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Adjacency Theory markAdjacency Theory

Roadmap

Stage gates AT-0 through AT-X

A gate opens only when its exit criteria are met. Interesting results from an earlier gate are not a reason to skip ahead.

  1. AT-0

    Reproduction

    in progressgate 1 / 8

    Reproduce known and hand-checkable relational-geometry behaviour. Validate implementation before novelty.

    Entry criteria

    • A specified transform and a deterministic seed pipeline.

    Exit criteria

    • Shortest-path results match hand calculation on chains and lattices.
    • Identical seed, model version and algorithm version reproduce identical metrics.
    • Metric audit runs on every result and can fail loudly.
  2. AT-1

    Relational Perturbation

    prototypegate 2 / 8

    Measure the response ΔD to a controlled ΔR; compute sensitivity and robustness.

    Entry criteria

    • AT-0 exit criteria met.

    Exit criteria

    • Sensitivity partials verified against analytic values on solvable graphs.
    • Noise ensembles with reported σ(D) and geodesic stability.
    • No unexplained non-monotonic response.
  3. AT-2

    Adjacency Transition

    prototypegate 3 / 8

    Search for nonlinear regimes where small relational changes produce large geometric responses.

    Entry criteria

    • AT-1 exit criteria met.

    Exit criteria

    • Leverage distributions that beat a shuffled null model reproducibly.
    • Path-switch thresholds characterised across topologies.
  4. AT-3

    Geometry Reconstruction

    lockedgate 4 / 8

    Test whether relational states reconstruct recognisable metric or geometric structure rather than arbitrary graph distances.

    Entry criteria

    • AT-2 exit criteria met.

    Exit criteria

    • Embedding distortion falling with system size for structured states.
    • A clear separation from random-state controls.
  5. AT-4

    Causal Geometry

    lockedgate 5 / 8

    Introduce time, Lorentzian structure, light cones and signalling constraints.

    Entry criteria

    • AT-3 exit criteria met.

    Exit criteria

    • A causality engine that can return PASS or FAIL rather than NOT MODELED.
    • No operation in the framework produces a spacelike signal.
  6. AT-5

    Energy Correspondence

    lockedgate 6 / 8

    Estimate or derive the stress-energy and energy-condition implications of candidate geometric changes.

    Entry criteria

    • AT-4 exit criteria met.

    Exit criteria

    • An explicit energy accounting with stated conditions and bounds.
  7. AT-6

    Physical Prediction

    lockedgate 7 / 8

    Produce an observable prediction that distinguishes the hypothesis from alternatives.

    Entry criteria

    • AT-5 exit criteria met.

    Exit criteria

    • A quantitative signature with an experimental regime and an error budget.
  8. AT-X

    Experimental Search

    lockedgate 8 / 8

    Only after every previous gate survives: identify physically accessible experiments.

    Entry criteria

    • AT-6 exit criteria met and independently reviewed.

    Exit criteria

    • Not defined. This gate is deliberately far away.

Next experiment registry · AT-0011 → AT-0023

What the gates are waiting on

AT-0011AT-2 · implemented

Adjacency Threshold Detection

Locate the relational state at which effective separation first satisfies D ≤ ε, and record the cost of reaching it.

ε is a chosen number in a graph model. Crossing it means nothing physical.

AT-0012AT-2 · prototype

Adjacency Stability

Determine whether a state satisfying D ≤ ε survives bounded perturbation of the relational state, or collapses immediately.

Stability of a simulated configuration is not stability of anything real.

AT-0013AT-2 · specified

Reversal and Hysteresis

Reverse an accepted transformation step by step and test whether the return path costs the same as the outbound path.

Path dependence in a greedy search is a property of the search, until shown otherwise.

AT-0014AT-2 · specified

Adjacency Debt

Measure whether reducing D between one pair systematically increases separation elsewhere in the same relational state.

Any conserved-looking quantity here is a bookkeeping artefact until derived, not assumed.

AT-0015AT-2 · specified

Multiple Simultaneous Adjacencies

Attempt to satisfy D ≤ ε for several pairs at once and find where the demands become mutually unsatisfiable.

Infeasibility in a toy optimiser is a statement about the optimiser.

AT-0016AT-2 · implemented

Identity Failure Boundary

Push the transformation until ΔI exceeds tolerance, and characterise where identity preservation fails.

Identity here is a stipulated vector. Its failure boundary is a property of that stipulation.

AT-0017AT-3 · specified

Conservation Surface Search

Search the space of transformations for any quantity that stays invariant across accepted moves.

An invariant of a model is not a conservation law. Deriving one would require the model to mean something first.

AT-0018AT-2 · specified

Path Independence

Test whether different transformation orders reaching the same final R also incur the same adjacency cost.

Order effects are combinatorics, not thermodynamics.

AT-0019AT-3 · specified

Self-Organised Adjacency

Let local update rules act on the relational state without a global objective, and see whether low-separation structure emerges unbidden.

Emergence in a cellular rule set is common and cheap. It carries no explanatory weight by itself.

AT-0020AT-2 · implemented

Discovery Sweep

Run the bounded optimiser across seeds and collect the candidate transformations, the failures, and the unexpected results.

A ranked candidate list is a ranked list of edits to numbers.

AT-0021AT-2 · implemented

Relational Relocation

Change a tracked object's relational neighbourhood from Origin to Destination while preserving its identity vector. The object never moves.

MATHEMATICAL / COMPUTATIONAL MODEL. PHYSICAL EVIDENCE: NONE. This is not relocation of anything.

AT-0022AT-2 · implemented

Minimum Relocation Cost

Grid-search the cheapest relational transformation that reaches the destination-similarity target inside the identity tolerance.

A minimum over a chosen grid, under a chosen cost function.

AT-0023AT-2 · implemented

Continuity Challenge

Inspect the accepted transformation history and report whether the modelled transition passed through intermediate relational states.

Absence of intermediate states in a graph model is not evidence that a physical transition can be discontinuous.

AT-0024AT-3 · implemented

Spectral Connectivity Response

Measure how algebraic connectivity λ₂ of the weighted Laplacian responds to bounded single-relation changes.

λ₂ is a whole-graph observable, not a separation between two objects.

AT-0025AT-3 · implemented

Topology Robustness Sweep

Run one perturbation protocol across random, small-world, scale-free and lattice families to see what survives a change of topology.

Robustness across toy families is not robustness across physical systems.

AT-0026AT-3 · implemented

Observable Competition

Rank geodesic, resistance, efficiency, λ₂ and spectral radius by measured response and noise robustness for one identical transformation.

A high rank makes an observable responsive, not real.

AT-0027AT-3 · implemented

Scale Sweep

Repeat the probe protocol across bounded graph sizes and fit a scaling trend only when the log–log diagnostic supports one.

Five bounded sizes cannot distinguish a power law from a logarithm.

AT-0028AT-3 · implemented

Noise and Adversarial Stability

Add bounded noise and randomised control changes, then check whether candidates persist, disappear or reverse sign.

Survival is measured inside one generator and one observable.

AT-0029AT-3 · implemented

Invariant Search

Look for quantities that stay fixed under accepted transformations, separating invariants imposed by construction from invariants actually discovered.

No invariant here is a conserved physical quantity; energy and causality stay NOT MODELED.

AT-0030AT-3 · implemented

Missing-Rule Search

Score candidate response laws O = F(R, I, T, Q) on response, cost, identity deviation, invariance and stability minus complexity, then attack the winner with seven countermodels.

A promoted candidate is a candidate response law inside a toy model. It is not new physics.

Standing rule