence NONE.", "route": "/lab/self-pulse" } ], "killed": [ { "id": "K1", "claim": "Identity and relational address can simply be decoupled.", "whyItFailed": "The independence was built into the model by construction, not discovered from it.", "experiments": "AT-0073 → AT-0080" }, { "id": "K2", "claim": "A protected nullspace shields identity during relocation.", "whyItFailed": "The protection came from a dimension mismatch. With a full-rank coupling it disappears entirely.", "experiments": "AT-0087 → AT-0094" }, { "id": "K3", "claim": "Identity is preserved because the observed state is unchanged.", "whyItFailed": "Incomplete observables manufacture equivalence. Measuring less is not preserving more.", "experiments": "AT-0127 → AT-0134" }, { "id": "K4", "claim": "A change of relational coordinates is a change of relational location.", "whyItFailed": "Gauge-redundant directions divide out. Once the physical quotient is taken, the shortcut vanishes.", "experiments": "AT-0135 → AT-0142" }, { "id": "K5", "claim": "Path choice can avoid identity damage.", "whyItFailed": "With constant linear coupling, endpoint identity change is path-independent. Any path dependence introduced afterwards produces loop residue and memory debt.", "experiments": "AT-0103 → AT-0118" }, { "id": "K6", "claim": "Soft modes of the coupling are the cheap directions to move along.", "whyItFailed": "Softness is not selectivity. Soft directions were no better aligned with useful relocation than random ones.", "experiments": "AT-0159 → AT-0166" }, { "id": "K7", "claim": "Nonlinearity protects identity.", "whyItFailed": "Strong damping explains most of the apparent protection, and the identity definition used was too loose.", "experiments": "AT-0183 → AT-0198" }, { "id": "K8", "claim": "Suppressing coupling late in the transition preserves identity.", "whyItFailed": "Peak damage is essentially unchanged. Classified ENDPOINT CLEANUP / NOT PATHWISE PROTECTION.", "experiments": "AT-0247 → AT-0254" }, { "id": "K9", "claim": "A rich nonlinear cross-term family contains a survivor.", "whyItFailed": "Six thousand candidates produced zero strict survivors.", "experiments": "AT-0167 → AT-0182" }, { "id": "K10", "claim": "All four constraints — progress, identity, invariance and locality — can hold together.", "whyItFailed": "The admissible intersection was empty in the toy model. The joint wall stands.", "experiments": "AT-0143 → AT-0158" }, { "id": "K11", "claim": "A deeper layer gives large projection leverage, so a short move below is a long move above.", "whyItFailed": "Generic random maps already amplify distances by their largest singular value. After operator-norm or Jacobian normalisation, no linear or smooth projection exceeded L = 1. EXPECTED BY MAP GEOMETRY.", "experiments": "AT-0264 → AT-0265" }, { "id": "K12", "claim": "Far-apart projected endpoints mean the transition skipped the intervening region.", "whyItFailed": "Sampling the whole projected path showed it walking through the ordinary intermediate locations. Endpoint separation is not non-traversal.", "experiments": "AT-0266 → AT-0267" }, { "id": "K13", "claim": "A deeper layer can let a continuous journey skip the middle.", "whyItFailed": "For a fixed smooth projection the image of a continuous path is continuous. The only escapes are Jacobian stretch and singularity, and both are artefacts we now build deliberately as controls.", "experiments": "AT-0273 → AT-0275" }, { "id": "K14", "claim": "Changing the geometry instead of moving the object avoids the cost of the journey.", "whyItFailed": "The cost migrated rather than vanished: total accounted action across both sectors exceeded ordinary traversal, and the geometry edit itself had to propagate across every intervening link.", "experiments": "AT-0276 → AT-0282" } ], "surviving": [ { "id": "S1", "clue": "Timing and coupling geometry matter more than controller complexity.", "strength": "At matched relational progress, a simple two-stage scheduled gate matched or beat the adaptive feedback rule on identity disturbance.", "caveat": "This downgrades adaptive control rather than promoting scheduling. It is a warning about our scoring, not a mechanism." }, { "id": "S2", "clue": "Constrained schedule search reduces peak identity disturbance with the coupling floor and restoration both enforced.", "strength": "Roughly a sixth to a fifth of peak damage removed across sampled cases at seed 255, with the interaction never switched off.", "caveat": "Schedules are re-tuned per system and remaining damage is still large. Label: RETUNED TOY IMPROVEMENT." }, { "id": "S3", "clue": "A local, bounded, frozen auxiliary term can suppress part of the transient excitation.", "strength": "The reduction survives explicit action charging and an ablation necessity test in the toy plant.", "caveat": "Purely mathematical toy control. No physical driving analogy is claimed, and it does not clear the peak-damage floor." }, { "id": "S4", "clue": "Finite propagation in the observable layer emerges from purely local interactions in the deeper layer.", "strength": "Arrival time grows linearly with graph distance with no speed inserted anywhere in the model, giving a dimensionless emergent front (AT-0268).", "caveat": "It is a benchmark our own model must reproduce, not a claim about physics, and the number has no units and is not a speed of light." }, { "id": "S5", "clue": "Moving the geometry rather than the traveller sharply reduces the traveller's own identity disturbance.", "strength": "The traveller's arc collapses to a single short local step, and peak identity deviation drops with it, at a genuinely large operational displacement (AT-0279).", "caveat": "The damage and the cost move into the geometry sector rather than disappearing, and the edit still propagates across the region. COST MIGRATION, NOT NON-TRAVERSAL." }, { "id": "S6", "clue": "A bounded corridor is far cheaper and far quieter than a global rewrite, and the rule that picks it transfers.", "strength": "At matched compression the corridor costs about a third of the action and moves unrelated distances by about a tenth as much; a single scale-relative width rule, frozen after fitting, carries to unseen sizes and separations with negligible penalty (AT-0293, AT-0301).", "caveat": "COMPUTATIONAL RESULT / MODEL-DEPENDENT. The comparison is decided by an assumed cost functional (B25), the advantage needs synchronisation (B26), and the cycle still costs more than ordinary traversal." } ], "blockers": [ { "id": "B124", "name": "Phase 66 is a proxy, not the fabric", "state": "OPEN", "summary": "Every concurrency number is produced by a queueing overlap model with L ~ 1.6 log2 N, ~4 active nodes per flow and one move per node per tick. The exact-graph sweep exceeded the runtime budget and was not run, so no Phase 66 figure may be quoted as a property of the address fabric. The specification for the exact run is published in AT-0639 precisely so it cannot be tuned to match these numbers (AT-0628, AT-0639)." }, { "id": "B125", "name": "Routes are drawn uniformly at random", "state": "OPEN", "summary": "The analytic law and the token simulation both assume route slots are spread uniformly over N nodes. Real routes on a single spanning tree concentrate near the root, so the benign 1.06-1.23x figures describe the easy case only. The adversarial test in AT-0633 is the honest one, and it fails (AT-0629, AT-0633)." }, { "id": "B126", "name": "The two stability boundaries disagree", "state": "OPEN", "summary": "At slowdown <= 2 the conservative analytic bound permits 5 → 24 concurrent flows over N = 256 … 4096 while the token simulation permits 48 → 256, because a token holds a node for a single tick rather than for its whole trip. Two defensible accounting choices differ by an order of magnitude and only the exact simulation can settle which one describes the fabric. Until then the conservative column is the one that stands (AT-0638)." }, { "id": "B136", "name": "Cost coefficients are declared, not measured", "state": "OPEN", "summary": "1.2, 2·K, 3.5, 1.8 and 1.2 are chosen normalized constants consistent with the measured scalings of Phases 63, 64 and 68. The exponents in N follow from the model; the prefactors follow from nothing, and every Qcost on the page moves with them (AT-0673)." }, { "id": "B137", "name": "The linear baseline is a modelling choice", "state": "OPEN", "summary": "Charging an ordinary point-to-point trip linearly in N is the comparator the whole gate is scored against. A different baseline could remove the advantage entirely (AT-0678)." }, { "id": "B138", "name": "High utilization is an assumption about the world", "state": "OPEN", "summary": "The gate fails below roughly 200 lifetime trips per fabric and only becomes strong near 10,000. Whether any candidate substrate reuses connectivity that heavily is unknown and is not a property of the model (AT-0682)." }, { "id": "B139", "name": "Closed form, so no dynamics", "state": "OPEN", "summary": "The amortisation sweep is analytic and does not re-run the doorway, the mesh or the concurrency simulator, so contention, failure clustering and repair storms are absent from the amortised number (AT-0680)." }, { "id": "B140", "name": "No discriminating measurement has been performed", "state": "OPEN", "summary": "Reuse-scaling of reconfiguration events is proposed as the measurement that would separate a two-phase moving-doorway architecture from an ordinary routed network. It has not been performed on any platform. Physical mapping stays NOT ESTABLISHED (AT-0688)." }, { "id": "B132", "name": "Route success is sampled, not proved", "state": "OPEN", "summary": "Fault-tolerance survival is measured over 40 sampled source/destination pairs per damaged configuration with 3 seeds per cell. A sampled 1.000 at K = 8 is not a theorem that no pair fails under adversarial high-impact cuts (AT-0661 … AT-0667)." }, { "id": "B133", "name": "Constant K = 8 is sufficient in range only", "state": "OPEN", "summary": "Eight independently rooted trees survived every tested failure count through N = 2048 at a flat 8x address-storage multiplier, and K did not have to grow. Whether K must grow with N, with the fault rate, or against a smarter adversary is untested and is the first item of the next phase (AT-0669)." }, { "id": "B134", "name": "Stretch under damage rises with size", "state": "OPEN", "summary": "Surviving routes at K = 8 run up to 1.236x the shortest path in the damaged graph, trending upward with N over four points. Redundancy is bought with distance and the trend is not converged (AT-0668)." }, { "id": "B135", "name": "The mesh routes around damage without repairing it", "state": "OPEN", "summary": "Post-cut handling costs zero messages precisely because nothing is rebuilt. Long-run degradation under accumulating faults with no repair is untested, and the maintenance term belongs to the uncharged lifecycle gate (AT-0670)." }, { "id": "B128", "name": "Completion does not reach 1 under the finite doorway window", "state": "OPEN", "summary": "Four generic roots with local two-choice selection lift mean completion at F = 16 from 38% to 82% across N = 256 … 4096, and from 16% to 72% under adversarial same-branch pairs, but payloads still exhaust the W = 12 blocked-tick window and abort. The scalability gate demands completion probability -> 1 and it is not met at any K in the measured grid (AT-0645, AT-0655)." }, { "id": "B129", "name": "Route stretch is the price of dispersion", "state": "OPEN", "summary": "Multi-root tree paths average 1.59x the graph-shortest path, and choosing the quieter tree lengthens them further. The concurrency benefit is bought with distance and is entered as a debt rather than netted off (AT-0651)." }, { "id": "B130", "name": "Tail latencies are measured over survivors", "state": "OPEN", "summary": "Median, p95 and p99 completion ticks are computed over completed flows only, which flatters the tail while completion is below 1. Reported rather than corrected; any bounded-slowdown claim inherits this bias (AT-0646)." }, { "id": "B131", "name": "Root loss during traffic costs completion", "state": "OPEN", "summary": "Destroying one of four roots at tick 3 of a live 16-flow run drops completion from 88% to 63% and stretches makespan from 21 to 32 ticks. Failover is local and triggers no global rebuild, but it is not free and the affected flows are not all recovered (AT-0652)." }, { "id": "B127", "name": "A single elected root deadlocks under adversarial load", "state": "OPEN", "summary": "With all flows forced through one root band under the plain QUEUE rule, 0 of 80 payloads complete across five sizes and the longest wait reaches 952 ticks: tokens hold band nodes while waiting for band nodes held by others. DETOUR and four-root local balancing both clear it in the proxy, and neither exists in the fabric. Root failure (B123) and root contention are now two separate reasons the single elected root has to go (AT-0633, AT-0634)." }, { "id": "B121", "name": "Survival degrades under heavy damage", "state": "OPEN", "summary": "At 8-10% random edge loss survival falls to 0.90-0.95 and some runs exceed the local chain bound and are charged as rebuild events; node loss at 5% reaches 0.90. Local repair is graded, not unconditional (AT-0610, AT-0611)." }, { "id": "B122", "name": "Total repair work is extensive in the damage", "state": "OPEN", "summary": "Per event the repair scope is 5.35 nodes with exponent 0.016 in N, but a fixed percentage of failed edges means the number of events grows with N, so total touched nodes grow roughly linearly with the damage: 83 at N = 256 and 1039 at N = 4096 at 5% loss. Locality is a per-event statement (AT-0613)." }, { "id": "B123", "name": "Root failure still unhandled", "state": "OPEN", "summary": "The elected minimum-identifier root is excluded from node-failure trials. Distributed re-election and re-addressing after root loss remain unmeasured, so one node remains a single point of failure (AT-0611)." }, { "id": "B117", "name": "Self-organizing reusable infrastructure debt", "state": "OPEN", "summary": "Phase 64 replaces the prebuilt address book with a distributed construction, and a distributed build must reach every node once, so it carries a one-time cost at least extensive in node count. It is endpoint-independent and reusable and therefore amortises over trips, but amortisation is not abolition: maintenance under change is unmeasured and no lifecycle ledger yet reports build plus repair against M trips with a stated break-even (AT-0603, AT-0604)." }, { "id": "B118", "name": "Tree routes are logarithmic but consistently long", "state": "OPEN", "summary": "Longest-common-prefix routing on the spanning tree gives 8 → 21.5 hops against shortest paths of 6 → 12, a stretch reaching ~2.3. Logarithmic and near-optimal are different objects, and the doorway has not been rerun on emergent addresses to see whether peak activation survives the detour. Bounded-stretch compact routing at O(log N) bits with local-only decisions is the standing target (AT-0600, AT-0605)." }, { "id": "B119", "name": "Nothing in the address layer has been broken yet", "state": "OPEN", "summary": "No edge deleted, no node killed, no rewire applied, no address corrupted, no second traveller. The elected root is a single point of failure that has never been removed, and self-healing, dynamic topology and concurrency are all UNMEASURED rather than passing. Four unmeasured clauses say one thing only — nothing has broken yet (AT-0596, AT-0605)." }, { "id": "B120", "name": "Six doublings cannot prove a logarithm", "state": "OPEN", "summary": "Setup 8 → 15 rounds, addresses 10 → 22 bits and routes 8 → 21.5 hops over N = 128 … 8192 give exponents 0.151, 0.187 and 0.222 with ratios to log2 N bounded at 1.15-1.22, 1.43-1.69 and 1.14-1.75. Consistent with O(log N) on these expander-like cubic substrates and NOT proven: a slow power reproduces the same window. No asymptotic claim is made (AT-0601)." }, { "id": "B97", "name": "The beacon is a per-trip global flood", "state": "OPEN", "summary": "Local gradient routing only works after B's scalar field has propagated to A, which on a low-diameter graph means touching essentially every node, once per trip. Setup is cheap in time (8 to 14 ticks, tracking eccentricity) and total in reach. The routing oracle debt is renamed, not discharged, and no sparse-activity claim may be made for the trip as a whole while the beacon stage is global (AT-0533, AT-0538)." }, { "id": "B98", "name": "The corridor is selected with global distance knowledge", "state": "OPEN", "summary": "Activation is restricted to nodes near an A-B geodesic, a condition the substrate cannot evaluate. The corridor exponent of ~0.192 is what sparse activation would cost IF a lawful local process could carve the same corridor - a target, not an achievement. Sparse activation stays PARTIAL until the geodesic condition is deleted and the corridor emerges from the same local dynamics as the payload (AT-0536, AT-0538)." }, { "id": "B99", "name": "Addressability is unsolved and random labels do not solve it", "state": "OPEN", "summary": "Pre-frozen random vector labels are lawfully prepared and endpoint-independent, and they fail outright: success 0.38-0.50 by N = 1024, stretch above ten, because label proximity is uncorrelated with graph proximity on an expander. Any replacement must derive its coordinates from the substrate while remaining endpoint-independent, and must report bits per node, preprocessing action, maintenance traffic, stretch and success as measured quantities (AT-0537, AT-0541)." }, { "id": "B100", "name": "Corridor counts are non-monotone and under-sampled", "state": "OPEN", "summary": "Median corridor sizes read 21.5, 25, 52, 31, 47, 41.5 - the N = 512 value exceeds both neighbours. Twenty runs per size on random substrates cannot support a confident scaling fit, so N^0.192 is a window observation about sparsity and must never be quoted as a scaling law (AT-0536)." }, { "id": "B101", "name": "Hierarchical address storage was (log N)^2", "state": "PARTIALLY ACCOUNTED", "summary": "Phase 60's multilevel landmark hierarchy cost 49, 64, 81, 100 bits per node at N = 128 … 1024 — the square of log2 N, not the O(log N) the objective demands, with the ~0.343 power fit disowned. Phase 61's generic tree scheme reduces this to exactly 4 · log2 N bits (28 → 48 at N = 128 … 4096), a constant multiple of the information-theoretic floor, so the blocker is reduced rather than closed: the constant four has not been attacked and neither scheme has been pushed past 4096 (AT-0550, AT-0561)." }, { "id": "B102", "name": "Address infrastructure construction and maintenance are uncharged", "state": "OPEN", "summary": "In both Phase 60 and Phase 61 the address structure is treated as already existing. Its construction action, message count, update cost and repair cost after topology change are unmeasured. A one-time construction that is never costed can hide an arbitrary amount of work, and no cost claim may be made until it is measured and an amortisation crossover across repeated trips is computed (AT-0555, AT-0564)." }, { "id": "B103", "name": "Address routing is not joined to the autonomous phase law", "state": "PARTIALLY ACCOUNTED", "summary": "Phase 61 joined routing and activation - the activated set is now the traversed path plus a one-hop halo rather than a globally selected corridor - but the path itself is resolved on a prebuilt tree, not grown by the c_i / r_i dynamics. The full trigger -> route -> restore clock has not been re-run on this architecture (AT-0560, AT-0568)." }, { "id": "B104", "name": "Stretch is above one and the windows are short", "state": "OPEN", "summary": "Phase 60 stretch climbed 1.50 → 2.88 over four sizes; Phase 61 reads 1.67, 1.67, 2.00, 1.71, 1.75, 1.90 over six. Flatter and longer, and still not O(1) - 19 hops against a shortest 10 at N = 4096. Six doublings cannot distinguish a constant from a slowly growing function (AT-0562)." }, { "id": "B105", "name": "Tree construction and storage remain a one-time uncharged debt", "state": "OPEN", "summary": "The generic BFS / landmark tree of Phase 61 requires at least a full traversal of the substrate. Storage is charged at 4 · log2 N bits per node; construction action, update traffic and the amortisation crossover trip count are not instrumented (AT-0564)." }, { "id": "B106", "name": "The route is read from precomputed tables, not grown by the law", "state": "OPEN", "summary": "Each hop resolves against precomputed tree parent and ancestor data, and the activated set is the resulting path plus a halo. Legitimate reusable infrastructure, and not autonomous address emergence. Until the same local dynamics recruit the next addressed neighbourhood as a moving catalytic front, Phase 61 is classified COMPACT-ADDRESS INFRASTRUCTURE TOY (AT-0565)." }, { "id": "B107", "name": "Resilience, maintenance, contention and aliasing are untested", "state": "OPEN", "summary": "No node or edge failed, no rewiring after freeze, no simultaneous routes, no false-address or collision rate, and no audit of whether the address system exposes latent structure S as an ordinary readable channel in C0. If a few failures force global recomputation, the infrastructure is a flood on a longer clock (AT-0566)." }, { "id": "B108", "name": "Activated node count is not an action integral", "state": "OPEN", "summary": "Every activation number in Phase 61 counts nodes that entered the active phase; it does not integrate how long they stayed, how hard they were driven, or what moving the front cost. The energy / action gate cannot advance on node counts, and reading a sublinear node count as a sublinear cost would repeat the exact error this programme keeps catching in itself (AT-0560, AT-0564)." }, { "id": "B113", "name": "The address infrastructure is still prebuilt", "state": "OPEN", "summary": "Unchanged from Phase 62 and now the largest item in this line. The compact routing information used by the gated doorway is a generic BFS-tree structure produced by an ordinary global traversal before endpoints exist. Endpoint-independent and reusable, therefore charged as background, and not autonomously emergent from the dynamics that move the doorway. Whether such a hierarchy can self-organise once and remain reusable is open (AT-0581, AT-0589)." }, { "id": "B114", "name": "The catalytic bias is aimed by the address relation", "state": "OPEN", "summary": "The gate that keeps the Phase 63 doorway localized reads the local next-hop relation to choose which neighbour receives drive. Legitimate local routing control in a toy, and it must be counted as part of the rule and the infrastructure rather than treated as free. The standing requirement is an audit that it never carries endpoint-specific global computation into the trip under a local-looking name (AT-0589)." }, { "id": "B115", "name": "Activity is a dimensionless proxy, not physical energy", "state": "OPEN", "summary": "Phase 63's 360.876 → 892.860 activity figures sum model state over model ticks. They do not separate trigger, local catalytic work, recovery and stored medium. If the directional bias injects work proportional to path length, a sublinear proxy would be hiding a linear bill, and the energy / action gate stays FAILED until that separation exists (AT-0586)." }, { "id": "B116", "name": "Five sizes, ten runs, nothing perturbed", "state": "OPEN", "summary": "Phase 63 stops at N = 2048 with ten runs per size, and the 0.341 activity exponent is high enough that three more doublings could change its reading. Nothing failed, nothing was rewired, no noise was applied, no address was corrupted and no second traveller competed for the same nodes. Identity error of exactly zero comes from an idealised deterministic payload representation with no damage mechanism in it (AT-0587, AT-0590)." }, { "id": "B109", "name": "The address tree is prebuilt, not grown by the phase law", "state": "OPEN", "summary": "Phase 62's BFS addressing infrastructure is constructed before endpoint selection by an ordinary global traversal and is not produced by the same local dynamics that move the front. Reusable and endpoint-independent, therefore charged as background rather than per trip, and still an uninstrumented one-time cost. Whether such structure can emerge once from generic local dynamics or is irreducible preinstalled structure is untouched (AT-0569, AT-0576)." }, { "id": "B110", "name": "The moving front is an abstract rule, not the autonomous equation", "state": "OPEN", "summary": "Each active node catalyses its addressed next hop and recovers after a hand-set refractory lifetime tau = 3. That is a local causal rule written to isolate the architecture question, not the cooperative c_i / r_i activator-recovery equation that passed the Phase 57 spark test under noise with a finite trigger threshold. Two separately working models are not one working model (AT-0577, AT-0580)." }, { "id": "B111", "name": "Active-node-time is not an action integral either", "state": "OPEN", "summary": "The 30 → 66 node-tick figures count binary active flags multiplied by ticks. They do not weight how hard a node was driven, they exclude construction of the address tree, and they assume steering the front is free. The energy / action gate cannot move off FAILED on node-ticks however flattering their scaling looks (AT-0571)." }, { "id": "B112", "name": "Trigger stability under address bias is untested", "state": "OPEN", "summary": "Biasing a cooperative excitable law toward a preferred neighbour is exactly the modification that can destroy what made the law worth having: a noise-stable ordinary phase with a finite deliberate trigger threshold. The Phase 57 pass does not transfer. C0 stability, threshold and absence of global avalanche must be re-measured on the integrated equation before integration may be claimed (AT-0578)." }, { "id": "B94", "name": "Collective activity is extensive — the cost crack is not established", "state": "OPEN", "summary": "The integrated local-activity proxy scales as N^1.031 with per-node activity flat at 2.90-3.22 across N = 128 … 4096. Global recruitment costs work proportional to the system however cheap the time becomes. Until the activation is made sublinear or a physical baseline with comparably extensive cost is defined, the energy/action gate is a FAIL and no advantage claim may cite cost (AT-0527)." }, { "id": "B95", "name": "The payload was routed by an oracle", "state": "OPEN", "summary": "Payload timings used a shortest path through S computed with global knowledge of the graph and of B's location. The phase opened the edges; no lawful local dynamics chose them. Every payload Q_time is a best-case bound and identity transport cannot pass until the next hop is selected from bounded-radius local state with no destination address (AT-0525, AT-0529)." }, { "id": "B96", "name": "Zero identity error is a property of a noiseless toy", "state": "OPEN", "summary": "The payload is carried rather than reconstructed and the model contains no decoherence, dispersion, loss or partial-arrival mechanism able to damage it. Exact zero shows the transport rule is self-consistent and must never be quoted as a fidelity result (AT-0525)." }, { "id": "B89", "name": "z = 0.317 is a five-point finite-size fit, not a law", "state": "OPEN", "summary": "A power law, a logarithm and a log-power all fit the phase-on times over N = 32 … 512 within the run-to-run spread, and the local exponent does not converge. No advantage claim may cite 0.317. Sizes of 1024, 2048 and 4096 with a sparse implementation are required before the forms separate (AT-0512)." }, { "id": "B90", "name": "The cooperative medium may be a pre-charged battery", "state": "OPEN", "summary": "The reaction term k*c(c-a)(1-c) gives every node a local potential with a stored well, so global recruitment may be releasing energy placed there when the medium was defined. If so the cheap front is paid for by an unaccounted Theta(N) preparation. Quantifying the stored landscape and charging its preparation is the next wall (AT-0509, AT-0520)." }, { "id": "B91", "name": "Restoration duration was being read off the wrong clock", "state": "CLOSED", "summary": "CORRECTED IN AT-0513. Absolute restoration timestamps contained the phase-on time because they were measured from the seed. Measured as durations between defined model events the restoration time is flat across N = 32 … 512. Every future timing in this programme is reported as a duration, never a timestamp." }, { "id": "B92", "name": "The trigger threshold has only been measured at one size", "state": "OPEN", "summary": "A finite amplitude threshold at N = 128 says nothing about whether the required seed energy stays O(1) or grows with N and with topology. A growing critical amplitude turns the trigger itself into a scaling cost and moves it into the action ledger (AT-0515)." }, { "id": "B93", "name": "One graph family is not robustness", "state": "OPEN", "summary": "Every Phase 57 number is on random cubic graphs. Which graph property sets the phase-on time - diameter, spectral gap or expansion - is unknown, and until Watts-Strogatz-like, geometric and degree-preserving-rewired substrates are run the result may be a property of one ensemble (AT-0511)." }, { "id": "B84", "name": "Corridor exposure is Omega(N) by construction", "state": "OPEN", "summary": "A latent edge is accessible only where the order field is ACTIVE, and a corridor reaching an endpoint drawn anywhere requires the field to have reached that endpoint. Any activation covering a constant fraction of the substrate excites Theta(N) nodes. Argued from the accessibility rule, not fitted, so no better simulation can improve the exponent (AT-0501)." }, { "id": "B85", "name": "Amortisation moves the coefficient, never the exponent", "state": "OPEN", "summary": "One activation window serves a number of crossings bounded by k_E divided by the substrate diameter - a constant in N. Dividing Theta(N) by a constant is still Theta(N). Any claim of sublinear net action must show one activation serving a number of crossings that GROWS with N (AT-0501)." }, { "id": "B86", "name": "Onset is the seed, so the quiet interval does not exist", "state": "OPEN", "summary": "The interval between the seed and the first open corridor cannot be treated as ordinary-local: the front itself moves on the substrate and is in principle measurable. Audits are timed from the seed tick, and no construction may buy locality by pointing at a later threshold (AT-0498)." }, { "id": "B87", "name": "Small-N sublinearity is not evidence of a logarithm", "state": "OPEN", "summary": "A Theta(N) term with a small coefficient looks logarithmic at accessible sizes. No component may be called sublinear on a fitted exponent alone - it needs a converged local exponent across the top half of the range AND an independent lower-bound argument. Applies retroactively to every scaling claim in the programme (AT-0496)." }, { "id": "B88", "name": "The activation window has to grow with the system", "state": "OPEN", "summary": "A frozen window caps the corridor at k_E chord hops while crossing needs about log2 N, so transit dies above a crossover size unless w(N) grows logarithmically. The window law is one rule applied blindly at every size and is sublinear, but it is still a parameter set by the system size, and a realisation would have to say what sets it (AT-0495)." }, { "id": "B80", "name": "The action ledger does not scale with the time ledger", "state": "OPEN", "summary": "Nucleating and restoring the anomalous phase flips Theta(N) order variables while the crossing time falls to O(log N). Time advantage grows; cost advantage does not exist. A candidate must change phase with sublinear action, or show the phase is already present for other reasons and amortises over many crossings (AT-0484)." }, { "id": "B81", "name": "Restoration under ordinary couplings costs Theta(N)", "state": "OPEN", "summary": "Sweeping the order field back while C* is active is O(log N); if a realisation requires restoration to proceed under ordinary-phase couplings the total returns to Theta(N) and the advantage dies. Which applies is a property of the unmodelled underlying dynamics (AT-0489)." }, { "id": "B82", "name": "One global time orientation is doing the anti-paradox work", "state": "OPEN", "summary": "The causal-loop audit passes because the model carries a single global tick. That is an assumption, not a result. Two independent triggers with observer-dependent ordering is the case that would generate a genuine consistency problem and it is NOT MODELED (AT-0487)." }, { "id": "B83", "name": "No generator produces the two-phase rule", "state": "OPEN", "summary": "The order-field dynamics is a stipulated local update rule, not something derived from one fixed generator with two stable sectors. Until H_eff(C0) and H_eff(C*) follow from the same written generator, phase-selective causality is a schema rather than a model (AT-0481, AT-0489)." }, { "id": "B79", "name": "No-signalling during the anomalous transition was never the right demand", "state": "CLOSED", "summary": "RETIRED BY AT-0479. Controllable identity-preserving transport faster than the ordinary cone is itself a channel, so the old gate was unsatisfiable and every failure recorded against it was a failure against a contradiction of ours. Earlier negative results that failed on cost, preparation depth, scaling or endpoint coding are unaffected and still stand." }, { "id": "B59", "name": "Observation is not transport", "state": "OPEN", "summary": "Where an observable metric shrank, the no-signalling trap still measured first arrival of a controllable bit at the cone bound: 9 observable hops against 64 sites of physical distance, first dependence at step 188. Emergent closeness buys no reach and may never be described as transport (AT-0422)." }, { "id": "B60", "name": "The cost of geometry tracks the separation it removes", "state": "OPEN", "summary": "For the weighted-path metric, the observation graph and the locally grown hierarchy alike, building the geometry rewrites Theta(N) sites to remove Theta(N) of separation. Every fitted exponent lies at or below zero within its interval: constants, not laws (AT-0418, AT-0423)." }, { "id": "B61", "name": "Large finite Q is bought with address bits or preloading", "state": "OPEN", "summary": "The endpoint-addressed drive needs ceil(log2 N) destination bits and the preloaded class field needs Theta(N). Both are disqualified before their numbers are read, and neither runs the same equations as the clean candidate (AT-0420)." }, { "id": "B62", "name": "Local coarsening pins before it reaches the pair", "state": "OPEN", "summary": "At N = 256 and N = 512 the quotient and observation metrics record exactly zero leverage: the domain walls stop moving while the pair is still separated. A rule with no destination information has no way to know it is not finished (AT-0418)." }, { "id": "B63", "name": "Parametric leverage is obtainable from the chart alone", "state": "OPEN", "summary": "Cutting a ring and unrolling it gives Q ~ N^1.0111 with L_N >= N-1, a genuine violation of the uniform-Lipschitz hypothesis E1 and a genuine scaling law. It is produced entirely by the observation map, and the seam sweep can place the same anomaly on any adjacent pair (AT-0425, AT-0426)." }, { "id": "B64", "name": "Large Q is not evidence without an invariance test", "state": "OPEN", "summary": "The identical microstate reads Q ~ N under the unwrapped line metric and Q = 1 under the intrinsic ring metric. Every future leverage number must be accompanied by a seam-free invariant control before it is reported (AT-0427)." }, { "id": "B66", "name": "A fixed local budget buys a fixed absolute saving", "state": "OPEN", "summary": "With the total excess conductance capped by a frozen budget, the best achievable reduction in arrival time is a constant independent of N. Divided into a distance that grows like N, any such saving forces the advantage ratio to decay toward 1. Growing the budget with N is a per-size parameter change and is disqualified (AT-0434, AT-0435)." }, { "id": "B67", "name": "Four-ruler coherence is necessary, not sufficient", "state": "OPEN", "summary": "Geometry, resistance, spectral gap and causal time all moving together rules out the Phase 50 coordinate artifact and is the strongest positive signal recorded so far. It still carries no weight on its own: the effect must also survive the scaling audit, and it does not (AT-0432, AT-0433)." }, { "id": "B68", "name": "Off criticality the correlation length is finite", "state": "OPEN", "summary": "The local phase organises over a fixed correlation length set by the frozen couplings, so its influence never spans a growing separation. A parametric effect requires xi and susceptibility to grow with N under one frozen rule with dynamic exponent z < 1. That regime has not been found (AT-0437)." }, { "id": "B69", "name": "The unlock front is the channel", "state": "OPEN", "summary": "Any latent sector that is faster through S, locally controllable and remotely detectable is already a communication channel, and the construction then describes a world whose causal structure is S rather than X. At least one of the three properties must be unavailable in the ordinary phase (AT-0443, AT-0451)." }, { "id": "B70", "name": "Global enabling conditions cost Theta(N) to prepare", "state": "OPEN", "summary": "Enabling a transition by global compatibility avoids an A->B signal but does not avoid the work: establishing the condition under the same local rules costs a pass over the substrate, and charging it drives Q_cost below one (AT-0446, AT-0450)." }, { "id": "B71", "name": "Only the uncontrollable branch survives", "state": "OPEN", "summary": "Of the four control and detectability cases, three are either a channel or operationally vacuous. The single surviving research target is the branch nobody can decide to use, which may be the correct shape of a lawful answer and may equally be the shape of no answer at all (AT-0445)." }, { "id": "B73", "name": "A realisation must name graph, norms or generator", "state": "OPEN", "summary": "Under a Lieb-Robinson-type bound, hidden connectivity outside the accessible algebra cannot signal. Escaping requires the accessible algebra, the interaction graph or the generator to change, and a candidate that names none of the three is not a candidate (AT-0454, AT-0456)." }, { "id": "B74", "name": "Structure changes inherit the Access-Channel Paradox", "state": "OPEN", "summary": "If the required structure change is locally controllable and remotely detectable, it is itself an operation with a shortcut, so AT-0443 applies to the change rather than the transition. The loophole must be a lawful structure change that is not locally selectable or not remotely readable (AT-0457)." }, { "id": "B75", "name": "A constant remote trace is a channel at scale", "state": "OPEN", "summary": "Repetition costs a constant while the ordinary route costs Theta(N), so any fixed remote distinguishability delta > 0 becomes the cheaper way to move a bit beyond a crossover size. Hiding requires delta to vanish with N at least about as fast as 1/sqrt(N) or be exactly forbidden by the observable algebra - and both of those also remove the operational advantage (AT-0459, AT-0460)." }, { "id": "B72", "name": "A costless mask does no work", "state": "OPEN", "summary": "The constraint layer restores perfectly because it never modified the substrate state. Reversibility this cheap indicates the construction has not yet done anything physical, and the identity test has not been run under it (AT-0448, AT-0452)." }, { "id": "B65", "name": "Spontaneous folds are still announced by the chart", "state": "OPEN", "summary": "Folds arising from frozen translation-invariant dynamics do produce untargeted high-Q pairs, but the winding or branch index is a locally readable invariant, so the anomaly is a visible property of the map rather than a hidden property of the physics (AT-0428, AT-0429)." }, { "id": "B55", "name": "Leverage is capped by L over c", "state": "OPEN", "summary": "Under a fixed single-valued emergence with uniform Lipschitz constant L, and a lawful cost floor C_S >= c d_S with c > 0, the sharpened leverage Q = D_X / C_S obeys Q <= L/c for every pair and every lawful path. Parametrically unbounded leverage requires the failure of at least one of these hypotheses. The theorem does not say which one, and it says nothing about physics (AT-0407)." }, { "id": "B56", "name": "Big number is not a scaling law", "state": "OPEN", "summary": "Any finite ceiling L/c is purchasable by inflating L or shrinking c, and every such ceiling has exponent zero against system scale. Normalisation choices, near-singular Jacobians, tuned cheap steps, preloaded edges and endpoint encoding all produced large Q at one scale and all saturated. Nothing may be reported as leverage unless Q grows with scale under frozen dynamics and frozen accounting (AT-0409, AT-0412)." }, { "id": "B57", "name": "The doors are a taxonomy, not a census of physics", "state": "OPEN", "summary": "The four escape doors exhaust the hypotheses of THIS theorem under the stated taxonomy. They are not a claim about conceivable physics, and none of them is physically priced — three were merely explored under prior toy cost functionals inside this project, which bounds those toys and nothing else (AT-0408)." }, { "id": "B58", "name": "No frozen dynamics shows both regimes", "state": "OPEN", "summary": "Across the blind search and the same-equations sweep, every setting that reproduced ordinary finite-speed propagation had exponent zero for Q, and every setting that inflated Q lost the finite cone. A candidate must show both from one frozen dynamics, with no parameter reset per destination and no prewritten endpoint data (AT-0410, AT-0411)." }, { "id": "B52", "name": "Fixed smooth emergence forbids leverage", "state": "OPEN", "summary": "If emergent geometry comes from the fundamental state space by a fixed, single-valued, globally L-Lipschitz map, then d_X <= L d_S and, after normalising L to 1, arbitrarily large leverage is impossible. Every mechanism family in this project so far sits downstream of such a map, which is why they all failed in the same way (AT-0401)." }, { "id": "B53", "name": "Only four doors, all with bills attached", "state": "OPEN", "summary": "The bound can fail only by negating one of its own hypotheses: critical or non-Lipschitz regions, a dynamical map or metric, a lawful path metric that differs from the static one, or a quotient / branching / topology change. Three are priced and cost more than ordinary traversal; the fourth is unpriced and therefore unavailable. No mechanism may be proposed unless it is first identified as one of these four (AT-0402, AT-0403)." }, { "id": "B54", "name": "One model must produce both regimes", "state": "OPEN", "summary": "No arm counts unless a single underlying model, with no second channel added by hand, reproduces ordinary finite-speed emergent behaviour AND the anomalous regime. In the minimal smooth family the anomalous regime was a units choice, and blind search on frozen geometry found nothing above the bound (AT-0404, AT-0405)." }, { "id": "B49", "name": "Compatibility forcing is not emergence", "state": "OPEN", "summary": "In the seed-363 null the bond tracks a pairwise compatibility term inserted into its own equation. Ablating it collapses selective bonding and shuffling it preserves the headline rate while destroying every pairwise association. No adjacency result may be quoted before an ablate-and-shuffle audit (AT-0391, AT-0392)." }, { "id": "B50", "name": "Adjacency addressing bottleneck", "state": "OPEN", "summary": "Aiming a bond at one destination out of many needs selection bits plus a description of the remote state, about ten bits against one bit of payload, and those bits must arrive over an ordinary channel first. A bond cannot be aimed at a place you have not already heard from the slow way (AT-0395, AT-0398)." }, { "id": "B51", "name": "Resonance without selectivity, tuning without transfer", "state": "OPEN", "summary": "Bond rules with no similarity hand-off produce bonds everywhere at once; tuned bonds exist only in a narrow detuning window, need continual retuning against drift, do not transfer to another pair, and cost more than ordinary traversal once fully charged (AT-0393, AT-0394, AT-0396, AT-0397)." }, { "id": "B1", "name": "Trivial construction", "state": "OPEN", "summary": "Any benefit that is a restatement of a modelling choice is vetoed by the nontriviality gate." }, { "id": "B2", "name": "Observable incompleteness", "state": "PARTIALLY ACCOUNTED", "summary": "Completeness is now audited, but the audit is only as good as the channel list." }, { "id": "B3", "name": "Gauge redundancy", "state": "PARTIALLY ACCOUNTED", "summary": "Physical quotients are taken explicitly; representational relocation is rejected." }, { "id": "B4", "name": "Hidden debt", "state": "OPEN", "summary": "Memory residue after coupling restoration remains nonzero for every mechanism tested." }, { "id": "B5", "name": "Locality and bounded propagation", "state": "PARTIALLY ACCOUNTED", "summary": "Controls are constrained to sparse local bands, but propagation bounds are still coarse." }, { "id": "B6", "name": "Action budget", "state": "PARTIALLY ACCOUNTED", "summary": "Coupling changes and auxiliary control are charged; the exchange rate between them is a modelling choice." }, { "id": "B7", "name": "Retuning", "state": "OPEN", "summary": "A rule that must be re-tuned per system is not a law. Frozen transfer is the discriminating test." }, { "id": "B8", "name": "Scale consistency", "state": "OPEN", "summary": "Coarse-grained agreement is untested for the Phase 33 mechanisms." }, { "id": "B9", "name": "Transient versus endpoint", "state": "CLOSED", "summary": "Scoring is pathwise. Endpoint identity is retired as a headline number." }, { "id": "B10", "name": "Identity vacuity", "state": "PARTIALLY ACCOUNTED", "summary": "Negative controls catch quotients that improve the score by measuring less." }, { "id": "B11", "name": "Memory and holonomy", "state": "OPEN", "summary": "Closed cycles do not return the system to its starting state without residue." }, { "id": "B12", "name": "Gauge-equivalent endpoints", "state": "PARTIALLY ACCOUNTED", "summary": "Endpoints identical up to representation are not counted as relocation." }, { "id": "B13", "name": "Rank deficiency", "state": "PARTIALLY ACCOUNTED", "summary": "Deficient coupling rank manufactures apparent protected subspaces." }, { "id": "B14", "name": "Physical versus representational address", "state": "OPEN", "summary": "No modelled quantity has been shown to be a physical address rather than a coordinate." }, { "id": "B15", "name": "Peak-damage floor", "state": "OPEN", "summary": "A positive lower bound on worst-case identity disturbance persists at matched progress and enforced coupling floor." }, { "id": "B16", "name": "Projection scaling", "state": "PARTIALLY ACCOUNTED", "summary": "Distance amplification through a map is generic; leverage means nothing until it is normalised by the operator norm or the peak local Jacobian." }, { "id": "B17", "name": "Projected traversal", "state": "OPEN", "summary": "A projected path that sweeps the ordinary intermediate region has skipped nothing, however far apart its endpoints look." }, { "id": "B18", "name": "Emergent causal consistency", "state": "OPEN", "summary": "Any channel faster than the emergent cone must come with a consistent deeper ordering, or it manufactures closed loops in the observable layer." }, { "id": "B19", "name": "Fixed-map continuity", "state": "CLOSED", "summary": "For a fixed smooth projection the image of a continuous path is continuous. No skip is available without making the map itself dynamical." }, { "id": "B20", "name": "Geometry-edit cost migration", "state": "OPEN", "summary": "Charging the geometry edit moves the cost between sectors rather than removing it; total accounted action still exceeds ordinary traversal." }, { "id": "B21", "name": "Geometry-control traversal", "state": "OPEN", "summary": "The control change itself has to propagate across the intervening region, so the region is crossed by something even when the traveller barely moves." }, { "id": "B22", "name": "Compression price", "state": "OPEN", "summary": "Once manipulation, equal restoration and roughness are charged, the cheapest control law achieving the target compression still costs several times ordinary traversal." }, { "id": "B23", "name": "Collateral geometry distortion", "state": "OPEN", "summary": "The action-cheapest compressions are the broadest, and they move a large fraction of unrelated pairwise distances. A short cut that distorts the whole universe is not a short cut." }, { "id": "B24", "name": "Corridor premium", "state": "OPEN", "summary": "Confining the deformation to a bounded relational channel removes the collateral distortion but raises the action per unit of compression sharply, and narrow corridors become infeasible under the deformation cap." }, { "id": "B25", "name": "Assumed action functional", "state": "OPEN", "summary": "Which compression is cheaper is decided by a cost rule we wrote down rather than derived. The corridor advantage survives three reasonable pricings, but no pricing is forced by the model." }, { "id": "B26", "name": "Synchronisation fragility", "state": "OPEN", "summary": "The corridor is open for a finite window and the traveller must arrive inside it. The advantage is conditional on coordinating an object with a geometry edit, and no mechanism for that coordination exists." }, { "id": "B27", "name": "Corridor is not dimension-free", "state": "OPEN", "summary": "In one dimension a corridor disturbs almost nothing. On a lattice the same corridor becomes a tube and collateral distortion among unrelated pairs rises by more than an order of magnitude." }, { "id": "B28", "name": "Problem transferred to the control field", "state": "OPEN", "summary": "The corridor does not exist until the control front arrives, and the front obeys the same locality bound as the traveller. Setting up the shortcut requires crossing the route once already." }, { "id": "B29", "name": "Front-speed tradeoff", "state": "OPEN", "summary": "A faster control front shortens completion but raises action superlinearly and widens collateral distortion. Speed is bought, never given." }, { "id": "B30", "name": "Infrastructure is not a shortcut", "state": "OPEN", "summary": "A pre-existing medium beats on-demand construction per crossing only after a large one-time preparation and a maintenance charge that never stops, and it still never beats traversal on time." }, { "id": "B31", "name": "Simple excitable medium insufficient", "state": "OPEN", "summary": "A one-time local trigger in a one-dimensional excitable reaction-diffusion geometry medium failed to launch a full-corridor pulse anywhere in the swept region: fronts decayed, pinned, or the medium blew up. Scope is the medium tested, not a universal no-go (AT-0313, AT-0314)." }, { "id": "B32", "name": "Propagation is not usefulness", "state": "OPEN", "summary": "Conservative dispersive structures that travel indefinitely without drive and restore the background afterwards still carry too little compression, too briefly, to help a traveller. Self-propagation and usefulness are separate requirements (AT-0315)." }, { "id": "B33", "name": "Prepositioned infrastructure", "state": "OPEN", "summary": "Every arm with a net advantage relies on a medium already prepared along the whole route before departure. Once one-time preparation is charged separately, the advantage is pre-established remote state, not a shortcut (AT-0318, AT-0321)." }, { "id": "B40", "name": "Local-scale power ceiling", "state": "OPEN", "summary": "Under bounded amplitude, bounded rate, a gradient bound and enforced restoration, the best gated apparent/local leverage found in the sampled family is about 1.5 (AT-0362)." }, { "id": "B41", "name": "Leverage is action-expensive", "state": "OPEN", "summary": "Accounted action grows superlinearly with leverage across the gated set; the top-leverage case costs a large toy action. No cheap regime found (AT-0367)." }, { "id": "B46", "name": "Marginal cost is not cost", "state": "OPEN", "summary": "After preload each trip draws only 4.40 units of fresh external input while the fully amortized cost is 49.40. No figure from the infrastructure branch may be quoted without preload, depletion, recharge and maintenance amortized into it (AT-0381, AT-0382)." }, { "id": "B47", "name": "Infrastructure energy scales with route length", "state": "OPEN", "summary": "Preload and per-transit depletion are linear in the number of edges at 6.00 units per edge, R² above 0.999, while the trigger stays flat. A small trigger covering a long route means a long route was charged in advance, and delivering that loading locally adds overhead and setup time (AT-0383, AT-0385)." }, { "id": "B48", "name": "Prepared geometry is route-specific", "state": "OPEN", "summary": "A prepared corridor serves only the endpoints it was built for, and a medium general enough for arbitrary endpoints costs with area rather than length. Prepared links change what a trip costs, not what distance is (AT-0386, AT-0389)." }, { "id": "B43", "name": "Phase-switch amplification is state debt", "state": "OPEN", "summary": "Enormous gain from a tiny trigger in the single-field bistable medium is bought by leaving the field in a persistent alternate state. Gain with a nonzero final field is spending, not control (AT-0371)." }, { "id": "B44", "name": "Restoration and propagation do not co-occur", "state": "OPEN", "summary": "Adding a recovery field restores the medium to 1e-8 … 1e-4 but confines the response to a few cells. Across the sampled parameter plane no configuration both propagated long-range and restored (AT-0372, AT-0373)." }, { "id": "B45", "name": "Long-range propagation is bought from a filled reservoir", "state": "OPEN", "summary": "With explicit per-cell free energy, reach tracks stored energy and preloaded infrastructure grows linearly with route length. Labelled PREPOSITIONED INFRASTRUCTURE, never free propagation (AT-0374, AT-0375, AT-0376)." }, { "id": "B42", "name": "Consistency is not power", "state": "OPEN", "summary": "Multi-observer agreement and clean causal ordering are hygiene requirements the branch meets. They carry no evidential weight and are never reported as progress (AT-0361, AT-0368)." }, { "id": "B34", "name": "Damage rides with the corridor", "state": "OPEN", "summary": "The traveller's internal state is driven by the compression gradient it sits in, so the corridor that carries it is also what disturbs it. At matched progress the ride peaks about twice as high as the walk (AT-0331, AT-0333)." }, { "id": "B35", "name": "Smooth or affordable, not both", "state": "OPEN", "summary": "Peak identity disturbance falls with corridor width while accounted action rises with it. The affordable corridors are exactly the sharp ones (AT-0334)." }, { "id": "B36", "name": "Round trips accumulate identity debt", "state": "OPEN", "summary": "The identity drive depends on the magnitude of the compression gradient, not its sign, so the return leg adds to the residue rather than cancelling it (AT-0338)." } ], "next": [ { "id": "Phase 218", "title": "Remove the assumed factor dimensions — compare all admissible decompositions", "question": "Drop the assumed 2×2×2×2 and compare every admissible direct-sum / tensor-product decomposition of the small Hilbert dimension, scoring each on the intrinsic criterion, and test whether a preferred class emerges without any dimension being put in by hand." }, { "id": "Phase 219", "title": "Basis-independent multi-gate factorization selection", "question": "Combine low-entanglement, approximate commutation, stable records / redundancy, and locality of H into a single basis-independent multi-gate selection functional, and check whether the gates are mutually consistent or select conflicting classes." }, { "id": "Phase 224", "title": "Derive a basis-independent, coefficient-free Pareto / feasibility principle", "question": "Replace the tuned three-gate score with a basis-independent, coefficient-free Pareto or feasibility principle, and test whether the stable factorization classes of Phases 220–223 form robustness basins — regions in factorization space that survive perturbations without a single hand-picked scalar optimum." }, { "id": "AT-0861", "title": "Rank accounting for every surviving candidate", "question": "Re-score all surviving architectures with the Interaction Rank Gate (Phase 167, rank(J) <= M for linear mediation): what rank does each require, where does that rank physically live, and does any candidate survive with rank below the number of channels it claims?" }, { "id": "AT-0862", "title": "Beyond polynomial feature maps", "question": "Phase 168 found required order p ~ 3.6K-4.7K for 1% leakage. Do non-polynomial kernels hit the same order wall, or is there a family whose interaction ORDER stays bounded while leakage stays within budget?" }, { "id": "AT-0863", "title": "Bounded-weight involution search", "question": "Phase 169 gave a full-rank degree-1 XOR matching with an O(K)-bit description, but Phase 170 charged it a Pauli-string generator of weight O(K). Does any involutive full-rank matching admit a generator of weight O(1), or is the weight bounded below by the bits it must flip?" }, { "id": "AT-0864", "title": "Subsystem separation criterion", "question": "Write a checkable criterion distinguishing basis relabelling from causal influence between independent physical subsystems (Phase 170), and apply it retroactively to every transfer toy in the ledger." }, { "id": "AT-0865", "title": "Primitive Search - first admissible candidate", "question": "Phase 171 opened the Generative Ontology track with six candidate primitives (relation/event, distinction, transformation, constraint, information/algebra, observer-relative accessibility). Carry one far enough to state a falsifiable consequence and a correspondence limit, or record the whole track as inadmissible. SPECULATIVE METHOD, NOT A RESULT." }, { "id": "AT-0801", "title": "Laplacian co-generation sanity test", "question": "On a toy weighted graph W, does a perturbation W -> W' change spectral distance and phi propagation consistently, or can the two be decoupled? If they decouple, co-generation fails." }, { "id": "AT-0802", "title": "Probe universality in simulation", "question": "Simulate three independent probe classes on the same perturbed W. Do all three infer the same metric change once translated into a common geometric quantity?" }, { "id": "AT-0803", "title": "Conventional-channel inventory", "question": "Enumerate every conventional channel for a candidate bench so that T_local,min is defensible and causal excess Xi becomes a usable statistic rather than a slogan." }, { "id": "AT-0804", "title": "Enlarged-graph accounting", "question": "For the off-resonant bus, does total cost (time x virtual occupation x hardware) ever beat a directly engineered edge? If never, the branch is architecture, not physics." }, { "id": "EXP-001", "title": "Build the oscillator fabric", "question": "Can a bench-scale array of locally coupled relaxation oscillators nucleate a bounded coherent cluster, translate it by moving only the boundary drive, and return to incoherence — with no interior writes and no global controller? Design frozen, hardware not started, physical evidence NONE." }, { "id": "AT-0706", "title": "Measure the local repair cone", "question": "Under a bounded local disturbance — one node loss, one destination move of k hops — how many distinct nodes change state at all? Fit N_repair against N across sizes. Is N_repair << N, and does N_repair / N fall toward zero, or is the persistent field a global object in disguise?" }, { "id": "AT-0707", "title": "Kill the p95 stretch tail", "question": "Median stretch improves as the field relaxes but p95 sits near 1.5. Is the tail a transient of incomplete relaxation, a structural property of local-only relaxation, or a set of pathological pairs? A local rule with bounded worst-case stretch, or an honest negative result." }, { "id": "AT-0708", "title": "Replicate the damage results properly", "question": "The N = 4096 repair numbers are single representative draws. Run the full grid across seeds, damage models (random, adversarial, correlated/spatial) and sizes before any of it is treated as a behaviour rather than an anecdote." }, { "id": "AT-0641", "title": "Run the exact sparse concurrency sweep", "question": "Execute the AT-0639 specification against the real address fabric: adjacency-list substrate, event stepping, real tree overlap, node and edge capacity. Does the measured slowdown follow rho = F L²/N at all, and which stability boundary is right (B124, B126)?" }, { "id": "AT-0642", "title": "Delete the single root", "question": "Multi-root election with local load balancing answers root contention (B127) and root failure (B123) with one change. What does it cost in address bits, election rounds and inter-root consistency traffic, and does it hold under damage?" }, { "id": "AT-0643", "title": "Prove the deadlock away, do not patch it", "question": "DETOUR clears the circular wait empirically. Is there a purely local ordering rule — a wait-for discipline on band nodes — under which deadlock is impossible by construction rather than avoided by luck (AT-0633)?" }, { "id": "AT-0644", "title": "Throughput per unit activation as the scored metric", "question": "Completions per 1,000 activated node-ticks FALL with N while latency improves. Re-score every prior phase on the activation metric rather than the latency metric and see which results survive (AT-0636, B108)." }, { "id": "AT-0628", "title": "Kill the elected root", "question": "Remove the minimum-identifier root and charge distributed re-election plus re-addressing in rounds, messages and bits changed per node. One root is one point of failure and it has still never been killed (B123)." }, { "id": "AT-0629", "title": "Churn instead of one-shot damage", "question": "Continuous failure and recovery over time rather than a single damage epoch. Does the fabric reach a stable steady-state maintenance traffic per node per unit time, or does repair never converge (B117, B122)?" }, { "id": "AT-0630", "title": "Bounded stretch after repair", "question": "Post-repair stretch drifts 1.55 → 2.29 with exponent 0.082 over four doublings. Is there a local repair rule with provably bounded stretch at O(log N) bits per node, or is the detour the price of self-organisation (B118, AT-0617)?" }, { "id": "AT-0631", "title": "Byzantine neighbours", "question": "One-hop symmetry defeats random corruption but not a neighbour that lies consistently. What is the cheapest purely local check that survives an adversarial neighbour, and what does it cost in bits and rounds (AT-0621)?" }, { "id": "AT-0632", "title": "Damage-proportional repair as a physical objection", "question": "If total repair work scales with the damage, any physical reading of this architecture inherits an extensive maintenance term. State that objection formally before any mapping is attempted (B122, B124)." }, { "id": "AT-0545", "title": "Build a structured address space", "question": "Can an endpoint-independent addressing structure be derived from the substrate before A and B are chosen - hierarchical coordinates, compact routing labels, landmark or tree schemes - that stays O(log N) bits per node while supporting neighbour-local routing with success approaching one and O(1) stretch (B99)?" }, { "id": "AT-0546", "title": "Delete the per-trip beacon", "question": "With no global field per trip, and the destination supplying only its compact address, can every hop decision be made from neighbour-local state plus that address? A scheme that still needs a flood has relabelled the debt as preparation, not removed it (B97)." }, { "id": "AT-0547", "title": "Charge the address structure as infrastructure", "question": "Entered in the ledger as one-off creation plus maintenance, does the address structure amortise across many arbitrary A-B pairs? A structure that only pays for itself over a single trip is a flood in disguise, and B41's stored-medium question applies to it in full." }, { "id": "AT-0548", "title": "Remove the model-assisted corridor", "question": "With the geodesic proximity condition deleted, can activation follow the same local routing and addressing dynamics as the payload - waking nodes only as needed - so the corridor becomes a consequence of the trip rather than a precondition for it (B98)?" }, { "id": "AT-0549", "title": "The joint objective", "question": "All six at once, or it does not count: route length and time O(log N), activated nodes per trip O(log N), address bits per node O(log N), per-trip preparation sublinear, stretch O(1), success approaching one as N grows. Five out of six is a partial result and will be published as such." }, { "id": "AT-0533", "title": "Remove the routing oracle", "question": "Can the payload choose its next hop from bounded-radius local state alone - no address for B, no global table - using a random walk, a local gradient, distributed routing or relational destination tags, and still show growing Q_time once the preparation and distribution of any destination information is charged (B95)?" }, { "id": "AT-0534", "title": "Make the activation sparse", "question": "Can a phase corridor, a percolating activation backbone, a localised moving C* bubble or a catalytic front activate only O(log N) nodes along a route - without the backbone being endpoint-targeted - so that total activated action becomes sublinear while autonomous routing and growing Q_time both survive (B94)?" }, { "id": "AT-0535", "title": "Is Theta(N) activity unavoidable?", "question": "Is extensive activity mathematically forced for ANY globally recruited C* phase on a bounded-degree substrate? If it is, global activation should be abandoned outright and the programme should move to localised catalytic fronts (B94, B90)." }, { "id": "AT-0536", "title": "Two triggers under the new law", "question": "Repeat the causal-consistency audit with two independent seeds and several payloads on the cooperative law. Does the fundamental event DAG stay acyclic, and does it still depend on one assumed global time orientation (B82)?" }, { "id": "AT-0521", "title": "Push N to 1024, 2048, 4096 and beyond", "question": "With a sparse implementation, fit log N, (log N)^p and N^z against each other on phase-on time and track the LOCAL effective exponent rather than the global fit. Does z = 0.317 survive, converge somewhere else, or dissolve into a logarithm (B89)?" }, { "id": "AT-0522", "title": "Critical trigger amplitude versus N and topology", "question": "Does the seed amplitude required to recruit stay O(1) as the substrate grows, or does it grow - in which case the trigger is itself a scaling cost and belongs in the action ledger (B92)?" }, { "id": "AT-0523", "title": "The energy ledger of the cooperative medium", "question": "Sum local activation and recovery action, separate external seed energy from energy released by the medium's own potential wells, and charge the preparation of the metastable landscape. Is the cheap front simply spending a battery somebody had to charge (B90, B80)?" }, { "id": "AT-0524", "title": "A structured payload gated on the activation field", "question": "Add a multi-component payload that may traverse the substrate only where and when c exceeds threshold, with A and B chosen after the substrate freezes. Measure full A->B completion including waiting for local availability and the subsequent restoration, and check whether the relational invariants survive." }, { "id": "AT-0525", "title": "Two triggers, multiple payloads, one event DAG", "question": "Repeat the causal-consistency audit under the new law with two independent seeds and several payloads. Does acyclicity in fundamental ticks survive, and does it still depend on the single global time orientation (B82)?" }, { "id": "AT-0526", "title": "Which graph property sets the phase time", "question": "Run cubic, Watts-Strogatz-like bounded-degree, geometric and degree-preserving-rewired substrates under the identical frozen law. Is phase-on time controlled by diameter, spectral gap or expansion (B93)?" }, { "id": "AT-0509", "title": "An activation that serves growing traffic", "question": "The cost gate fails only because one activation serves a constant number of crossings. Is there a lawful dynamics in which a single phase activation serves a number of crossings that grows with N - many payloads through one window - so that net action per crossing becomes sublinear without the window itself becoming a standing background channel (B84, B85)?" }, { "id": "AT-0510", "title": "Partial activation with endpoint-blind reach", "question": "Corridor exposure is Omega(N) because the field must reach wherever the endpoints are. Can a sub-linear activation pattern be chosen without endpoint knowledge and still connect a post-freeze pair, or is covering a constant fraction provably forced (B84)?" }, { "id": "AT-0511", "title": "What sets the window", "question": "Write a generator whose refractory period follows from the same dynamics rather than from a rule we wrote, and check whether it naturally scales like the substrate radius or is pinned to a microscopic constant that would cap the crossing (B83, B88)?" }, { "id": "AT-0512", "title": "Consistency without a global tick", "question": "Repeat the two-trigger audit with observer-dependent ordering of the two seeds. Does the acyclicity survive removal of the single global time orientation, and what does an emergent-coordinate observer reconstruct from the inversions we recorded (B82)?" }, { "id": "AT-0493", "title": "A phase that is already there", "question": "The two-phase crack fails only on an unpaid Theta(N) activation bill. Is there a lawful dynamics in which C* is the pre-existing background state of some region, so that no agent pays to open it and the cost amortises over unboundedly many crossings, without that background itself constituting hidden access available in the ordinary phase (B80)?" }, { "id": "AT-0494", "title": "Sublinear phase change", "question": "Can any local rule move a bounded-degree substrate between two stable accessibility sectors with o(N) total action, or is Theta(N) forced by the fact that every site must change what it is coupled to (B80)?" }, { "id": "AT-0495", "title": "Write the generator", "question": "Produce one fixed generator with two stable sectors from which H_eff(C0) and H_eff(C*) both follow, so that the order-field rule is derived rather than stipulated, and the restoration branch is decided rather than reported twice (B81, B83)?" }, { "id": "AT-0496", "title": "Consistency without a global clock", "question": "Repeat the causal-loop audit in a model with observer-dependent ordering of two independent triggers. Does the two-phase construction still admit a consistent event order, or does phase-selective causality generate closed loops the moment the global tick is removed (B82)?" }, { "id": "AT-0464", "title": "Name the object that changes", "question": "Under the Operational Locality Bound, a controllable shortcut requires the accessible algebra, the interaction graph or the generator to change. Can any candidate in this programme name which one, in a model with an explicit local generator, rather than asserting that constraints change (B73, AT-0456)?" }, { "id": "AT-0465", "title": "A structure change with no local selector", "question": "Loophole L5 is the only one left standing that is not closed by cost. Is there a lawful dynamics in which the accessible algebra changes as a consequence of a global conserved compatibility condition that no local agent can select, whose preparation is not Theta(N) charged to the trip (B70, B71, B74)?" }, { "id": "AT-0466", "title": "Exactly forbidden rather than merely small", "question": "AT-0460 says the remote trace must vanish with N or be forbidden exactly. Can an ordinary-phase observable algebra be written in which the latent sector is exactly invisible by construction, and does anything operational survive that exactness (B75)?" }, { "id": "AT-0467", "title": "Beyond the illustrative detection model", "question": "The k/delta^2 repetition count assumes independent trials and shot-noise discrimination. Do adaptive or correlated strategies change the crossover exponent, and is there a distinguishability bound that holds independently of the readout model (B75)?" }, { "id": "AT-0468", "title": "Latent sector that cannot be locally switched", "question": "The only surviving branch of the control matrix is the uncontrollable one. Is there a lawful dynamics in which the constraint sector C* is entered by a global compatibility condition that no local agent can decide, yet whose preparation is not itself Theta(N) work charged to the trip (B70, B71)?" }, { "id": "AT-0469", "title": "Cost-side growth, not just time-side", "question": "Q_time now grows with N and Q_cost does not. Is there any construction in which both grow together under one frozen rule with preparation, transition and restoration all charged (AT-0450, B70)?" }, { "id": "AT-0470", "title": "Identity through a constraint cycle", "question": "Carry a structured multi-component state with relational and internal invariants through C_0 -> C* -> C_0. Do the invariants survive, and does the debt stay bounded once the mask is made to do real work (AT-0452, B72)?" }, { "id": "AT-0471", "title": "Collective critical regime with z < 1", "question": "Is there a frozen local rule whose correlation length and susceptibility grow with N while phase-formation time scales as T_phase ~ N^z with z < 1, and do all four rulers still move by O(1) at every size, so that total completion time scales sublinearly (B66, B68)?" }, { "id": "AT-0472", "title": "Budget that grows lawfully with N", "question": "Is there any local dynamics in which the usable conductance budget grows with system size without being handed in by fiat — grown by the system itself under the same equations and charged in full — or is a constant budget forced (B66)?" }, { "id": "AT-0473", "title": "Coherence without decay", "question": "Four-ruler coherence and parametric growth have never yet co-occurred. Is their co-occurrence forbidden by an argument, or merely unobserved (B66, B67)?" }, { "id": "AT-0442", "title": "Invariant fold with no readable index", "question": "The ring cut is exposed by a locally readable winding index. Is there any local dynamics whose folds carry parametric leverage while no local invariant observable can detect that a fold is present, or is detectability of the chart forced (B63, B65)?" }, { "id": "AT-0443", "title": "Physical cost of unfolding", "question": "If the unwrapped line is what an apparatus is actually forced to read, unfolding it must cost something. Can the price of maintaining a non-Lipschitz observation map be derived and charged, and does charging it restore the ceiling (B63)?" }, { "id": "AT-0444", "title": "Mandatory invariance control", "question": "Formalise the seam-free control as a permanent gate: every future leverage claim must reproduce under at least two independent chart-independent metrics before it is reported at all (B64)." }, { "id": "AT-0445", "title": "Forced observables", "question": "Is there a lawful observable whose parametric shrinkage is also what an apparatus is forced to measure — a quotient no observer can decline — or is every parametric crack necessarily a change of bookkeeping that nothing can read (B59)?" }, { "id": "AT-0446", "title": "Unpinning without addresses", "question": "Can a translation-invariant local rule with zero destination bits drive coarsening to completion at every scale, so that the zero-leverage points at large N disappear and the exponent is measured rather than truncated (B62)?" }, { "id": "AT-0447", "title": "Sublinear geometry construction", "question": "Is there any local dynamics in which removing Theta(N) of observable separation costs o(N), or is cost-tracks-separation a theorem rather than a repeated observation (B60)?" }, { "id": "AT-0415", "title": "Scale-growing effective Lipschitz constant", "question": "Is there a single frozen dynamics whose effective Lipschitz constant grows with system scale faster than the lawful cost floor shrinks, so that Q grows parametrically, while small perturbations of that same dynamics still travel at a finite emergent speed (B55, B58)?" }, { "id": "AT-0416", "title": "Deriving the lawful cost floor", "question": "The constant c is currently declared. Can a positive lower bound on lawful completion cost be DERIVED from a dynamics rather than assumed, and does any derived floor change the ceiling L/c qualitatively (B55, B56)?" }, { "id": "AT-0417", "title": "Pricing the multivalued door", "question": "The door that negates single-valuedness on a fixed topology remains unpriced and therefore unavailable. Can a quotient, branching or topology change be given a local, bounded, restorable cost inside a toy model so that it becomes auditable (B57)?" }, { "id": "AT-0341", "title": "Coupling-law generality", "question": "Is the gradient-to-identity coupling forced in any model where geometry is dynamical, or can a lawful coupling be written in which a moving compression leaves internal state untouched (B34)?" }, { "id": "AT-0342", "title": "Front-precedence theorem", "question": "Prove or refute: for every local control field with a bounded edit rate, the control front must reach the destination before the traveller can gain any time. AT-0332 supports it for one family only (B28)." }, { "id": "AT-0343", "title": "Derived geometry price", "question": "Can a cost for editing a link be derived from an action principle inside the model rather than declared, and does any derived price change the verdict (B25, AT-0337)?" }, { "id": "AT-0344", "title": "Carried traveller on a lattice", "question": "Repeat AT-0331 in two dimensions and under coarse-graining. G13 of the Carried-Traveller Gate is NOT MODELED (B8, B27)." }, { "id": "AT-0345", "title": "Sign-sensitive identity coupling", "question": "Is there a lawful identity observable whose drive is sign-sensitive in the gradient, so that a closed cycle can return the traveller without residue (B36, B11)?" } ], "resumeInstructions": [ "Open /lab/localized and rerun the Phase 61 package at seed 557 before changing anything. Reproduce success 1.000, route 10 → 19, active 23 → 42 and bits 28 → 48 across N = 128 … 4096.", "Quote route, active nodes and address bits as ratios against log2 N, never as the fitted powers 0.203, 0.185 and 0.155. Those powers are artefacts of fitting a line to a logarithm and must be disowned wherever they appear.", "Never call Phase 61 an address-emergence result. Hops read precomputed tree parent and ancestor tables; the correct label is COMPACT-ADDRESS INFRASTRUCTURE TOY (B106).", "Never read a sublinear activated-node count as a sublinear cost. Node counts are not integrated action, and the energy/action gate stays FAILED until AT-0571 exists (B108).", "Tree construction, maintenance and repair are uncharged and the amortisation crossover is uncomputed. Do not describe the infrastructure as cheap, free or fundamental (B102, B105).", "Open /lab/hierarchy for the Phase 60 comparison at seed 545: the (log2 N)^2 storage debt is the baseline Phase 61 improved on, and it stays visible.", "Start at /lab/crack and rerun the Phase 49 package at seed 415. Reproduce the recorded rows — cone excess 0, exponents -1.19, +0.21 and -1.15, first arrival at step 188 against a cone bound of 64, six candidates and zero survivors, verdict NO CRACK — before trusting anything downstream.", "Never present a shrinking observable metric as movement, transport, signalling or anything faster than anything. AT-0422 is the control that decides it, and it must be run and quoted with any such number (B59).", "A candidate is only interesting if the exponent of Q against system size is positive outside its confidence interval. A large Q at one scale is not a result (B56, B60).", "Any candidate must first be checked for destination bits. If the setup knows where B is, the answer was handed over and the numbers are meaningless (B61).", "Start at /lab/sharpened and rerun the Phase 48 package at seed 407. Reproduce the recorded rows — zero violations of Q <= L/c across scales 8 to 128, zero positive scaling exponents among the frozen blind systems, every mirage control saturating, and Foundational Gate v2 not cleared — before trusting anything downstream.", "Q = D_X / C_S is now the only admissible leverage quantity. Never compare observable separation against a static state distance again; that was the wrong ruler (B55).", "Never report a large Q at one scale. Report the exponent of Q against system scale, or report nothing (B56).", "Do not write that the four doors exhaust conceivable physics, and do not write that three of them are physically priced. They exhaust this theorem's hypotheses, and they were explored under toy cost functionals only (B57).", "'Einstein-like benchmark' means finite local causal propagation and nothing else. No field equation is derived anywhere in this project (AT-0413).", "Then open /lab/foundation and rerun the Phase 47 package at seed 373. Reproduce the recorded row — 9,600 pairs in dimensions 3, 5, 8, 12, largest ratio 0.99982, zero violations, best blind leverage 0.962, gate 5 of 10 — before trusting anything downstream.", "The bound is the frame for the whole programme. Do not open a new mechanism family. Any proposal must first be identified as escape class E1, E2, E3 or E4, and must arrive with its bill (B52, B53).", "Never quote an unnormalised stretch or leverage figure. Normalise the Lipschitz constant first; the flattering column is meaningless on its own (AT-0404).", "Open /lab/resonance and rerun the Phase 46 null at seed 363 before quoting any adjacency statistic, and run the ablate-and-shuffle audit with it (B49).", "Open /lab/infrastructure and rerun the Phase 45 package at seed 353. Reproduce the recorded lifecycle — 360 units preloaded, 33.6 recharged, 1.6 in triggers, eight completed trips, marginal 4.40 per trip against fully amortized 49.40 and ordinary traversal 48.00 — before trusting anything downstream.", "Never quote a marginal per-trip figure anywhere in this project without the fully amortized figure beside it (B46).", "Open /lab/stored-medium and rerun the Phase 44 stored-medium package at seed 343. Reproduce the recorded rows — several-hundred-fold gain with a persistent final field in the single-field medium, end debt of 1e-8 … 1e-4 with a front of only a few cells in the two-field medium, and a balanced energy ledger with zero violations — before trusting anything downstream.", "Never quote an amplification number without the reservoir debit beside it (B43, B45), and never mix the three accounting models of AT-0379.", "Open /lab/scale-power and rerun the Phase 43 package at seed 343. Reproduce the recorded row — leverage about 1.5 at accounted action of a few hundred toy units, endpoint debt under 0.02, |dλ/dt| inside the bound of 3 — before trusting anything downstream.", "Never quote observer agreement as a result. It is hygiene (B42). The result is the ceiling: weak leverage bought at superlinear action (B40, B41).", "Always report the coupled-backreaction number, never the free-ride control, and keep the normalised null control on the same chart.", "Open /lab/pulse and rerun the Phase 38 package at seed 303. Reproduce the recorded net-time row — traveller arc about 13.3 against a baseline of 24, net completion about 43.2 against ordinary traversal about 24.0 — before trusting anything downstream.", "Never quote the traveller's shortened arc on its own. The honest number is net completion including front propagation and restoration, and it is currently 1.8x slower than walking (B28).", "Treat the standing medium as infrastructure with a break-even crossing count, never as spontaneous travel. It wins on amortized action after about nine crossings and never wins on time (B30).", "Open /lab/corridor and rerun the Phase 37 package at seed 293. Reproduce the recorded benchmark row (Gaussian corridor action about 36.4 at shrink 0.449, global rewrite about 101) before trusting anything downstream.", "Quote the corridor advantage only as COMPUTATIONAL RESULT / MODEL-DEPENDENT. It is a statement about an assumed cost rule, never about energy or physical space.", "The two open gate items are the work: identity is not yet coupled through the corridor (G10, NOT MODELED), and the full cycle still costs more than simply covering the distance (G14).", "Open /lab/geometry and rerun the Phase 35 dynamic-geometry package at seed 273. The continuity no-go is the frame for everything that follows it.", "Never claim a skip from a fixed map. AT-0273 closes that route as a model theorem; only a dynamical projection or metric remains open, and it must be charged.", "Score the dynamic arm on total action across both sectors and on whether the geometry edit itself had to cross the region (B20, B21), not on the traveller's arc alone.", "Open /lab/deeper and rerun the Phase 34 two-layer package at seed 263. Reproduce the random-map null benchmark before trusting any leverage number.", "Never quote raw projection leverage. It is EXPECTED BY MAP GEOMETRY until normalised and compared against a matched random map.", "The one positive result to protect is AT-0268: finite emergent propagation recovered from local Y interactions with no speed inserted. Any new model must keep it.", "Open /lab/schedules and rerun the Phase 33 package at seed 255 to reproduce the recorded end-of-session numbers before changing anything.", "Read the end-of-day gate on that page. The status to beat is NONE PASSED; note which requirements currently fail.", "Treat the peak-damage floor (AT-0258, blocker B15) as the primary target. Every new candidate is scored against it.", "Do not optimise endpoint identity. The score is peak_t |ΔI| at matched destination error, with residue read after coupling is restored.", "Any new mechanism must be frozen before evaluation on unseen systems. Per-case retuning is recorded as retuning debt, not as progress.", "Preserve all rejected history. Killed shortcuts stay on the site with their evidence, and no result is relabelled upward without new experiments." ], "mostImportantUnresolved": "PHYSICAL MAPPING IS NOW THE ONLY GATE LEFT, and Phase 69 hands it a hard constraint rather than a free hand. The lifecycle accounting says the toy architecture is neither cheap nor expensive — it is reuse-dependent. Charged in full and amortised against a linear point-to-point baseline, it is strictly worse than baseline at one, ten and a hundred lifetime trips (z = 1.133, 1.131, 1.103, advantage absent at every size), breaks even near 197 trips (median per-size), with the fitted exponent crossing 1 near M ≈ 574, and only then turns sublinear: z = 0.933 at M = 1,000 and 0.514 at M = 10,000, with Qcost reaching 33.74 at N = 16,384. Those are normalized counts of modelled operations and bit-hops — NOT joules, NOT seconds, NOT an efficiency claim. The consequence is a design law: rebuilding the addressing substrate per trip is dead, so physical mapping must prioritise platforms that already provide reusable background connectivity and low marginal reconfiguration cost. Five candidate ANALOGUE platforms are mapped variable by variable and none is a spacetime claim. The open work is the discriminator: find a measurement in which a two-phase moving-doorway architecture and an ordinary routed network give different answers. Reuse-scaling of reconfiguration events is the leading candidate; speed is excluded in advance by the locality bounds of Phases 47-55. Until such a measurement exists on a real platform, the ladder's last rung stays NOT ESTABLISHED and the programme label is unchanged: LOCALIZED AUTONOMOUS DOORWAY — TOY CANDIDATE / PHYSICAL EVIDENCE NONE. Phase 68 closes the fault-tolerance question to FIRST PASS and leaves exactly one toy gate standing. The cheap design died first: one address tree with a single stored backup neighbour per node repaired only 17.6% of severed nodes on median, and 4.8% at eight targeted cuts, because a high-impact cut severs a whole subtree and every backup inside that subtree points back into it. That negative result is preserved. Architectural redundancy replaced it — eight independently rooted BFS trees over one shared degree-4 substrate, frozen before endpoints exist, K·O(log N) address bits, flows re-selecting among survivors with zero rebuild messages — and held sampled route success 1.000 at every tested adversarial failure count through N = 2048, worst cell 0.983, worst median stretch 1.236x, with K constant. Four trees were not enough and two collapsed. What remains is the LIFECYCLE COST gate: formation of K address trees, storage bits per node, maintenance and repair communication, moving-doorway activity, payload and restoration, all in dimensionless operations and bit-hops, amortised over M trips at a given failure rate against an ordinary point-to-point baseline, with break-even M(N) identified rather than assumed. The gate fails if amortised cost per trip is not sublinear in N at constant K for realistic reuse, or if K must grow with N or fault rate beyond the tested range. No physical energy claim will be made either way. PHYSICAL EVIDENCE: NONE. Phase 67 answers the Phase 66 question structurally and leaves it open empirically. Building K generic BFS roots before endpoints exist, storing K compact O(log N) addresses per node and letting each trip pick a tree from two sampled candidates using only local congestion counters is enough to disperse the traffic that froze the single-root band: mean completion at F = 16 goes 38% -> 82%, adversarial same-branch completion 16% -> 72%, busiest-node load grows only as F^0.472, footprint as F^0.846, root-load entropy holds at 0.921 of maximum, and it all costs a constant 4x multiplier on logarithmic address storage with no global coordination per trip. Six of nine gates pass on the exact layer. The decisive one does not: completion probability never reaches 1 inside the finite doorway window, so the fabric disperses traffic without guaranteeing delivery, and killing one root mid-run still costs a quarter of the completions. The open question is therefore sharp — what local rule, if any, converts dispersion into a delivery guarantee without a per-trip oracle, and can it be had for polylogarithmic storage. Everything remains a toy router measured in ticks and bits. PHYSICAL EVIDENCE: NONE. Phase 66 asks the question every previous phase avoided: one trip is not a network. Sixty-five phases moved a single payload through an empty world. Here many doorways are open at once on the same substrate, and the first honest thing to report is a limitation rather than a result — the exact-graph concurrency sweep exceeded the runtime budget, so what is published is a declared QUEUEING OVERLAP PROXY (route length L ~ 1.6 log2 N, about four locally active nodes per live flow, node capacity one move per tick) and not a measurement of the address fabric (B124). Inside that proxy the congestion law is exactly the textbook one: expected shared slots C(F,2)L^2/N, per-trip slowdown 1 + (F-1)L^2/2N, reading 1.125x to 4.875x at N = 1024 for two to thirty-two flows and only 1.044x to 2.366x at N = 4096 because the same traffic spreads over more substrate; the event-driven token simulation, which counts overlap rather than predicting it, agrees in shape at 1.208x down to 1.056x at F = 16. Everything collapses onto one load parameter rho = F L^2 / N, so the question how many users is really the question how much of the substrate is occupied, and the conservative slowdown-<=-2 boundary F <= 1 + 2N/L^2 grows as N^0.855, the shape F(N) ~ N/log^2 N. That is the entirety of the good news and it rests on routes drawn uniformly at random (B125), which real routes on a single spanning tree are not. The adversarial test is the real finding, and it is worse than congestion. When all sixteen flows climb into the single elected-root band and hold a contiguous run of about L/3 band nodes - what an actual tree path does - the plain QUEUE rule does not degrade, it stops: zero of eighty payloads complete across N = 256 to 4096, tokens hold band nodes while waiting for band nodes held by other tokens, and the longest wait reaches 952 ticks before the run is cut off. This is circular-wait deadlock, a property of the collision policy as much as of the topology, and it is exactly why the four policies were written down as explicit local rules before any number was taken. Two purely local fixes clear it in the proxy: DETOUR completes every flow at no worse than 1.36x with no topology change, and four elected roots with two extra address bits plus a least-loaded local band choice complete every flow at 1.17x against 1.23x for random endpoints, addresses still O(log N) and the sender still blind to the destination. ABORT also clears it, by losing forty-one of eighty payloads, and those losses are scored as failures rather than averaged away. Neither fix exists in the fabric, so both are INCONCLUSIVE (B127). Three further things are recorded against the programme rather than for it. The analytic and simulated stability boundaries disagree by an order of magnitude - five to twenty-four permitted flows against forty-eight to two hundred and fifty-six - because a token holds a node for one tick rather than for its whole trip, and until the exact run settles it the conservative column is the one that stands (B126). Lifecycle throughput, completions per thousand activated node-ticks, FALLS from 17.241 to 13.158 with exponent -0.113 while latency improves: the design gets faster per trip and less efficient per unit of awakened substrate, which is the same accounting error this programme keeps catching in itself (B108). Tail behaviour under random endpoints is genuinely benign - longest single wait four ticks, Jain fairness at least 0.979 - and one link cut with eight doorways open leaves every other flow unchanged with no global rebuild, which is the Phase 65 repair rule surviving contact with concurrency. The breakthrough ladder therefore gains one new row, MULTI-USER SCALABILITY = UNRESOLVED, and the next moves are specific: run the AT-0639 specification exactly as published so it cannot be tuned toward the proxy, delete the single root - which answers contention and single-point failure with one change - and look for a local wait-for ordering under which deadlock is impossible by construction rather than avoided by luck. Programme label unchanged: LOCALIZED AUTONOMOUS DOORWAY - TOY CANDIDATE. NO PHYSICAL MECHANISM. PHYSICAL EVIDENCE: NONE." } }