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Adjacency Theory markAdjacency Theory

Programme specification · August 30, 2026 · E-Ladder v1

The Road to Physical Evidence — What It Would Actually Take

Every result this programme owns is a computation. A computation is never evidence about spacetime. This page defines the exact ladder from where we stand (E0) to a defensible physical measurement (E6), the apparatus each rung needs, what it costs, and — most importantly — the measurement that would end the hypothesis.

CURRENT RUNG: E0 · PHYSICAL EVIDENCE: NONE · NO APPARATUS BUILT · NO DATA TAKEN · NOTHING BELOW IS A RESULT

Invent the walls. Then try to break them.

01 · What counts as physical evidence

Counts

  • A measurement on physical hardware, taken by instruments with a stated calibration chain and a stated timing reference.
  • A preregistered discriminator: two architectures, one fixed input, and a predicted DIFFERENCE that is stated in writing before the apparatus is switched on.
  • An effect that survives a null-architecture control built by someone who wants it to fail.
  • A replication on a second apparatus, in a second lab, from the written protocol alone.

Never counts

  • Any simulation, however large. Simulations test our reasoning, not nature.
  • A speedup that a conventional engineered network also achieves. Ordinary routing is not evidence of new physics.
  • Any effect whose size is inside the calibration uncertainty of the timing chain.
  • A result that only appears in the analysis pipeline of its own authors.
  • Agreement between our model and a published result we did not predict in advance.

02 · The discriminator requirement

A discriminator is a single measurable quantity Q, an apparatus that produces Q, and two architectures — ADJACENCY and ORDINARY — that our own model predicts give DIFFERENT values of Q under identical input, identical energy budget, and identical preparation.

Q_ADJACENCY ≠ Q_ORDINARY, at identical input, identical energy budget, identical preparation
No discriminator, no experiment. Everything else is instrumentation.

Already excluded by our own gates

Raw signal speed (first arrival)

Excluded by our own Phases 47–55 locality bounds and the Causal-Cone gates (C1–C8). Every architecture we built respects the ordinary causal cone exactly. Speed cannot discriminate; measuring it faster only measures our clocks.

Entanglement distribution rate

Excluded by the Phase 251 Pair-Resource Fare Gate. A pair-owned resource costs its full distribution distance. An engineered quantum network reproduces every number, so a positive result would be conventional quantum networking, not new physics.

End-to-end latency of a routed fabric

Excluded by the Phase 73 Frontier Theorem. Architecture alone cannot beat the bound; any win is a routing win and is already explained.

Total energy or work to complete a transfer

Excluded by lifecycle accounting (AT-0673→688). Sublinear cost appears only under high reuse (~574 trips to break even), which is an infrastructure economics claim, not a physics claim.

Surviving candidates — specified, never measured

Sector-dependent response geometry

SPECIFIED, NEVER MEASURED

Prepare the same fabric in two global sectors that our model says carry different effective adjacency. Drive one endpoint. Measure the SHAPE of the response cone at fixed time — not its speed. ADJACENCY predicts a sector-dependent cone shape at fixed first-arrival time; ORDINARY predicts identical shapes.

Spectral-dimension drift under load

SPECIFIED, NEVER MEASURED

Measure the effective spectral dimension d_s of a physical coupled-oscillator fabric via its diffusion return probability, while a second control parameter is swept. ADJACENCY predicts a measurable drift in d_s with no change in nearest-neighbour coupling; ORDINARY predicts d_s pinned by the wiring.

Holonomy defect residue

SPECIFIED, NEVER MEASURED

Transport a state around a closed loop in parameter space in a physical fabric. Measure the residue after return. ADJACENCY predicts a defect-charge-dependent residue that is invariant under loop reparameterization; ORDINARY predicts a residue fully accounted for by dissipation.

03 · The E-Ladder — E0 to E6

E0

Computational specification

REACHED

Can the hypothesis be stated as a finite model with gates that can fail?

Deliverable · The ledger through Phase 252: 250+ toy phases, an explicit gate stack, a falsification register, and a documented record of every branch that was closed.

Pass · A written model whose predictions are numerically definite and whose failures are published alongside its survivals.

Kill · The model cannot be made definite enough to predict a difference. (Not triggered — but note that most branches HAVE been closed here.)

Cost

Complete. Compute only.

Time

Complete.

E1

Preregistered discriminator

IN SPEC

Is there ONE measurable quantity where our model and ordinary physics disagree, written down before any apparatus exists?

Deliverable · A single-page registered report per candidate: apparatus, quantity Q, both predicted values with uncertainty, the analysis pipeline frozen, and the null-result statement pre-written.

Pass · A time-stamped, externally-hosted preregistration that a hostile reader agrees is falsifiable.

Kill · Every candidate discriminator reduces, on analysis, to a quantity ordinary physics already predicts identically. If that happens, the physical programme ends here and the result is published as a no-go.

Cost

≈ $0 (writing + registry fees).

Time

4–8 weeks.

E2

Bench apparatus and calibration chain

NOT STARTED

Can we build hardware whose timing and amplitude uncertainty is smaller than the predicted difference?

Deliverable · A coupled nonlinear-oscillator array (Experiment 001 design) or an FPGA/NoC fabric, with a traceable timing reference, a documented calibration chain, and a measured noise floor.

Pass · Measured instrument uncertainty on Q is at least 5× smaller than the smallest predicted ADJACENCY–ORDINARY difference.

Kill · The predicted difference is smaller than any achievable noise floor on any accessible platform. Then the hypothesis is untestable with current technology and must be labelled as such — permanently, and on the front page.

Cost

$40k–$180k depending on platform (FPGA fabric cheapest; cryogenic platforms far higher).

Time

6–12 months.

E3

Null-architecture control

NOT STARTED

Does the ordinary architecture, built on the same hardware by the same hands, give the ordinary answer?

Deliverable · The identical apparatus wired as a conventional fabric, measured with the identical pipeline, producing the ORDINARY prediction inside error.

Pass · The control reproduces textbook physics to within stated uncertainty. Without this, no positive result means anything.

Kill · The control disagrees with textbook physics — the apparatus is wrong, and every other number taken on it is void.

Cost

Included in E2 build; ≈ 20% additional run time.

Time

1–3 months.

E4

First discriminator run

NOT STARTED

Under the frozen protocol, does Q differ between the two architectures?

Deliverable · Raw data, the frozen pipeline's output, and the effect size with confidence interval — published whichever way it lands.

Pass · A difference in Q exceeding 5σ, stable across ≥3 independent runs, in the direction preregistered at E1.

Kill · No difference above the noise floor. This is a PHYSICAL RESULT and would be the programme's first one: a measured null that constrains the hypothesis. It would be published as prominently as any positive.

Cost

$15k–$50k in run time and personnel.

Time

3–6 months.

E5

Independent replication

NOT STARTED

Does a lab with no stake in the outcome get the same number from the written protocol alone?

Deliverable · A second apparatus, a second team, no contact during the run, and a comparison of blinded results.

Pass · Effect reproduced within stated uncertainty by a group that did not build the original apparatus.

Kill · Non-replication. The original result is retracted from every page of this site within one week.

Cost

$60k–$250k, or a collaboration in kind.

Time

12–24 months.

E6

Mechanism, not anomaly

NOT STARTED

Is the replicated effect derivable from a Hamiltonian, and does it predict something else we then find?

Deliverable · A microscopic derivation, plus one NEW preregistered prediction confirmed on a different platform.

Pass · A derivation plus a confirmed out-of-sample prediction. Only at this rung may the word 'evidence' be used without qualification.

Kill · The effect is real but is explained by a conventional mechanism. Then it is a nice piece of engineering physics and the adjacency hypothesis is still unsupported.

Cost

Programme-scale.

Time

3–10 years.

04 · The single blocker between E0 and E1

The single blocker between E0 and E1

Everything above E1 is money and time — solvable, ordinary, fundable. E1 is not. The programme has spent 250 phases closing branches precisely because a discriminator must survive our own gates before it can be preregistered, and almost none do. Speed is gone. Entanglement rate is gone. Latency is gone. Energy is gone. What remains are three shape-of-response candidates that have never been tested even in simulation against a matched ordinary control at physical parameter values.

Next concrete step · Phases 253–256

Phase 253–256: take the three surviving discriminator candidates and run them in simulation with PHYSICAL parameters — real oscillator Q factors, real coupling strengths, real thermal noise floors — against a matched ordinary control. Output a single number per candidate: predicted fractional difference in Q, and the instrument precision required to see it. Any candidate whose required precision exceeds what a real bench can deliver is removed from the list and recorded as closed.

05 · Candidate platforms

Best first platform

FPGA / network-on-chip fabric

Cheapest, fully instrumented, sub-nanosecond timing, and the architecture is reconfigurable so ADJACENCY and ORDINARY run on the same silicon.

It is a classical engineered network. A positive result here is an engineering result about routing, NOT about spacetime — and must be labelled that way regardless of how striking it looks.

$40k–$70k

Best physics platform

Coupled nonlinear oscillator array (Experiment 001)

Real continuous dynamics, measurable spectral dimension, a genuine noise floor, and the response-cone shape is directly observable.

Fabrication tolerance sets the achievable precision; the predicted differences may sit under it.

$90k–$180k

Only meaningful at E5+

Superconducting or photonic quantum testbed

The only platform where a pair-owned relational degree of freedom could be probed at all.

Expensive, oversubscribed, and every result there has a conventional quantum-networking explanation available. Not a starting point.

$250k+ or beam-time collaboration

06 · Standing integrity statement

PHYSICAL EVIDENCE: NONE. This page describes tests that have not been performed.

No apparatus described here has been built. No data described here has been taken.

The rung states on this page are programme status, not results. E0 is 'reached' only in the sense that a computational specification exists.

A positive result on any rung below E6 is an anomaly, not evidence of spacetime modification, and will be reported as an anomaly.

Every kill criterion above is binding. If one triggers, it is published on this page before it is discussed anywhere else.