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Adjacency Theory markAdjacency Theory

Lab · AT-0

Reproduction engine

Reproduce known and hand-checkable relational-geometry behaviour. Every run is deterministic in its seed, model version and algorithm version.

User parameters

Click any edge in the graph to override its coupling directly.

Emergent geometry

AT-RDH-0 v0.1.0 · dijkstra-log-coupling-1.0.0
Edge 0-1 — R = 0.500Edge 1-2 — R = 0.500Edge 2-3 — R = 0.500Edge 3-4 — R = 0.500Edge 4-5 — R = 0.500Edge 5-6 — R = 0.500Edge 6-7 — R = 0.500ABCDEFGH

D(A,B)

4.8520

Hops

7

Mean R

0.500

Edges

7

Runtime

0.0 ms

geodesic = A → B → C → D → E → F → G → H

Sensitivity matrix ∂D/∂R_ij

Central-difference partials. Violet bars sit on the current geodesic.

  • 0-1-2.000
  • 1-2-2.000
  • 2-3-2.000
  • 3-4-2.000
  • 4-5-2.000
  • 5-6-2.000
  • 6-7-2.000

Topology sweep · AT-0005

Same node count, coupling statistics and seed across five topologies.

TopologyDHopsEdges
chain4.85277
ring0.69318
lattice2.079310
small-world0.693110
random0.693113

Constraint engines

An unimplemented constraint returns NOT MODELED. It never returns PASS.

PASSMetric validity

non-negativity ok · symmetry ok · triangle inequality ok · identity of indiscernibles ok

PASSNumerical stability

Graph connected; shortest-path solution finite and NaN-free.

NOT MODELEDCausality / signalling

AT-0 has no time coordinate, no Lorentzian structure and no light cones. Causal behaviour cannot be evaluated until AT-4.

NOT MODELEDEnergy conditions

No stress-energy tensor is defined in this model. Energy-condition analysis begins at AT-5.

NOT MODELEDGeometric reconstruction

Whether these graph distances embed into a recognisable manifold is untested until AT-3.

NOT MODELEDPhysical correspondence

No mapping from relational couplings to measurable physical quantities exists. Graph-distance reduction is not physical distance reduction.

The transform under test

d_ij = −L · ln(R_ij)
A modelling convention chosen for monotonicity and additivity. It is not a derived law of physical spacetime, and no result on this page is a physical claim.
Inspect result object
{
  "modelId": "AT-RDH-0",
  "modelVersion": "0.1.0",
  "algorithmVersion": "dijkstra-log-coupling-1.0.0",
  "experimentId": "AT-0001",
  "inputs": {
    "topology": "chain",
    "nodeCount": 8,
    "baseCoupling": 0.5,
    "noise": 0,
    "lengthScale": 1,
    "source": 0,
    "target": 7,
    "seed": "AT-0001"
  },
  "metrics": {
    "effectiveDistance": 4.852030263919617,
    "hops": 7,
    "edgeCount": 7,
    "nodeCount": 8,
    "meanDegree": 1.75,
    "meanCoupling": 0.5,
    "maxSensitivity": 2.000000026667557,
    "runtimeMs": 0
  },
  "constraintResults": [
    {
      "id": "metric-validity",
      "status": "PASS"
    },
    {
      "id": "numerical-stability",
      "status": "PASS"
    },
    {
      "id": "causality",
      "status": "NOT_MODELED"
    },
    {
      "id": "energy-conditions",
      "status": "NOT_MODELED"
    },
    {
      "id": "geometric-reconstruction",
      "status": "NOT_MODELED"
    },
    {
      "id": "physical-correspondence",
      "status": "NOT_MODELED"
    }
  ],
  "physicalClaim": false,
  "warnings": [],
  "randomSeed": "AT-0001",
  "timestamp": "2026-08-25T06:49:40.316Z"
}