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Adjacency Theory markAdjacency Theory

Phase 79 · Peer-review readiness

Stage-1 Package

A Registered-Report-shaped dossier for a study that has not been reviewed, registered, built or run. Everything below is fixed before data exists, so that no result can be rescued after the fact.

internal red team: ACTIVE / SUBSTANTIALexternal technical review: NOT STARTEDformal peer review: NOT STARTEDpreregistration: NOT FILEDhardware: NOT BUILTphysical evidence: NONE

Section 1

Research question

In a programmable locally-coupled oscillator apparatus, can genuinely new information — a payload generated by a hardware TRNG only after arming — be decoded at endpoint B earlier than the conservative empirical lower bound of every inventoried physical causal path from endpoint A?

The expected answer is no. The study is designed so that 'no' is publishable, informative and fully specified in advance.

Section 2

Competing models M0–M5

Every model that could produce the data, with our own hypothesis ranked last on prior plausibility.

M0

prior high

Ordinary local finite-speed physics (null)

T_decode is consistent with D_tau at every inserted delay setting. Δ ≈ 0 within the uncertainty budget.

M1

prior moderate

Latent-connectivity / architecture effect

T_decode beats the intended logical route C0 but never beats D_tau. Margin does not scale with inserted delay.

M2

prior moderate

Instrumentation artefact

A roughly constant apparent margin, independent of inserted delay, and disagreement between the two timing stacks.

M3

prior moderate

Hidden conventional shortcut

Margin tracks the bypass delay and is caught by the channel-inventory audit and the B3 positive controls.

M4

prior moderate

Conventional nonlinear mimic

Target-like latency and sparsity scaling produced by ordinary local nonlinearity, caching or scheduling; fails the mechanism audit.

M5

prior extremely low

Causal-bound anomaly (Adjacency Theory hypothesis)

Δ > 0 by the preregistered guard band, preserved or growing across delay settings, surviving every control.

Section 3

Hypotheses

H0primary

T_decode(B) ≥ D_tau(A,B) − ε_cal at every delay setting.

Supports M0/M1. This is the expected outcome and is accepted, not merely 'not rejected'.

H1primary

Δ = D_tau,lower − T_decode,upper ≥ G at every delay setting, where G is the fixed guard band.

Only outcome that opens a causal-bound anomaly candidate. Requires all quality gates and all controls to pass.

H2secondary

T_decode < T_C0 while T_decode ≥ D_tau − ε_cal.

Latent-connectivity / architecture effect. Interesting engineering, no causal claim.

H3secondary

Observed margin is independent of inserted calibrated delay.

Fixed instrumentation offset (M2). Auto-classifies as artefact regardless of magnitude.

H4secondary

Observed margin scales with a specific port, node ID or wiring instance.

Topology dependence (M3/M4). Invalidates the run set.

Section 4

Apparatus diagram

Placeholder — schematic not frozen

ENDPOINT ATRNG payloadtimestamp A16-node oscillator substratecalibrated delay banktimestamp BENDPOINT B decode

Independent timing stacks at A and B, offline blinded DAQ, RF and power isolation, environmental sensing, and a hidden-shortcut injection fixture sit around this chain. The frozen wiring diagram is a B0 deliverable and does not exist yet.

Section 5

Stage gates B0–B8

Each gate has entry criteria, a test, a pass condition and a stated failure response. Gates run in order and none may be skipped.

B0Clock loopback + uncertainty budgetnot run
Entry
Both timing stacks powered, calibration standards in place.
Test
Loopback timestamping of a known path with both stacks, across temperature.
Pass
Measured σ_total established and both stacks agree within their combined uncertainty.
On failure
Programme halts. No later phase runs on an unmeasured budget.
B1Post-arming entropy and decodenot run
Entry
B0 passed. TRNG installed at A.
Test
Payload generated strictly after arming; hashed at creation; decoded at B over a known route.
Pass
Entropy health logged and ≥99% payload fidelity over the baseline route.
On failure
Fix entropy chain or decoder before any timing claim.
B2Delay bank calibration and driftnot run
Entry
B1 passed.
Test
Bidirectional group-delay characterisation of every delay segment, repeated over temperature and time.
Pass
Per-segment delay known to within budget and drift bounded over a run window.
On failure
Re-characterise or replace segments; extend guard band only before freeze.
B3Hidden-shortcut detection challengenot run
Entry
B2 passed. Custodian installs secret bypasses.
Test
Blind set of runs, some containing a deliberately concealed conventional bypass.
Pass
100% detection. Anything below 100% is a hard stop.
On failure
Channel inventory is incomplete by demonstration. No confirmatory run is permitted.
B4Ordinary C0 propagation baselinenot run
Entry
B3 passed.
Test
Measure conventional route latency under strongest permitted signalling.
Pass
Stable, reproducible T_C0 with characterised spread.
On failure
Diagnose apparatus instability before proceeding.
B5Nonlinear / moving-front analoguenot run
Entry
B4 passed.
Test
Run the oscillator substrate dynamics with the three-ruler mechanism audit active.
Pass
Dynamics reproducible and auditable. No causal claim is made at this gate.
On failure
Substrate redesign; verification clock does not advance.
B6Blinded mixed controlsnot run
Entry
B5 passed. Sealed schedule held outside the run team.
Test
Interleaved null, sham, cable-swap and bypass conditions under blinding.
Pass
Analysis pipeline classifies every control condition correctly while blind.
On failure
Pipeline or blinding repaired, then B6 repeats in full.
B7Frozen confirmatory causal-bound campaignnot run
Entry
B0–B6 all passed. Protocol, firmware, topology and analysis hashes lodged.
Test
The preregistered run counts, executed once, against the frozen decision rule.
Pass
The rule returns its verdict. Any verdict is a result.
On failure
Deviation logged and published. No re-run under a revised rule.
B8Independently assembled second apparatusnot run
Entry
B7 complete with any outcome.
Test
A second rig built from the specification by different hands reproduces the campaign.
Pass
Preregistered result reproduces, or does not, and both are published.
On failure
Single-apparatus results are downgraded, not defended.

Section 6

Causal-channel inventory

Every physical route by which influence could travel from A to B, and how each will be calibrated.

ChannelCalibration methodRisk
E1Intended optical / fibre delay routesBidirectional group delay per spool, OTDR continuity, thermal sweep.low
E2Analogue coupling wires between oscillator nodesPairwise pulse-response earliest onset.medium
E3Digital FPGA IO and control linksPer-pin loopback with firmware frozen.high
E4Clock distribution and any shared referenceExplicit inventory; independence demonstrated, never assumed.high
E5Power rail and ground couplingIsolated / battery domains where possible; coupling characterised where not.high
E6RF, capacitive and inductive leakageShielded enclosure comparison, spectrum scans, radios disabled.high
E7DAQ, storage and analysis host pathsOffline and blinded; no live path between endpoints during a run.medium
E8Optical leakage and stray line-of-sightDark-box checks and photodiode scans.medium

Section 7

Primary statistic, guard band and uncertainty budget

Δ = Dτ,lower(A,B) − Tdecode,upper(B)
The single preregistered statistic. Nothing else decides the outcome.

D_tau,lower is the minimum over all inventoried physical paths of the summed per-edge earliest influence delays, each taken at its conservative lower confidence limit.

T_decode,upper is the upper confidence limit on the earliest time B decodes the post-arming payload above the preregistered bit-error threshold. First physical influence and first valid decode are recorded separately; only decode enters the statistic.

A positive Δ that does not exceed the guard band is reported as null. There is no 'suggestive' category.

Fixed guard band

G = max(10 · σ_total, 2 ns engineering floor)

G is fixed at protocol freeze and cannot be revised after any data exists, in either direction.

The delay-amplified design puts µs-scale delay on every permitted route, so a ns-scale guard band is a vanishing fraction of the bound rather than a knife-edge.

Uncertainty budget — design only

source trigger jitter15 psArming-to-emission latency spread at A.
timestamp A25 psTDC quantisation plus differential nonlinearity.
timestamp B25 psIndependent stack, different calibration model.
cable / fibre group-delay model20 psResidual after bidirectional characterisation.
FPGA IO calibration30 psDominant term; must be measured at B0.
environmental drift20 psThermal and supply drift between calibration and run.
σ_total (quadrature)56 psAssumed, not measured.

Section 8

Sampling, exclusions and stop rules

Sample size and power

Delay settings
≥4 inserted calibrated delays spanning at least one decade.
Runs per condition
≥20 valid runs per condition per delay setting, fixed before collection.
Conditions
Target, null, sham, cable-swap, hidden-bypass positive control.
Stopping rule
Collection stops at the preregistered count. No optional stopping, no extension on an interesting trend.
Power basis
Guard band G against measured σ_total from B0. The full calculation requires a metrologist and is not yet complete.

Exclusion criteria

  • Calibration certificate expired at run time.
  • Configuration, firmware or topology hash mismatch against the frozen record.
  • The two timing stacks disagree beyond their combined uncertainty.
  • Entropy health check failed or payload generated before arming.
  • Environmental sensor out of the preregistered window.
  • Raw-data integrity checksum failure.

Every exclusion criterion is outcome-neutral: it can be evaluated while blind, and none references the value of Δ. Excluded runs are published alongside valid runs with their exclusion reason.

Stop rules

  • B3 hidden-shortcut detection below 100% — hard stop, no confirmatory campaign.
  • Any prohibited controller read or write during a run — the entire run set is invalidated, not the sample.
  • Timing-stack disagreement persisting across a session — stop and recalibrate from B0.
  • Blind key exposure to any member of the run or analysis team — campaign restarts with a new schedule.
  • Any change to frozen firmware, topology or analysis code — the freeze is broken and the campaign is exploratory from that point.

Section 9

Blinding, randomisation and controls

Blinding

  • Sealed condition schedule generated and held by a custodian outside the run team.
  • Analysts blind to condition labels until the frozen analysis has been executed and its output hashed.
  • Destination decoder blind to the source bits.
  • Fake timing-offset injection used to verify that analysts cannot infer condition from the data.

Randomisation

  • Condition order randomised within the sealed schedule; controls interleaved, never batched at the end.
  • Physical wiring randomised after firmware freeze.
  • Topology relabelling and endpoint remapping between run sets so no lookup can key off fixed node IDs.
  • Independently generated topologies loaded post-freeze; behaviour must transfer with no retuning.

Controls — null, sham and hidden-shortcut positive

K1Hidden-shortcut positive controlConcealed conventional bypasses installed by the custodian; audit must detect 100%.
K2Null conditionApparatus armed, no payload emitted. Any decode is a pipeline failure.
K3Sham conditionPayload emitted into a disconnected route. Decode must not occur.
K4Cable-swap equivalenceLong route replaced by an equivalent short route; classification must change exactly as predicted.
K5Shuffled payloadDecoder run against a shuffled payload; must fail the bit-error threshold.
K6Source disconnectionPhysical disconnection at A mid-set; all downstream decode must cease.
K7Shielding comparisonRuns with and without RF enclosure and absorber; margin must not track shielding state.
K8Sham firmwareAdaptive caching and centralised scheduling firmware loaded as positive controls; mechanism audit must reject them.
K9Delay-scaling artefact testMargin plotted against inserted delay; a flat margin classifies as artefact automatically.

Section 10

Data, code, hashes and deviations

Raw-data policy

  • Raw unsmoothed timestamps and waveforms published for every run, valid or excluded.
  • Analysis code published with the hash lodged before unblinding.
  • Firmware, topology, wiring map and calibration certificate IDs published with each run manifest.
  • Lab log published, including the entries that record mistakes.
  • No arrival metric may depend on smoothing, windowing or any parameter chosen after data exists.

Code and firmware hashes

Protocol documentAt freeze, before B0PENDING
Analysis codeBefore any unblindingPENDING
Endpoint firmware (A and B)Before wiring randomisationPENDING
Topology / wiring mapPer run setPENDING
Raw datasetAt acquisition closePENDING
Sealed blind scheduleAt generation, held by custodianPENDING

Section 11

Replication plan and claim ladder

R1 — same rig, new operators

Removes operator-specific procedure effects.

R2 — independently rebuilt timing stack

Removes shared calibration-model error.

R3 — second apparatus, same specification

Removes apparatus-specific systematics.

R4 — external laboratory, independent team

The only rung that permits language beyond 'candidate'.

C0Synthetic / exploratory resultStatements about our own code. Nothing about nature. Everything published so far sits here.
C1Apparatus characterisationStatements about this rig's measured behaviour.
C2Architecture / latent-connectivity effectStatements about routing efficiency. Explicitly not causal.
C3Causal-bound anomaly candidate (single apparatus)A request for replication. No physical interpretation.
C4Replicated causal-bound anomalyA statement that something is unexplained. Still not a mechanism, still not FTL.
C5New physicsRequires an independent theory, external confirmation and exclusion of every systematic. Not reachable by this programme alone.

Section 12

OSF preregistration checklist

Rigorous preregistration requires every decision to exist before the data does.

NOT YET REGISTERED10 of 12 items drafted
P1Hypotheses stated explicitly and directionallyH0–H4 written with quantitative thresholds.drafted
P2All variables defined operationallyΔ, D_tau, T_decode, fidelity, active fraction and audit outcome are defined with measurement procedures.drafted
P3Every decision made before data existsGuard band, run counts, exclusions and decision rule fixed at freeze.drafted
P4If/then contingencies for each possible outcomeThe classification ladder maps every outcome branch in advance.drafted
P5Statistical tests and decision criteria namedFrozen decision rule with zero free parameters; slope and endpoint thresholds fixed.drafted
P6Exclusion criteria stated and outcome-neutralSix criteria, all evaluable while blind.drafted
P7Model forms and covariates specifiedRegression form across log2 N and delay settings specified; covariates limited to temperature and supply.drafted
P8Commitment to report all outcomesPublication of valid and excluded runs regardless of result.drafted
P9Planned exploratory analyses labelled as suchExploratory analyses enumerated and firewalled from the confirmatory rule.drafted
P10Sample size and power justificationRun counts drafted; the formal power calculation needs a metrologist and measured σ_total.not ready
P11Deviation reporting policyWritten and published.drafted
P12Registration lodged, timestamped and publicNot filed. Nothing above counts until this is done.not ready

Section 13

Reviewer attack log

Written against ourselves, using role IDs because no real reviewer exists yet.

attacks logged

14

critical

7

open

6

closed

0

need hardware to close

10

X01R-MET-1 · MetrologycriticalOPENhardware required

The causal-path inventory is incomplete, so D_tau is too slow and any advance is an unlisted wire.

Owner
Metrology lead (unfilled)
Evidence required to close
Per-channel empirical calibration on built hardware plus 100% detection in the B3 bypass challenge.
X02R-EXP-1 · Experimental physicscriticalMITIGATED BY DESIGNhardware required

Entropy leaked before t0 — the payload was knowable to B before arming.

Owner
FPGA lead (unfilled)
Evidence required to close
Arming-order traces, TRNG health logs and payload hash timestamps from B1.
X03R-MET-2 · MetrologycriticalMITIGATED BY DESIGNhardware required

Common-mode clock error makes both stacks wrong in the same direction.

Owner
Timing lead (unfilled)
Evidence required to close
Demonstrated absence of a shared reference chain plus two calibration models that disagree by construction.
X04R-RF-1 · RF / EMIcriticalOPENhardware required

RF, ground or power-rail leakage carried the payload outside the inventory.

Owner
RF engineer (unfilled)
Evidence required to close
Shielded/unshielded comparison, spectrum scans, isolated supply runs, all showing no margin dependence.
X05R-NLD-1 · Nonlinear dynamicscriticalOPEN

An ordinary local nonlinear mechanism reproduces the behaviour; uniqueness is unproven.

Owner
Nonlinear dynamics lead (unfilled)
Evidence required to close
A mechanism-discrimination experiment, not an argument. None currently exists.
X06R-FPGA-1 · FPGA / embeddedcriticalMITIGATED BY DESIGNhardware required

A hidden path inside the FPGA fabric or its IO carries state between endpoints.

Owner
FPGA lead (unfilled)
Evidence required to close
Frozen bitstream hash, per-pin loopback calibration and independent netlist review.
X07R-STAT-1 · StatisticsmajorMITIGATED BY DESIGN

Analysis flexibility: window, threshold or smoothing chosen after seeing data.

Owner
Independent statistician (unfilled)
Evidence required to close
Hash of the analysis code lodged before unblinding; zero free parameters in the rule.
X08R-NLD-2 · Nonlinear dynamicsmajorMITIGATED BY DESIGNhardware required

The effect follows specific ports or node IDs rather than the dynamics.

Owner
Experimental lead (unfilled)
Evidence required to close
Post-freeze topology relabelling with behaviour transferring untuned.
X09R-EXP-2 · Experimental physicsmajorOPENhardware required

Scaling beyond N=64 is unverified, so the claimed trend may not exist.

Owner
Architecture lead
Evidence required to close
Substrate runs at larger N, in simulation first and then on hardware.
X10R-SKEP-1 · Adversarial skepticmajorOPEN

Exact-fabric concurrency remains unresolved on your own kill board; the architecture is not ready to be built.

Owner
Architecture lead
Evidence required to close
A concurrency resolution or an explicit statement that the bench test does not depend on it.
X11R-MET-3 · MetrologymajorMITIGATED BY DESIGNhardware required

Calibration drifts between characterisation and run, so D_tau is stale.

Owner
Timing lead (unfilled)
Evidence required to close
Drift bounds measured at B2 and calibration expiry enforced as a stop rule.
X12R-STAT-2 · StatisticsmoderateMITIGATED BY DESIGN

Multiple testing across delay settings and conditions inflates the false-positive rate.

Owner
Independent statistician (unfilled)
Evidence required to close
A single joint decision rule requiring the signature at every delay setting, not a family of tests.
X13R-SKEP-2 · Adversarial skepticmajorMITIGATED BY DESIGNhardware required

The blind was compromised — the run team could infer conditions.

Owner
Blind custodian (unfilled)
Evidence required to close
Custodian outside the team, fake-offset injection and a post-hoc guessing test the team must fail.
X14R-SKEP-3 · Adversarial skepticcriticalOPENhardware required

Replication is not independent — same people, same parts, same assumptions.

Owner
Programme lead
Evidence required to close
R4: an external laboratory reproducing from the specification with no shared personnel.

Section 14

Journal fit

PROCESS OPTION — FIT NOT ASSESSED

Nature Methods (Registered Reports)

Its Registered Report format is aimed at comprehensive comparisons of established, related methods and tools, and it states explicitly that the format is not suitable for method-development papers.

LIKELY NOT A FIT — listed to prevent us assuming otherwise.

Scientific Reports

Operates a two-stage Registered Report format: Stage 1 review of methods and analysis before data collection, Stage 2 review after the study.

POSSIBLE FIT TO INVESTIGATE — not a target guarantee.

Other multidisciplinary or metrology venues

Scope, format eligibility and editorial interest all unknown.

TO BE IDENTIFIED WITH COLLABORATORS.

Section 15

Partner review board

Target 5–7 external reviewers, at least 2 fully independent. Currently 0 filled.

Precision timing / metrology

unfilled

Attack the uncertainty budget, the calibration chain and the independence of the two timing stacks.

Experimental physics

unfilled

Decide whether the measurement can answer the question at all.

Nonlinear dynamics

unfilled

Propose ordinary local mechanisms that reproduce the behaviour.

FPGA / embedded

unfilled

Attack firmware freeze, arming order and every path where a bit could arrive early.

RF / EMI

unfilled

Assume an unlisted coupling path exists and find it.

Statistics / reproducibility

unfilled

Attack power, sampling, exclusions, blinding and remaining analytic freedom.

Adversarial skeptic

unfilled

No stake, no relationship, mandated to recommend rejection if rejection is right.

Reviewer outputs required

  • A signed and dated written critique.
  • Objections ranked by severity, using the same scale as the attack log.
  • An explicit list of protocol changes required before Stage 1 submission.
  • A final readiness vote: ready / ready with changes / not ready.

At least two reviewers must hold no funding, equity, advisory or employment relationship with the programme. Independence is declared in writing and published with the critique.

Workflow

  1. 1Technical brief issuedTwo pages plus the frozen protocol and its hash.
  2. 230-minute scientific critique callNo NDA unless the reviewer requires one. Criticism is the deliverable.
  3. 3Protocol review windowTwo weeks with full access to models, code and synthetic red-team results.
  4. 4Written critique returnedSigned, dated, severity-ranked, published verbatim with our response.
  5. 5Revision cycleWe rewrite against the critique, including the parts that hurt.
  6. 6Readiness voteRecorded per reviewer. A split vote is published as a split vote.

Section 16

Infrastructure relevance

Potential infrastructure relevance — not an endorsement

The Brookhaven National Laboratory Quantum Network Facility is open to the user community to benchmark performance and validate concepts, and the BNL–Stony Brook prototype uses White Rabbit-supported timing switches with purpose-built classical control across a roughly 70 km fibre span. That combination — long calibrated fibre, distributed sub-nanosecond timing and instrumentation expertise — is exactly the class of infrastructure a delay-amplified causal-bound test needs.

  • We have not approached this facility and no relationship exists.
  • Our experiment is not a quantum experiment; the relevance is timing, fibre and metrology expertise.
  • Listing a facility is not endorsement by that facility, and access would be decided by them on scientific merit.