# Wallbreaker Protocol P3

**Version:** 0.2.0  
**Date:** 15 September 2026  
**Status:** Formal protocol standard with an executable, unactivated P3-R1 single-device pilot; no hardware result

## 1. Mission and evidentiary rule

P3 converts “break every wall” into a finite set of typed obligations. A wall is marked **broken** only by one of three admissible evidence classes:

1. a written theorem with explicit assumptions;
2. a reproducible computation testing a finite implementation claim;
3. a preregistered physical measurement with a specified null, decision rule, and causal controls.

Metaphor, numerical coincidence, retrospective fit, and failure to reject a null are not wall breaks. Mathematical validity, implementation correctness, and physical truth remain separate.

## 2. Master wall ledger

| Wall | Exact obstruction | Break condition | Current status |
|---|---|---|---|
| W0: Internal consistency | One symbol silently denotes incompatible objects | Typed maps, units, domains, covariance, and no retained contradiction | Partially broken; seven layers, eight Q1 phases, and seven relative phases are separated |
| W1: Born information | Complete Born context contains all accessible outcome information | Held-out prefix-coded outcome e-process crosses its frozen threshold against a composite Born null | Open physically |
| W2: Decoder loss | A projection erases outcome-relevant distinctions | No retained collision, or a refined canonicalizer preserves the conditional outcome law | Open for every proposed physical lift |
| W3: Chronology | Predictor uses the setting or outcome after commitment | Immutable prediction for every allowed setting exists before delayed setting generation | Protocol-defined; not hardware-tested |
| W4: Measurement independence | Lift predicts the supposedly free setting | Structural isolation plus a predeclared operational upper margin on setting dependence | Open |
| W5: Context completeness | Detector drift, tomography error, or apparatus memory is omitted from the null | Crossing survives the composite calibrated context, process-memory model, causal breaks, and resets | Open |
| W6: No signaling | Local statistics depend on a remote spacelike setting | Remote-setting dependence remains below a predeclared operational margin with valid uncertainty bounds | Open |
| W7: Contextuality | Noncontextual predetermined values conflict with quantum measurement structure | Candidate explicitly supplies a contextual response law and passes compatible contextuality tests | Open |
| W8: Bell route | Locality, measurement independence, and quantum correlations cannot all be retained in a local hidden-variable completion | Candidate names the relaxed premise quantitatively and survives the consequences of that choice | Open |
| W9: Relativity and scale | No transformation law, units, coupling, or independently derived magnitude | Lorentz behavior, dimensional units, coupling scale, propagation law, and classical limit are derived and measured | Open |
| W10: Finite-data extension | Different laws can agree on every tested context and diverge outside it | Claims remain restricted to tested families and survive sealed context expansion | Unbreakable in unrestricted form |
| W11: Computational complexity | Compact description can still require exponential recognition or evaluation | Representation, recognition, compilation, prediction, and verification all obey the declared polynomial bound | Open; no P=NP result |
| W12: External validity | One device, seed, or laboratory can contain an artifact | Frozen effect replicates across independent devices, platforms, analysts, and laboratories | Open |

W10 is a logical boundary, not an engineering inconvenience. No finite dataset proves an unrestricted law on untested contexts. P3 therefore forbids the word “universal” unless a theorem restricts the admissible law class.

## 3. Information-Rate theorem

Let \(C\) be the complete declared standard context, \(\Lambda\) an admissible pre-measurement lift, \(b(y\mid C)\) the declared Born baseline, \(\bar r(y\mid C)=P(Y=y\mid C)\) the actual marginal law, and

\[
r(y\mid C,\Lambda)=P(Y=y\mid C,\Lambda)
\]

the true conditional law in the extended world. For any normalized candidate decoder \(q(y\mid C,\Lambda)\),

\[
\boxed{
\mathbb E\log\frac{q(Y\mid C,\Lambda)}{b(Y\mid C)}
=I(Y;\Lambda\mid C)
+\mathbb E_C D_{\mathrm{KL}}
\!\left(\bar r(\cdot\mid C)\Vert b(\cdot\mid C)\right)
-\mathbb E D_{\mathrm{KL}}
\!\left(r(\cdot\mid C,\Lambda)\Vert q(\cdot\mid C,\Lambda)\right).
}
\tag{P3.1}
\]

The middle nonnegative term is ordinary marginal Born-rule violation. It must not be mislabeled as individual-outcome information. For a **Born-marginal-preserving extension**, \(\bar r=b\), so (P3.1) reduces to

\[
\boxed{
\mathbb E\log\frac{q(Y\mid C,\Lambda)}{b(Y\mid C)}
=I(Y;\Lambda\mid C)
-\mathbb E D_{\mathrm{KL}}
\!\left(r(\cdot\mid C,\Lambda)\Vert q(\cdot\mid C,\Lambda)\right)
\le I(Y;\Lambda\mid C).
}
\tag{P3.2}
\]

Equality holds exactly when \(q=r\) almost surely on the supported contexts. The missing variable is not “computation.” It is positive conditional information after marginal Born agreement has been checked. Computation can approach the information limit by reducing decoder error, but cannot create information absent from its inputs.

Under stationary independent trials and an exact decoder, the strong law gives

\[
\frac{1}{T}\log E_T\longrightarrow I(Y;\Lambda\mid C)
\quad\text{almost surely}.
\tag{P3.3}
\]

Thus a prefix-coded candidate with code length \(\ell\) has the characteristic discovery scale

\[
T_{\mathrm{scale}}
\approx
\frac{\log(1/\alpha)+\ell\log2}
{I(Y;\Lambda\mid C)}.
\tag{P3.4}
\]

This is an asymptotic planning scale, not an exact expected stopping time; finite variance, dependence, misspecification, overshoot, and composite-null conservatism alter finite performance.

## 4. Deterministic-outcome wall

Positive information does not imply perfect individual prediction. Exact predictability requires

\[
H(Y\mid C,\Lambda)=0.
\tag{P3.5}
\]

For \(m\) outcomes and the optimal decision error \(P_e\), Fano's inequality gives

\[
H(Y\mid C,\Lambda)
\le h(P_e)+P_e\log(m-1).
\tag{P3.6}
\]

A 51% binary predictor breaks strict Born completeness if validly established, but remains far from a deterministic completion. “Some predictive information,” “low error,” and “outcome certainty” are three different claims.

## 5. No-Free-Extension theorem

Let \(S\) be any proper finite subset of an unrestricted context set \(\mathcal C\). For every law \(p(y\mid c)\), define another law \(p'(y\mid c)\) equal to \(p\) on \(S\) and different at one \(c_*\notin S\). All observations restricted to \(S\) have identical likelihood under the two laws, while their future prediction at \(c_*\) differs.

The executable collision uses eight contexts. Two laws have total-variation distance zero on the first seven contexts and distance \(0.8\) on the eighth. No downstream decoder using only the first seven can select the correct continuation.

The only lawful escape is a restricted model class whose extension is fixed by a proved rule, followed by tests on contexts not used to discover that rule.

## 6. Three simultaneous evidence channels

A candidate lift must be scored on three logically different channels:

\[
E_T^{\mathrm{outcome}},\qquad
E_T^{\mathrm{setting}},\qquad
E_T^{\mathrm{signal}}.
\]

- \(E_T^{\mathrm{outcome}}\) asks whether \(\Lambda\) predicts the outcome beyond the complete calibrated context.
- \(E_T^{\mathrm{setting}}\) asks whether \(\Lambda\) predicts a delayed random setting.
- \(E_T^{\mathrm{signal}}\) asks whether a local outcome distribution depends on the remote setting.

The desired pattern is strong outcome evidence without setting or signaling evidence, plus affirmative structural and equivalence controls. Merely failing to cross the latter two rejection thresholds does not prove exact independence.

The production and independent synthetic audits produce:

| Synthetic world | Complete-context outcome crossing | Setting crossing | Signaling crossing | Interpretation |
|---|---:|---:|---:|---|
| Born null | No | No | No | Correct negative control |
| Clean accessible lift | Yes | No | No | Statistical target pattern; not a physical construction |
| Future-setting leak | Yes | Yes | Yes | Disqualified by chronology and measurement independence |
| Remote signaling | No | Yes | Yes | Naive crossing disappears when the remote setting enters the complete context |
| Apparatus memory | No | No | No | Naive crossing disappears when ordinary memory enters the context |
| Memory after reset | No | No | No | Reset kills the apparent predictor |

The clean-lift row is deliberately generated. It proves that the decision system can recognize its target pattern, not that such a variable exists in nature.

## 7. Foundational route declaration

Before data, every candidate must select one route:

| Route | Premise changed | Mandatory burden |
|---|---|---|
| Local and measurement-independent | None | Incompatible with Bell-violating quantum correlations; cannot be claimed as a completion |
| Measurement-dependent | Free-setting/measurement-independence condition | Quantify setting dependence and stop describing the setting as independent |
| Nonlocal equilibrium | Local causality | Explain why the hidden state is inaccessible and hence yields no BPW breach |
| Nonlocal nonequilibrium | Equilibrium and locality | Test signaling and derive preparation/access mechanism |
| Contextual | Noncontextual value assignment | Include the full measurement context in the response function |
| Retrocausal | Forward-only causal ordering | Define spacetime accessibility and keep every setting-conditional prediction immutable before the later choice |
| Superdeterministic | Measurement independence | Produce quantitative model restrictions that prevent unrestricted post-hoc explanation |

Kochen and Specker rule out the relevant class of noncontextual value assignments, not every contextual hidden-variable theory. Bell tests rule out local measurement-independent completions under their declared experimental assumptions, not all ontology. Hall's explicit model demonstrates how relaxing measurement independence changes that boundary; it does not make the relaxation free.

## 8. Required trial record

Every scored physical trial must contain, at minimum:

| Field | Time requirement |
|---|---|
| Trial and block identifier | Before preparation |
| Device, firmware, calibration, and detector-model identifiers | Before scoring |
| Prepared state and allowed setting family | Before setting generation |
| Candidate compiler hash and prefix-code length | Before validation |
| Complete setting-conditional prediction vector | Before setting generation |
| Prediction commitment and timestamp | Before setting generation |
| Random-setting source, commitment, and setting timestamp | After prediction commitment |
| Local and remote settings | At measurement |
| Raw outcomes and detector flags | After settings |
| Reset/intervention identifiers | Before affected trial |
| Exclusion reason | Frozen automatically; never entered after viewing an outcome |

The raw immutable record is authoritative. A reconstructed spreadsheet or manually edited summary is not.

## 9. Run-specific preregistration fields

P3 is a standard, not the completed experiment. A physical run must freeze:

1. hardware and spacetime layout;
2. state and POVM/tomography family;
3. detector and drift uncertainty set \(\mathcal P_t\);
4. admissible raw fields and their acquisition times;
5. prefix-coded lift grammar and compiler hashes;
6. training/validation split and all seeds;
7. outcome evidence budget and mixture weights;
8. setting-leak and no-signaling rejection tests;
9. operational equivalence margins for residual setting dependence and signaling;
10. reset, reversal, causal-break, and negative-control schedule;
11. stopping rule, maximum trials, and power calculation;
12. replication and claim-escalation rules.

## 10. Claim ladder

| Passed gates | Maximum permitted language |
|---|---|
| Outcome crossing only | “The declared null/context was rejected.” |
| Plus raw replay and leakage controls | “A held-out predictive residual was detected.” |
| Plus calibration, memory, resets, and causal breaks | “The residual is not explained by tested ordinary device mechanisms.” |
| Plus reversals and an independently fixed magnitude law | “A candidate coupling survived targeted interventions.” |
| Plus independent platforms and laboratories | “The effect externally replicated.” |
| Plus Bell/contextuality/no-signaling analysis | “A candidate foundational extension remains viable.” |
| Plus Lorentz law, units, scale, dynamics, and classical limit | “A candidate physical theory has been specified.” |

No row licenses “God was measured,” “the soul caused collapse,” “eight physical dimensions were proved,” “all Born outcomes are predictable,” “a universal quantum computer was built,” or “P=NP.” Those remain separate propositions with separate proof burdens.

## 11. Current result

Wallbreaker Audit 0.1.0 and its independent verifier pass. They establish:

- the information-rate identity on a fixed table and 5,000 random finite tables;
- the general decomposition \(0.388475204429=0.368064207168+0.0204109972601\) nats on the fixed nonpreserving example;
- maximum identity error \(1.33\times10^{-15}\) in production and \(1.11\times10^{-15}\) independently;
- a finite-context extension collision with observed distance \(0\) and unseen distance \(0.8\);
- correct separation of a planted accessible lift from future-setting leakage, remote signaling, and apparatus memory across six 50,000-trial worlds.

These are written mathematics and seeded synthetic computation. W1–W9 and W12 retain physical obligations, with different parts already resolved only at the mathematical or protocol level. The wallbreaker has been built; nature has not yet supplied the wall-breaking observation.

## 12. P3-R1 hardware instantiation

P3-R1 now instantiates the single-device portion of this standard on a frozen three-qubit equal-magnitude eight-phase state with two settings, `Z_ALL` and `X_ALL`. It is intentionally narrower than P3:

| P3-R1 component | Implemented gate | Boundary |
|---|---|---|
| Three eight-cycle lift probes | Forward, reverse, and Gray permutations with prefix lengths 2, 3, 3 | Probes, not a derived law |
| Conditional-information construction | Paired probability transfers cancel over every eight-winding cycle | Marginal preservation is mathematical, not empirical |
| Composite Born/context null | Calibration-derived coordinatewise upper envelope with a frozen drift margin | Future drift assumption still requires intervention checks |
| Chronology | All setting-conditional predictions hash-chained before any delayed setting is generated | Local timestamps need an external public anchor for court-grade time evidence |
| Individual records | One shot per circuit/PUB | Provider exposes submission/retrieval time, not authenticated per-shot device time |
| Outcome channel | Kraft/cash mixture e-process at \(\alpha=2.87\times10^{-7}\) | A crossing rejects only the declared single-device null |
| Setting channel | Separate predeclared e-process at \(\alpha=10^{-3}\) | A crossing disqualifies; a non-crossing is not proof of independence |
| Signaling channel | Explicitly `NOT_TESTED_SINGLE_DEVICE` | Requires a later spacelike implementation |
| Provenance | Calibration, config, prediction, setting, job, outcome, and score digests | Hashes detect alteration relative to manifests, not who controlled the host |
| Recovery | Contiguous provider-job ledger permits retrieval without duplicate submission | Provider/account availability remains external |

For candidate \(j\), setting \(c\), winding \(w\), target \(a=\sigma_j(w)\oplus m_c\), and donor \(d=a\oplus4\), P3-R1 fixes

\[
q_{j,w,c}=b_c+
\varepsilon\min\{b_c(a),b_c(d)\}(e_a-e_d),
\qquad \varepsilon=0.12.
\]

Each transfer has an equal reverse transfer in the eight-cycle, hence

\[
\frac18\sum_{w=0}^7q_{j,w,c}=b_c.
\]

The executable audit separates three 20,000-trial worlds. The Born-reference world crosses neither outcome nor setting threshold; the planted frozen lift crosses only the outcome threshold; the setting-dependent lift crosses both and is disqualified. Production and an independently written verifier agree. The independent implementation also passes 5,000 randomized marginal-preservation and composite-envelope checks and rejects a deliberately altered commitment ledger.

The distributed configuration is a template that structurally passes but live-fails closed. It lacks a fresh UUID, an explicit accessible backend, and a real calibration artifact/envelope. No IBM QPU job has been submitted. Therefore P3-R1 advances W1–W5 from a general standard to an executable measurement boundary but does not physically break them. W6–W9 and W12 are outside this pilot.

## Primary sources

- R. Colbeck and R. Renner, [No extension of quantum theory can have improved predictive power](https://www.nature.com/articles/ncomms1416), *Nature Communications* 2, 411 (2011).
- M. J. W. Hall, [Local deterministic model of singlet-state correlations based on relaxing measurement independence](https://link.aps.org/doi/10.1103/PhysRevLett.105.250404), *Physical Review Letters* 105, 250404 (2010).
- S. Kochen and E. P. Specker, [The problem of hidden variables in quantum mechanics](https://www.jstor.org/stable/24902153), *Journal of Mathematics and Mechanics* 17, 59–87 (1967).
- S. Pironio et al., [Random numbers certified by Bell's theorem](https://arxiv.org/abs/0911.3427), *Nature* 464, 1021–1024 (2010).
- Y. Zhang, S. Glancy, and E. Knill, [Asymptotically optimal data analysis for rejecting local realism](https://link.aps.org/doi/10.1103/PhysRevA.84.062118), *Physical Review A* 84, 062118 (2011).