{ "schema": "adjacency-theory-archive/v1", "generatedISO": "2026-08-26T16:05:54.411Z", "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.", "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[]." ], "checkpoint": { "version": "3.2.0", "label": "Research Checkpoint — End of Session", "dateISO": "2026-08-26", "dateLabel": "August 26, 2026", "experimentRange": "AT-0 → AT-0544 (through 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" ], "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.", "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": "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": "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": "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": "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": [ "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": "Phase 59 attacked both Phase 58 debts and moved both without clearing either, and in the process replaced a vague problem with a precise one. The routing oracle is genuinely gone: the destination emits a locally propagating scalar beacon, the payload compares only the beacon values of its immediate neighbours, and with no shortest-path computation anywhere in the loop it arrives 100% of the time from N = 128 to N = 4096, along paths of five to ten hops with stretch approximately one, while Q_time climbs 4.571 to 81.92. Activation stopped being extensive: a corridor of tens of nodes replaces the Phase 58 whole-network wake-up, roughly N^0.192 against N^1.031, about one per cent of the network at the largest size. Both of those are real measurements and both are built on information the substrate does not have. Spreading the beacon touches essentially every node, once per trip, so the map debt was renamed rather than paid; and the corridor is defined by proximity to an A-B geodesic, a global distance condition, so the routing debt is not solved. The attempt to remove the beacon in the cleanest possible way - a frozen random vector label on every node, assigned before the endpoints were chosen - failed outright, with success falling to 0.38-0.50 by N = 1024 and greedy paths wandering past a hundred hops to reach a node eight or nine hops away, because label proximity is uncorrelated with graph proximity on an expander. That failure is the most useful result of the phase, because it rules out an entire class of solutions and forces the real question into the open. The wall is not pathfinding; greedy descent on a good field already solves pathfinding here with stretch one. The wall is that a low-diameter substrate gives a traveller nowhere to aim. What is needed is an addressing geometry derived from the substrate itself, endpoint-independent, prepared before endpoints are selected, compact at O(log N) bits per node, and charged as infrastructure that must amortise over many arbitrary trips. Until such a structure is built and costed, the joint objective stands and is deliberately hard: route time O(log N), activated nodes O(log N), address bits O(log N), per-trip preparation sublinear, stretch O(1), success approaching one - all six, or it is a partial result. PHYSICAL EVIDENCE: NONE." } }