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Adjacency Theory markAdjacency Theory

Research dashboard

Experiment matrix, fingerprints and negative results

One table for the state of the programme: every experiment from AT-0011 to AT-0368 with its seed, model version, reproducibility fingerprint, epistemic classification and verdict — plus everything that failed.

Where the programme actually stands

FIXED SMOOTH EMERGENCE INSUFFICIENT — mathematical bound and computational framework, no physical mechanism, no physical evidence.

If the geometry we observe comes from a deeper state space through a fixed, globally Lipschitz map, then d_X ≤ L·d_S: being close underneath bounds how far apart you can be above. Every mechanism family this project has built — resonance, stored media, travelling pulses, corridors, adaptive coupling — was written downstream of such a map, which is why they all failed in the same way. Those branches stay preserved and rerunnable, but they are no longer the front of the programme. The work now is to identify which of exactly four escape conditions is mathematically necessary, and whether it can come from the same equations that already reproduce ordinary finite-speed behaviour.

The Wall — AT-0373 → AT-0378 →

Session checkpoint

A durable record of where the programme stands — core objective, formulation, killed shortcuts, surviving clues, the blocker ledger and exact resume instructions, versioned in the project rather than in anyone's memory.

Research Checkpoint — End of Session →

Experiments tracked

7

Pass

4

Fail

0

Inconclusive

2

Physical evidence

NONE

Blocker matrix — what currently stands between us and the objective

AT-0103 → AT-0110

computing live blocker standings…

Negative controls · plain language

A simulation can only surprise us if we did not secretly put the answer into its rules

Suppose we build a model where a thing’s identity and its position are stored as two separate lists of numbers, and we let ourselves edit either list freely. Then we run the model and announce that position changed while identity stayed the same. That is not a finding. It is a restatement of how we set up the lists.

When a result is guaranteed by the way we wrote the model, we label it EXPECTED BY CONSTRUCTION and it is not allowed to count as a discovery.

AT-0011 → AT-0368 matrix

computing live rows…
IDExperimentSeedModel / algoFingerprintClassificationVerdictPhysicalEvidence frame
AT-0020Transition operator surveyAllowability structure T(R_i,R_j) is specified but not yet computed.———MODEL HYPOTHESISNOT RUNNONE—
AT-0021Relational relocationTraveler changes relational neighborhood while identity is tracked. Mathematical model only.AT-RU-21phase2—COMPUTATIONAL RESULTPASSNONEopen lab
AT-0022Minimum relocation costOptimizer reproduces the analytic L1 minima of 14.0 (two-sided) and 7.0 (one-sided).reloc-benchreloc-bench-1.0.0—MATHEMATICAL PROPERTYPASSNONEopen lab
AT-0023Continuity challengeDirect and monotonic multi-step transformations cost the same, so step count cannot decide continuity.reloc-benchreloc-bench-1.0.0—MODEL HYPOTHESISINCONCLUSIVENONEopen lab
AT-0366Blind small-integer automorphism enumerationAll 19,683 matrices with entries in {−1,0,1}; 6,960 unimodular, 3,120 hyperbolic. No filter referenced shortcut strength or the number 3. Frozen dataset at366-distortion-001.none — exhaustiveat366-distortion/1.0.0d81d37beCOMPUTATIONAL RESULTPASSNONEopen lab
AT-0367Constant-description distortion demonstrationA = [[1,1,1],[1,0,0],[0,1,0]], spectral radius = tribonacci constant ≈ 1.8392867552; word proxy 2n+1 vs exact L1 displacement of A^n v, n = 1–32. Label displacement, not physical distance.none — exact BigIntat366-distortion/1.0.0cb25c202COMPUTATIONAL RESULTPASSNONEopen lab
AT-0368Distortion realization wallAlgebraic logarithmic displacement PASSED for the toy construction; physical shortcut NOT MODELED; natural dynamical selection of A remains OPEN.—at366-distortion/1.0.0—MATHEMATICAL PROPERTYINCONCLUSIVENONEopen lab

Composite robustness ranking — promising is not the same as robust

Candidates are never ranked by effect magnitude alone. Each must repeat across seeds, hold on multiple substrate variants, survive bounded noise, avoid a near-zero denominator, keep the identity core and the selected model invariants within tolerance, and stay low in complexity. Failing any one gate downgrades the candidate visibly, whatever its raw effect.

computing the deterministic robustness ladder…

Scale-aware discovery ranking — does the effect survive zooming out?

The discovery engine adds a seventh term: scale persistence. Effect size, relational cost, composite robustness, identity-core preservation, invariant drift, countermodel survival and scale persistence are weighted together, so a spectacular result at one resolution ranks below a smaller result that still exists after coarse-graining.

running the deterministic scale sweep…

Ranking terms are properties of a toy graph model. A high score means a candidate is worth more computation, never that it describes nature.

Full sweep and the ZOOM OUT viewer: AT-0044 → AT-0050.

Lawful transformation ladder — identity, information and reachability

Phase 8 adds three more filters before anything is promoted: the transformation must leave the traveller inside its identity-equivalence class, the information ledger must balance, and the move must be reachable under the toy ordering rule. Every failed filter stays on the card.

running the deterministic identity and information sweep…

Full sweep and the Identity & Information Lab: AT-0051 → AT-0058. Physical evidence: none.

Negative results and falsification register

Ceilings, failed optimizations, unstable adjacency, identity failures, unmodeled invariants and null results are kept visible and versioned. Nothing is deleted for being unflattering.

HARD CEILINGNR-01

Γ_A cannot exceed 1 under this metric definition

When effective distance is the weighted shortest path and adjacency cost is the total L1 reduction of those same positive edge lengths, |ΔD| ≤ Σ|Δw|, so Γ = |ΔD| / C_A ≤ 1 for simple path shortening. This is a limitation of the chosen metric and cost definition, not a universal theorem about all relational observables — a different observable such as effective resistance requires its own separate derivation.

NULL RESULTNR-02

No hysteresis in a reversible static rule

The round trip R₀ → R₁ → R₀ leaves zero residual because the transformation rule carries no state. We report zero rather than manufacturing an effect.

NULL RESULTNR-03

Step count cannot establish discontinuity

Monotonic multi-step and single-step transformations between the same endpoints have identical L1 cost, so the number of stored intermediate relational states is a bookkeeping choice, not an observable. No physical continuity conclusion follows.

INVARIANT NOT MODELEDNR-04

Energy, momentum and causal ordering remain NOT MODELED

No energy, mass, dynamics or ordering relation exists anywhere in these models. Graph invariants that do hold say nothing about physical conservation.

NULL RESULTNR-05

No physical evidence has been produced by any experiment

Every experiment in this laboratory computes properties of a chosen graph model. Zero experiments to date bear on physical spacetime. physicalClaim = false throughout.

Run the instruments

Every live row above is produced by the Phase 3 instrument suite, which exposes the substrate controls, the feasible frontier and the identity boundary map. The metric-sanity layer sits in model sanity.