The Canonical Execution Standard for Constraint-Based Realization

Constructive Admissibility, Calibrated Accessibility, and Strong-Null Adjudication

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A Pre-Registered Framework for Applying, Testing, and Invalidating Canonical CBR

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Abstract

This paper defines the canonical execution standard for Constraint-Based Realization, or CBR, as a candidate law of quantum outcome realization. It does not extend CBR beyond its canonical formulation and does not claim empirical confirmation.

Instead, it specifies the conditions under which canonical CBR may count as executable, testable, and invalidable. The canonical law selects a realization channel Φ⋆_C by minimizing ℛ_C over a restricted admissible class 𝒜(C), with ℛ_C(Φ) = αΞ_C(Φ) + βΩ_C(Φ) + γΛ_C(Φ). The present work fixes the execution tuple required for public adjudication: the tested context, admissible class, operational quotient, burden evaluation, coefficient convention, accessibility calibration, critical accessibility domain, standard quantum baseline, nuisance envelope, rival-model exclusions, statistical threshold, verdict taxonomy, and no-rescue rules. It then instantiates that standard for a delayed-choice record-accessibility context. Under detectability-valid conditions, baseline-class behavior across the declared accessibility-critical domain entails failure of the instantiated canonical CBR model. Conversely, a CBR-compatible non-baseline result requires independent η calibration, nuisance separation, hostile-rival exclusion, replication, and the declared accessibility-critical form. The result is not a new CBR theory, but a binding public standard for applying, testing, and invalidating the canonical one.

Formal Proposition Spine

The paper is organized around seven execution-level propositions. These propositions do not add new physical-law content to canonical CBR. They specify the procedural conditions under which canonical CBR is publicly adjudicable.

Proposition 1 — Admissibility Construction.
For the designated delayed-choice record-accessibility context C_DCE, the admissibility pipeline yields a nonempty restricted admissible class 𝒜(C_DCE).

Proposition 2 — Operational Quotient.
ℛ_C descends to operational equivalence classes in 𝒜(C) ÷ ∼ₒₚ.

Proposition 3 — Burden Executability.
Ξ_C, Ω_C, and Λ_C are evaluable or boundable for declared channel classes in C_DCE.

Proposition 4 — Coefficient Non-Rescue.
Once α, β, and γ are fixed, failure cannot be avoided by post hoc coefficient adjustment.

Proposition 5 — η Independence.
η is estimable from record-accessibility data independently of V_obs(η).

Proposition 6 — Null Fixity.
𝔅_SQM + 𝒩 is fixed before adjudication.

Proposition 7 — Strong-Null Failure.
Under detectability-valid conditions, baseline-class behavior across D_crit entails F₃: failure of the instantiated canonical CBR model.

Together, these propositions define the execution standard. They do not establish that CBR is true. They define what must be fixed for canonical CBR to be tested without post hoc rescue.

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1. Introduction: Why Canonical CBR Needs an Execution Standard

1.1 Opening claim

Canonical CBR is not executable merely because its law form is defined. It is executable only when that law form is tied to a fixed admissible class, fixed burden evaluation, fixed coefficient convention, fixed accessibility calibration, fixed null comparator, fixed nuisance envelope, fixed statistical threshold, fixed verdict taxonomy, and fixed no-rescue rule.

The canonical closure paper states Constraint-Based Realization as a candidate law of quantum outcome realization. It defines the mature law form, burden functional, restricted admissibility, operational uniqueness, accessibility parameter, critical accessibility regime, delayed-choice record-accessibility protocol family, and strong-null failure criterion. That work states what canonical CBR is. The present paper states the conditions under which canonical CBR may be executed.

The distinction is essential. A candidate law may be formally specified and still remain insufficiently public if its application conditions are fluid. If the admissible class can be rebuilt after data, if the accessibility parameter can be inferred from the anomaly it is supposed to test, if the nuisance envelope can be expanded after a deviation appears, or if the critical regime can be moved after inspection of the result, then the model is not yet publicly adjudicable. It remains protected by procedural flexibility.

This paper removes that flexibility.

A canonical CBR test is valid only if the required locks are declared before data interpretation. A lock is a pre-adjudication commitment that prevents a theory component from being altered after empirical information is available. The purpose of the lock structure is not to make CBR harder to apply. It is to make the result meaningful when CBR is applied.

This paper therefore does not ask how CBR can be expanded. It asks under what fixed conditions canonical CBR is executable, testable, and invalidable.

1.2 Definitions: executable, testable, invalidable

Definition 1 — Executable canonical CBR.
Canonical CBR is executable in a context C only when the execution tuple is fixed, the admissible class 𝒜(C) is constructively generated, the burden functional ℛ_C is evaluable or bounded over declared channel classes, η is independently calibrated, the baseline-plus-nuisance class 𝔅_SQM + 𝒩 is fixed, and the verdict rule is pre-registered.

Definition 2 — Testable canonical CBR.
Canonical CBR is testable when its executable form yields a declared empirical contrast between the standard baseline class and a CBR-compatible accessibility-sensitive response in a specified domain D_crit.

Definition 3 — Invalidable canonical CBR.
An instantiated canonical CBR model is invalidable when there exists a predeclared detectability-valid regime in which baseline-class behavior entails failure of that instantiated model.

These definitions are procedural rather than ontological. They do not change canonical CBR. They define when canonical CBR is sufficiently fixed to face public adjudication.

1.3 The canonical law

Canonical CBR begins with a physically specified measurement context C and a restricted admissible class 𝒜(C) of realization-compatible channels. A candidate realization channel Φ belongs to 𝒜(C) only if it survives the canonical admissibility constraints. The selected realization channel is then given by constrained minimization:

Φ⋆_C = argmin{ℛ_C(Φ) : Φ ∈ 𝒜(C)}

The realization burden is:

ℛ_C(Φ) = αΞ_C(Φ) + βΩ_C(Φ) + γΛ_C(Φ)

Here Ξ_C is the representational-invariance burden, Ω_C is the record-structural-coherence burden, and Λ_C is the accessibility-consistency burden. The coefficients α, β, and γ are fixed theory-level coefficients rather than post hoc fitting parameters. In the canonical formulation, this law is tied to restricted admissibility, operational equivalence, local probability closure, accessibility-sensitive empirical exposure, and a strong-null failure condition.

The interpretation of this law is deliberately narrow. It is not a replacement for ordinary quantum dynamics. It is not a theory of decoherence. It is not a generic interpretation of observation. It is a candidate realization law: a rule for selecting an outcome-realization channel from a restricted admissible class once the physical context has been specified.

The present paper does not change this law. It fixes the conditions under which the law can be instantiated and judged.

1.4 The execution problem

The canonical law form is necessary but not sufficient for adjudication. A law of the form Φ⋆_C = argmin{ℛ_C(Φ) : Φ ∈ 𝒜(C)} becomes executable only when each formal and empirical object required for application has been fixed in advance.

The full execution tuple is:

(C, 𝒜(C), ℛ_C, α, β, γ, η, η_c, 𝔅_SQM, 𝒩, δ_min, D_crit, U(η_c), H₀, H₁)

This tuple fixes three things.

First, it fixes the formal model: C, 𝒜(C), ℛ_C, α, β, and γ.

Second, it fixes the empirical comparison: η, η_c, 𝔅_SQM, 𝒩, δ_min, D_crit, and U(η_c).

Third, it fixes the decision structure: H₀ and H₁.

If the tuple is incomplete, CBR may remain a canonical law-candidate, but it is not yet fully executable. If the tuple is fixed, CBR can be applied, tested, and invalidated under public rules.

1.5 Contribution

This paper contributes procedural closure.

It does not add a new ontology, a new realization law, or a new empirical target. It does not revise the canonical law form. It does not claim that CBR is established physics. It defines the execution standard for applying and judging the canonical model.

The standard is intentionally severe. The same instantiated canonical model must either survive, fail, or remain unadjudicated under the predeclared rules. It cannot be redefined into survival after the fact. A revised model may be proposed after failure, but it must be labeled as a modified model rather than treated as the survival of the failed canonical instantiation.

This is the scientific function of the execution standard: it protects the theory from vagueness, protects the experiment from post hoc reinterpretation, and protects the reader from confusing model survival with model revision.

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2. Source Base and Non-Expansion Rule

2.1 Source base

This paper builds only on the current canonical CBR corpus and the canonical closure paper.

The source base is deliberately narrow. It consists of the current canonical CBR sequence identified by the CBR landing page and the mature canonical formulation given in “Constraint-Based Realization: Canonical Closure and Exact Empirical Exposure.” The canonical closure paper presents CBR as a restricted, canonically specified, and empirically vulnerable candidate law of quantum outcome realization. It states the canonical law form, the burden functional, restricted uniqueness up to operational equivalence, local probability closure within canonical admissibility, the operational accessibility parameter η, the critical accessibility regime η_c, the delayed-choice record-accessibility protocol family, and the strong-null failure criterion.

This paper treats that canonical formulation as the source of record. It does not attempt to reconstruct the entire historical development of CBR. It does not rely on older developmental formulations unless they are part of the current canonical CBR sequence. It does not widen the program by importing earlier speculative, ontological, or noncanonical material.

The purpose of this restriction is not merely bibliographic. It is required for adjudication. A theory cannot be tested cleanly if its operative formulation is allowed to shift among historical versions. The object tested here is canonical CBR in its mature form, not every idea that may have appeared in the broader developmental background.

2.2 Non-expansion rule

Any structure introduced in this paper is procedural, not theoretical.

The paper introduces locks, execution tuples, pre-registration conditions, nuisance envelopes, hostile-rival exclusions, verdict categories, and no-rescue rules. These are not new physical postulates. They do not modify the canonical law form. They do not introduce a second realization law. They do not add a new interpretation of quantum mechanics. They do not expand the empirical domain beyond the designated accessibility-sensitive protocol family.

They specify how canonical CBR is applied, calibrated, tested, adjudicated, and invalidated.

This non-expansion rule is binding: claims not required by the canonical execution tuple are not used as premises in this paper. Historical motivation is not evidential support for the executable model. Conceptual appeal is not a substitute for a fixed admissible class, calibrated accessibility parameter, locked null comparator, and predeclared failure condition.

The paper’s additions are therefore rules of execution. They answer questions of application and judgment, not questions of new ontology.

2.3 Excluded scope

This paper does not defend broad CBR, historical CBR, QAU-style CBR, or any noncanonical extension. It does not treat CBR as a general metaphysical theory. It does not claim to settle all interpretations of quantum mechanics. It does not argue that every possible realization-law framework outside canonical CBR has been eliminated.

It also does not report an experiment and does not claim empirical support for CBR. It defines the conditions under which future empirical support, failure, or non-adjudication would be judged.

This exclusion is important because CBR’s strength depends on its restraint. The canonical formulation limits its claim: it does not claim universal closure over all possible realization-law alternatives, does not claim final universal Born-neutrality closure across every possible admissibility geometry, and does not claim broad empirical deviation across ordinary measurement settings. The present paper preserves that discipline.

The execution standard applies to canonical CBR as presently instantiated. If a future paper proposes a different admissible class, a different accessibility variable, a different burden functional, or a different empirical domain, then that future proposal may be valuable, but it is not the same tested model unless it preserves the locked execution tuple.

2.4 Relation to the canonical closure paper

The canonical closure paper states what CBR is.

This paper states when canonical CBR counts as executable.

The relationship is therefore:

canonical closure = law-candidate specification;

canonical execution standard = application and adjudication specification.

The canonical closure paper gives the mature theory object. It specifies the law form Φ⋆_C = argmin{ℛ_C(Φ) : Φ ∈ 𝒜(C)}, the burden structure ℛ_C(Φ) = αΞ_C(Φ) + βΩ_C(Φ) + γΛ_C(Φ), the restricted admissible class, the accessibility-sensitive empirical regime, and the strong-null failure condition.

The present paper does not restate those results as if they were new. It assumes them and asks what must be fixed before they can function as public test conditions.

That is why the execution standard is framed as a sequence of locks. A lock is a pre-adjudication commitment preventing an existing theory component from being altered after empirical information is available. The model lock prevents changing the tested object. The admissibility lock prevents changing 𝒜(C). The burden and coefficient locks prevent changing ℛ_C or its weights. The accessibility and critical-regime locks prevent redefining η or η_c. The baseline, nuisance, and rival locks prevent changing the comparison class. The statistical and verdict locks prevent changing the decision rule. The failure-level and no-rescue locks prevent treating failure as survival.

The result is a binding public standard. Canonical CBR is not executable merely because its law form can be written down. It is executable when the law form is tied to fixed admissibility construction, fixed empirical calibration, fixed null comparison, fixed statistical adjudication, and fixed no-rescue rules.

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3. The Tested Object: The Canonical CBR Model Lock

3.1 Purpose

The first condition of executable CBR is that the tested model be fixed before empirical interpretation begins. A candidate realization law cannot be publicly adjudicated if the object under test remains adjustable after data are available.

The model lock therefore fixes the complete canonical execution tuple:

(C, 𝒜(C), ℛ_C, α, β, γ, η, η_c, 𝔅_SQM, 𝒩, δ_min, D_crit, U(η_c), H₀, H₁)

This tuple, not the law form alone, is the object of adjudication.

The law form supplies the canonical structure:

Φ⋆_C = argmin{ℛ_C(Φ) : Φ ∈ 𝒜(C)}

with

ℛ_C(Φ) = αΞ_C(Φ) + βΩ_C(Φ) + γΛ_C(Φ).

The execution tuple supplies the conditions under which that structure is applied, compared with the standard baseline, and judged.

The purpose of the model lock is simple:

No change to the tested model after empirical information is available.

If any element of the tuple is changed after data interpretation begins, the original instantiated model has not survived. A modified model has been introduced.

3.2 Formal model objects

A physically specified measurement context C contains the realization-relevant structure of the experiment. It is not merely an observable label or basis choice. It includes the system, apparatus, record, eraser or control degrees of freedom, environment, timing structure, measurement interaction, record-bearing correlations, and accessibility structure.

A candidate realization channel Φ is a candidate outcome-realization structure in C. It is not automatically admissible. It first belongs, at most, to an initial candidate class 𝒞₀(C). It becomes eligible for canonical selection only if it survives the admissibility construction defining 𝒜(C).

The restricted admissible class 𝒜(C) is the domain over which canonical CBR selects. The canonical law is not defined over all formally writable maps. It is defined over channels that survive the declared admissibility filters.

The realization burden is:

ℛ_C(Φ) = αΞ_C(Φ) + βΩ_C(Φ) + γΛ_C(Φ)

where Ξ_C penalizes representational non-invariance, Ω_C penalizes record-structural incoherence, and Λ_C penalizes accessibility inconsistency.

The selected realization channel is:

Φ⋆_C = argmin{ℛ_C(Φ) : Φ ∈ 𝒜(C)}.

Because canonical CBR identifies channels up to operational equivalence, the selected object is more precisely an operational verdict class:

[Φ⋆_C] = argmin{ℛ_C([Φ]) : [Φ] ∈ 𝒜(C) ÷ ∼ₒₚ}.

Here Φ ∼ₒₚ Ψ means that no admissible experiment in context C distinguishes Φ and Ψ at the level relevant to realization selection.

3.3 Empirical execution objects

The model becomes testable only when its empirical execution objects are fixed.

η is the operational accessibility parameter.

η_c is the critical accessibility regime.

𝔅_SQM is the declared standard quantum baseline class.

𝒩 is the bounded nuisance envelope.

ν(η) is an allowed nuisance deformation.

V_obs(η) is the observed visibility curve.

V_SQM(η) is the standard quantum baseline visibility curve.

V_null(η) = V_SQM(η) + ν(η), with ν ∈ 𝒩.

δ_min is the minimum deviation threshold.

D_crit is the experimentally accessible critical η-domain.

U(η_c) is the declared neighborhood of η_c.

These objects are not optional supplements. They are part of the executable model. Without them, the claim that CBR predicts an accessibility-sensitive empirical signature is not yet adjudicable.

3.4 Null and alternative

The strong-null comparator is:

H₀: V(η) ∈ 𝔅_SQM + 𝒩 across D_crit.

The CBR-compatible alternative is:

H₁: there exists η ∈ U(η_c) such that V_obs(η) leaves 𝔅_SQM + 𝒩 by more than δ_min with the declared accessibility-critical form.

This alternative is intentionally strict. A non-baseline deviation alone is not sufficient. The deviation must occur in the declared critical region, exceed the predeclared threshold, have the declared accessibility-critical form, survive nuisance separation, survive hostile-rival exclusion, and replicate under the declared standard.

Conversely, if detectability-valid conditions hold and V_obs(η) remains inside 𝔅_SQM + 𝒩 across D_crit, the instantiated canonical CBR model reaches F₃: failure of the instantiated canonical model.

3.5 Binding model-lock rule

After empirical interpretation begins, no element of the execution tuple may be changed while claiming survival of the same instantiated canonical model.

No post-data change is permitted to:

C, 𝒜(C), ℛ_C, α, β, γ, η, η_c, 𝔅_SQM, 𝒩, δ_min, D_crit, U(η_c), H₀, or H₁.

Changing any of these objects is allowed only as model revision. It cannot be counted as survival of the original model.

This is the model-lock rule.

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4. Constructive Admissibility: The 𝒜(C) Lock

4.1 Purpose

The admissibility lock fixes the construction of 𝒜(C). Since canonical CBR selects over 𝒜(C), the theory is not executable unless 𝒜(C) is generated by a declared procedure before adjudication.

The admissibility lock has one purpose:

No changing what counts as admissible after empirical information is available.

The construction has the form:

𝒞₀(C) → admissibility filters → 𝒜(C) → 𝒜(C) ÷ ∼ₒₚ.

The output is the selection domain for canonical minimization.

4.2 Initial candidate class

Let 𝒞₀(C) be the broad initial class of candidate realization channels in context C.

The paper must declare what belongs to 𝒞₀(C). Depending on implementation, 𝒞₀(C) may consist of CPTP maps, operational maps, context-relative realization maps, or another explicitly defined class.

The only strict requirement is that 𝒞₀(C) be declared before filtering and before data interpretation. If a candidate type is excluded from 𝒞₀(C), the exclusion must be justified by physical or operational structure, not by empirical convenience.

4.3 Admissibility filters

The admissible class 𝒜(C) is obtained by applying six filters.

Filter 1 — Dynamical compatibility.
Remove channels that modify ordinary quantum dynamics outside realization selection. CBR is not a replacement for standard quantum evolution. A candidate channel fails this filter if it obtains its verdict by changing baseline dynamics rather than selecting among realization-compatible structures.

Filter 2 — Representational invariance.
Remove channels whose verdict changes under physically irrelevant reformulation. A candidate channel fails this filter if relabeling, equivalent encoding, basis redescription, or notation change alters its realization verdict without changing the physical context.

Filter 3 — Record-structural coherence.
Remove channels that ignore physically meaningful record-bearing structure. A candidate channel fails this filter if it treats unsupported formal branches as equivalent to durable physical records.

Filter 4 — Accessibility consistency.
Remove channels that treat accessibility-equivalent contexts differently. A candidate channel fails this filter if two contexts with the same operational accessibility structure receive different realization verdicts without a declared physical distinction.

Filter 5 — Probabilistic non-insertion.
Remove channels that smuggle target probability weighting into the law. A candidate channel fails this filter if the desired weighting is built into the admissibility metric, burden geometry, refinement rule, or normalization convention without independent justification.

Filter 6 — Admissibility separation.
Remove pathological constructions that collapse operationally distinct candidates before selection. A candidate fails this filter if it erases distinctions that should remain available to the realization law.

After these filters are applied, the surviving class is 𝒜(C).

4.4 Operational quotient

The admissible class is then quotient-labeled by operational equivalence.

Define:

Φ ∼ₒₚ Ψ

if no admissible experiment in context C distinguishes Φ and Ψ at the level relevant to realization selection.

The quotient selection domain is:

𝒜(C) ÷ ∼ₒₚ.

The selected object is:

[Φ⋆_C] = argmin{ℛ_C([Φ]) : [Φ] ∈ 𝒜(C) ÷ ∼ₒₚ}.

The quotient prevents notational multiplicity from being mistaken for physical multiplicity. It also prevents canonical CBR from claiming representative-level uniqueness where only operational uniqueness is warranted.

4.5 Proposition 1 — Admissibility Construction

Claim.
For the designated delayed-choice record-accessibility context C_DCE, the admissibility pipeline yields a nonempty restricted admissible class 𝒜(C_DCE).

Proof sketch.
Begin with the declared initial candidate class 𝒞₀(C_DCE). At least one baseline-compatible candidate preserves ordinary dynamics, remains invariant under physically irrelevant reformulation, respects the declared record-bearing structure, treats accessibility-equivalent contexts equivalently, contains no hidden probability insertion, and preserves admissibility separation. Therefore the filtering pipeline does not yield the empty class.

Execution consequence.
If 𝒜(C_DCE) were empty, canonical CBR would not be executable in the declared context. Since the pipeline yields at least one admissible class, the selection rule has a nonempty domain.

4.6 Proposition 2 — Operational Quotient

Claim.
ℛ_C descends to operational equivalence classes in 𝒜(C) ÷ ∼ₒₚ.

Proof sketch.
If Φ ∼ₒₚ Ψ, then Φ and Ψ differ only by operationally null structure in context C. A burden functional that assigned different physical verdicts to Φ and Ψ would reintroduce dependence on representation, formal surplus, or operationally inaccessible distinctions. That would violate the admissibility constraints encoded by Ξ_C, Ω_C, and Λ_C. Therefore ℛ_C induces a well-defined burden over operational equivalence classes.

Execution consequence.
Canonical selection is well-defined over 𝒜(C) ÷ ∼ₒₚ. The model selects an operational verdict class rather than a notation-dependent representative.

4.7 Binding admissibility-lock rule

After data interpretation begins, canonical CBR may not alter the admissibility filters, reclassify excluded channels as admissible, change 𝒞₀(C), or redefine ∼ₒₚ while claiming survival of the same instantiated model.

Any such change is a model revision.

The original locked model either survives, fails, or remains unadjudicated under the admissibility construction declared before interpretation.

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5. Burden Evaluation and Coefficient Lock

5.1 Purpose

The burden-and-coefficient lock fixes the ordering rule used by canonical CBR.

The admissibility lock determines which channels are eligible for selection. The burden lock determines how the eligible channels are ordered. The coefficient lock determines how the burden components are aggregated. Together, they make the canonical selection rule executable:

Φ⋆_C = argmin{ℛ_C(Φ) : Φ ∈ 𝒜(C)}

with

ℛ_C(Φ) = αΞ_C(Φ) + βΩ_C(Φ) + γΛ_C(Φ).

The purpose of this lock is:

No changing the meaning, scale, evaluation, or coefficient weighting of ℛ_C after empirical information is available.

A model that can redefine its burden terms after data can preserve the appearance of the same law form while changing its selection rule. That is not survival of the same model. It is model replacement.

Therefore, executable CBR requires a pre-adjudication burden evaluation certificate: a declared specification stating how Ξ_C, Ω_C, and Λ_C are evaluated, bounded, ranked, or treated as exclusionary for each declared channel class.

5.2 Exclusion versus burden

The execution standard distinguishes two kinds of failure.

First, admissibility failure. A channel that violates a non-negotiable admissibility filter is excluded from 𝒜(C) before minimization.

Second, burden-bearing imperfection. A channel that remains admissible but imperfect with respect to a canonical burden may remain in 𝒜(C) while incurring positive Ξ_C, Ω_C, or Λ_C.

This distinction is essential.

If every violation is treated as exclusionary, the admissible class may become artificially narrow. If every violation is treated as merely burden-bearing, inadmissible channels may enter the selection domain. The execution standard therefore requires each burden criterion to declare whether a violation is:

exclusionary;

burden-bearing;

or context-dependent under a predeclared threshold.

This declaration must be made before adjudication.

5.3 Representational-invariance burden Ξ_C

Ξ_C(Φ) measures failure of invariance under physically irrelevant reformulation.

An admissible form of Φ preserves its operational verdict under relabeling, equivalent encoding, coordinate redescription, or basis change that leaves the realization-relevant context unchanged.

An inadmissible form of Φ changes its realization verdict merely because the same physical context has been redescribed.

A burden-bearing form of Φ may preserve the final verdict but introduce representation-dependent intermediate structure. Such a channel may remain admissible only if the representation dependence is operationally null and accounted for in Ξ_C.

The ideal condition is:

Ξ_C(Φ) = 0

when Φ is invariant under all declared representation-preserving transformations of C.

A positive burden occurs when:

Ξ_C(Φ) > 0

because Φ carries representation-dependent structure not eliminated by quotienting.

An exclusion occurs when representation dependence changes the operational realization verdict.

For C_DCE, the burden evaluation certificate must declare the relevant representation transformations, including path relabeling, equivalent record encoding, basis redescription that preserves record accessibility, and equivalent parametrization of the eraser/control subsystem.

5.4 Record-structural-coherence burden Ω_C

Ω_C(Φ) measures failure to track physically meaningful record-bearing structure.

An admissible form of Φ respects the declared record subsystem R and its correlation with the which-path variable W.

An inadmissible form of Φ selects over unsupported formal branch decompositions as if they were physically record-bearing alternatives.

A burden-bearing form of Φ may track R imperfectly or incompletely while still preserving the physical distinction between record-bearing and non-record-bearing structures.

The ideal condition is:

Ω_C(Φ) = 0

when Φ is fully coherent with the record architecture declared in C.

A positive burden occurs when:

Ω_C(Φ) > 0

because Φ partially misaligns with declared record structure.

An exclusion occurs when Φ ignores the record architecture entirely or treats arbitrary branch decompositions as equivalent to physical records.

For C_DCE, the burden evaluation certificate must specify R, W, the W–R correlation, the durability or retrievability condition for record-bearing status, and the distinction between formal branch structure and operational record structure.

5.5 Accessibility-consistency burden Λ_C

Λ_C(Φ) measures failure to handle operational accessibility coherently.

An admissible form of Φ treats accessibility-equivalent contexts equivalently and responds coherently to declared accessibility differences.

An inadmissible form of Φ distinguishes accessibility-equivalent contexts without physical reason or defines accessibility using the same observable whose deviation is being tested.

A burden-bearing form of Φ may have imperfect accessibility dependence but remains admissible if the dependence is predeclared, operationally meaningful, and separable from nuisance effects.

The ideal condition is:

Λ_C(Φ) = 0

when Φ is fully consistent with the declared accessibility structure of C.

A positive burden occurs when:

Λ_C(Φ) > 0

because Φ is imperfectly but non-arbitrarily accessibility-sensitive.

An exclusion occurs when Φ uses circular accessibility, arbitrary accessibility distinctions, or post hoc η dependence.

For C_DCE, Λ_C must be evaluated relative to the independently calibrated η procedure. The same η-calibration standard used for empirical adjudication must be used in admissibility evaluation.

5.6 Burden codomain and burden evaluation certificate

The burden codomain must be declared before adjudication.

The abstract admissible options are:

Ξ_C, Ω_C, Λ_C ∈ ℝ_≥0

or, for a normalized worked example:

Ξ_C, Ω_C, Λ_C ∈ [0, 1].

The preferred execution standard for C_DCE is normalized burdens in [0, 1].

The burden evaluation certificate must declare, for each candidate channel class:

whether it is admitted, excluded, or assigned to nuisance modeling;

whether any violation is exclusionary or burden-bearing;

how Ξ_C is evaluated or bounded;

how Ω_C is evaluated or bounded;

how Λ_C is evaluated or bounded;

how ℛ_C is computed or ordered;

whether the ordering is sufficient to determine the selected operational verdict class.

The certificate may use exact values, bounds, or ordinal rankings, but only if the declared information is sufficient to determine the minimizer or to declare non-executability.

5.7 Proposition 3 — Burden Executability

Claim.
Ξ_C, Ω_C, and Λ_C are evaluable or boundable for declared channel classes in C_DCE.

Assumptions.
C_DCE declares the path degree of freedom, record subsystem, eraser/control mechanism, environment, timing structure, η-calibration procedure, representation transformations, and primary observable. The channel catalogue is fixed before adjudication.

Proof sketch.
The declared representation transformations determine whether Ξ_C vanishes, is positive, or triggers exclusion. The declared record subsystem and W–R correlation determine whether Ω_C vanishes, is positive, or triggers exclusion. The independent η-calibration procedure determines whether Λ_C vanishes, is positive, or triggers exclusion. Since each channel class is evaluated against predeclared structures, the burdens are evaluable, boundable, or exclusionary by construction.

Execution consequence.
If the burden evaluation certificate determines an ordering over 𝒜(C_DCE) ÷ ∼ₒₚ, canonical selection is executable. If it does not determine an ordering sufficient for selection, the model is not falsified; it is not executable in that instantiation.

5.8 Coefficient convention

The coefficients α, β, and γ aggregate the three burden terms.

The execution standard requires:

α, β, γ ≥ 0.

The preferred normalization is:

α + β + γ = 1.

The coefficients are part of the execution tuple. They must be declared before adjudication. They may not be inferred from V_obs(η), adjusted after failure, or selected to preserve the model after the fact.

The strongest version of the execution standard proves coefficient insensitivity. The minimum acceptable version declares a fixed coefficient convention and enforces the no-refit rule.

5.9 Coefficient-insensitivity target

A coefficient-insensitivity result has the form:

For all (α, β, γ) ∈ K, with α, β, γ ≥ 0 and α + β + γ = 1, the strong-null adjudication rule yields the same verdict.

Here K is a predeclared admissible coefficient domain.

A weaker result may show verdict stability in a neighborhood of a canonical coefficient choice.

If no coefficient-insensitivity result is available, the model may still be executable, but only with a fixed coefficient convention declared before testing.

5.10 Proposition 4 — Coefficient Non-Rescue

Claim.
Once α, β, and γ are fixed, failure cannot be avoided by post hoc coefficient adjustment.

Assumptions.
The execution tuple includes a declared coefficient convention. The adjudication rule is applied under that convention.

Proof sketch.
The coefficient convention is part of the tested model. If baseline-class behavior across D_crit entails failure under the declared convention, then changing α, β, or γ creates a different execution tuple. A different tuple is a modified model, not survival of the original model.

Execution consequence.
Coefficient revision after data is allowed only as model revision. It cannot count as survival of the failed instantiated model.

5.11 Binding burden-and-coefficient rule

After data interpretation begins, canonical CBR may not change:

the definitions of Ξ_C, Ω_C, or Λ_C;

the burden codomain;

the burden evaluation certificate;

the exclusion versus burden-bearing classification;

α, β, or γ;

the coefficient normalization;

or the coefficient domain K.

Any such change is model revision.

The same instantiated model either remains executable under the declared burden-and-coefficient lock, fails under it, or becomes unadjudicated because the lock was insufficient.

6. Canonical Instantiation Lock

6.1 Purpose

The instantiation lock fixes the concrete context in which canonical CBR is applied.

The canonical law is not adjudicated in abstraction. It is adjudicated only when instantiated in a physically specified context with declared degrees of freedom, channel catalogue, accessibility structure, baseline comparator, nuisance envelope, and verdict rule.

The purpose of this lock is:

No changing the experimental target after empirical information is available.

For the present execution standard, the designated context is a delayed-choice record-accessibility interferometer.

6.2 Minimal operational stages of C_DCE

C_DCE must be specified as a sequence of operational stages.

Stage 1 — Preparation.
Prepare the path degree of freedom and any ancillary degrees of freedom required for the interferometric context.

Stage 2 — Record formation.
Create or control a which-path record correlation between W and R.

Stage 3 — Accessibility manipulation.
Manipulate the operational accessibility of the record through the eraser/control subsystem.

Stage 4 — η calibration.
Estimate η from record-accessibility data independently of V_obs(η).

Stage 5 — Interference readout.
Measure the visibility observable V_obs(η).

Stage 6 — Adjudication.
Compare V_obs(η) against 𝔅_SQM + 𝒩 under the pre-registered decision rule.

These stages are part of the instantiation lock. A context that lacks one of these stages may be physically interesting, but it is not the declared C_DCE execution context.

6.3 Hilbert-space structure

Use the finite-dimensional decomposition:

ℋ = ℋ_path ⊗ ℋ_record ⊗ ℋ_eraser ⊗ ℋ_environment.

ℋ_path carries the path variable W.

ℋ_record carries the record system R.

ℋ_eraser carries erasure or accessibility-control degrees of freedom.

ℋ_environment carries uncontrolled or nuisance degrees of freedom.

This decomposition is not claimed to be the only possible representation of a delayed-choice experiment. It is the locked representation for this execution standard. Equivalent representations may be used only if they preserve the declared operational structure and are identified before adjudication.

6.4 Context contents

C_DCE must include:

the interferometer structure;

the path variable W;

the which-path record subsystem R;

the W–R correlation mechanism;

the eraser/accessibility-control mechanism;

the timing relation among preparation, record formation, accessibility manipulation, η calibration, and visibility readout;

the visibility observable V_obs(η);

the η-calibration method;

the standard baseline V_SQM(η);

the nuisance envelope 𝒩;

the critical domain D_crit;

the critical neighborhood U(η_c);

and the pre-registered verdict rule.

These are not optional implementation details. They define the test context.

6.5 Candidate channel catalogue

Before testing, C_DCE must declare the candidate channel catalogue.

At minimum, the catalogue includes:

Φ_base = baseline-compatible candidate;

Φ_acc = accessibility-sensitive candidate;

Φ_rep = representation-dependent excluded candidate;

Φ_rec = record-incoherent excluded candidate;

Φ_prob = probability-inserting excluded candidate;

Φ_noise = nuisance-induced effective channel, not a realization-law candidate.

Each entry must have a declared status: admitted, excluded, burden-bearing, or assigned to nuisance modeling.

6.6 Admissibility status

Φ_rep is excluded if its verdict changes under representation-preserving transformations.

Φ_rec is excluded if it ignores the declared record subsystem or treats unsupported branch decompositions as physical records.

Φ_prob is excluded if it inserts target probability weighting into the selection rule.

Φ_noise is assigned to 𝒩. It may affect the observed curve, but it is not selected as a realization-law candidate.

Φ_base and Φ_acc are evaluated as candidate admissible classes under the declared burden evaluation certificate.

This declaration must be made before adjudication.

6.7 Burden evaluation in C_DCE

For each declared channel class, the burden evaluation certificate must state:

admissibility status;

Ξ_C value, bound, or ordinal status;

Ω_C value, bound, or ordinal status;

Λ_C value, bound, or ordinal status;

total ℛ_C value, bound, or ordering;

whether the channel is eligible for minimization;

whether the channel belongs to 𝒩 rather than 𝒜(C_DCE).

If the certificate cannot distinguish the relevant minimizer class, then the model is not executable in C_DCE.

6.8 Selection in C_DCE

Selection is performed over the operational quotient:

[Φ⋆_C] = argmin{ℛ_C([Φ]) : [Φ] ∈ 𝒜(C_DCE) ÷ ∼ₒₚ}.

The selected verdict class must follow from:

the declared candidate catalogue;

the admissibility filters;

the operational quotient;

the burden evaluation certificate;

and the coefficient convention.

It may not be supplied by interpretive preference or adjusted after the empirical result.

6.9 Empirical exposure of the selected class

The selected class determines the empirical exposure of the instantiated model.

If Φ_acc is selected, the model must declare the accessibility-sensitive response associated with that selection and the critical-regime condition under which it is exposed.

If Φ_base is selected, the model does not predict a non-baseline accessibility signature in that instantiation.

If the declared burden evaluation cannot select between Φ_base and Φ_acc, the model is not executable in C_DCE until the ambiguity is resolved before testing.

This prevents the model from treating baseline behavior as expected after failure while also treating non-baseline behavior as support before failure.

6.10 Binding instantiation rule

After data interpretation begins, canonical CBR may not change:

C_DCE;

the operational stages;

the Hilbert-space decomposition;

the record subsystem R;

the eraser/control subsystem;

the visibility observable;

the channel catalogue;

the admissibility status of channel classes;

or the assignment of Φ_noise to 𝒩.

Any such change is a modified instantiation.

The original locked instantiation either survives, fails, or remains unadjudicated under the predeclared execution standard.

7. Accessibility and Critical-Regime Lock

7.1 Purpose

The accessibility lock fixes η, η_c, D_crit, and U(η_c) before adjudication.

This lock is required because accessibility is the empirical bridge between canonical CBR and its designated test domain. The canonical model becomes empirically vulnerable only if accessibility is operationally calibrated, separated from nuisance effects, and fixed before interpretation of the visibility data.

The purpose of this lock is:

No circular accessibility definition and no movement of the critical regime after empirical information is available.

In executable CBR, η is not inferred from the anomaly the model seeks to explain. It is calibrated from record-accessibility data independently of V_obs(η). Likewise, η_c is not moved after inspection of the result. It is derived, pre-registered, or estimated under an explicit statistical penalty.

The accessibility lock also distinguishes three outcomes that must not be conflated:

First, valid accessibility calibration: η is independently estimated with declared uncertainty.

Second, invalid accessibility calibration: η is not independently estimated or is confounded with the visibility result.

Third, model failure: baseline-class behavior persists across D_crit under detectability-valid conditions after valid η calibration.

Only the third outcome can trigger strong-null failure. If η calibration fails, the model has not failed; the test is inconclusive.

7.2 Definition of η

The operational accessibility parameter is defined as:

η = I_acc(W; R) ÷ H(W)

where W is the which-path variable, R is the record subsystem, I_acc(W; R) is the accessible which-path mutual information, and H(W) is the entropy of W.

η measures the fraction of which-path information operationally accessible through the declared record subsystem under the declared calibration procedure.

η = 0 indicates no accessible which-path information under the calibration procedure.

η = 1 indicates full accessible which-path information under the calibration procedure.

Intermediate values indicate partial accessibility.

This definition intentionally separates accessibility from mere entanglement, mere decoherence, and mere formal record existence. A record may exist formally while not being accessible under the declared procedure. Conversely, accessibility must be tied to recoverable or measurable record information, not to interpretive assertion.

7.3 Accessibility validity conditions

A declared η calibration is valid only if all of the following hold.

The which-path variable W is defined before testing.

The record subsystem R is identified before testing.

The procedure estimating I_acc(W; R) is fixed before testing.

The normalization H(W) is fixed or estimated by a declared method.

η uncertainty is quantified.

η calibration is independent of V_obs(η).

η calibration is not confounded with ordinary decoherence, detector drift, phase noise, postselection, source instability, environmental leakage, or record-readout failure beyond the declared nuisance allowance.

These are accessibility-validity conditions. If they are not met, the experiment cannot trigger strong-null failure. It may reveal a platform problem, a calibration failure, or a need for revised implementation, but it does not adjudicate the canonical model.

7.4 Independence requirement

The central rule is:

η must be calibrated from record-accessibility data, not inferred from V_obs(η).

This rule prevents circularity.

If η were inferred from the same visibility anomaly used to test CBR, then the empirical comparison would be compromised. The theory would effectively define the accessibility parameter by the deviation it seeks to explain. That would make the accessibility signature non-independent.

The execution standard therefore requires a two-channel structure:

An η-calibration channel, which estimates accessibility from record-accessibility data.

A visibility-adjudication channel, which measures V_obs(η) and compares it to 𝔅_SQM + 𝒩.

The two channels may be implemented on the same physical platform, but their evidential roles must be distinct. The η-calibration channel supplies the independent variable. The visibility-adjudication channel supplies the dependent observable.

7.5 Estimation procedure

The paper must declare the η-estimation procedure before adjudication.

At minimum, the procedure must specify:

how W is prepared;

what physical subsystem counts as R;

which measurement, retrieval task, or reconstruction method estimates I_acc(W; R);

how H(W) is measured or fixed by preparation;

how finite-sample error is handled;

how calibration drift is monitored;

how uncertainty in η is propagated into 𝒩;

how η values are binned or sampled;

and how η calibration is separated from visibility readout.

For a binary which-path variable, H(W) may be fixed by preparation if path probabilities are controlled. If the path distribution is not exactly balanced, H(W) must be estimated or bounded under the predeclared procedure.

I_acc(W; R) may be estimated through an operational retrieval task, tomographic reconstruction, bounded accessible-information estimation, or another declared procedure. The estimator is part of the execution tuple and may not be changed after data.

7.6 Proposition 5 — η Independence

Claim.
η is estimable from record-accessibility data independently of V_obs(η).

Assumptions.
C_DCE includes a declared record subsystem R, a which-path variable W, a record-accessibility calibration procedure, and a visibility observable V_obs(η). The η-estimation procedure is fixed before adjudication and does not use visibility anomaly data as the estimator.

Proof sketch.
η is defined by I_acc(W; R) ÷ H(W). Both W and R are specified as part of the context. I_acc(W; R) is estimated through record-accessibility measurements or retrieval tasks, while V_obs(η) is measured through interference readout. Since the η estimator uses record-accessibility data rather than visibility-deviation data, η can be calibrated independently of the empirical observable used for strong-null adjudication.

Execution consequence.
If η is not independently estimable, canonical CBR is not executable in the declared context. A visibility anomaly cannot be used both to define η and to test the accessibility signature.

7.7 Critical accessibility regime η_c

The critical accessibility regime η_c marks the accessibility region in which the canonical model asserts empirical exposure.

η_c must be handled in one of three ways:

derived from the canonical model;

pre-registered before testing;

or estimated with an explicit statistical penalty.

The strongest option is derivation. In that case, η_c follows from the declared canonical response structure and is not an additional empirical fitting parameter.

The second strongest option is pre-registration. In that case, η_c is fixed before data interpretation and treated as part of the execution tuple.

The weakest admissible option is penalized estimation. In that case, the test may scan over η_c only if the scan range, penalty, and decision rule are predeclared. An unpenalized post hoc choice of η_c is inadmissible.

The paper must state which option is used. If no valid η_c rule is declared, the test cannot trigger strong-null failure.

7.8 Critical domain and neighborhood

The execution standard distinguishes the broader critical domain from the local critical neighborhood.

D_crit is the experimentally accessible critical η-domain over which strong-null behavior is assessed.

U(η_c) is the declared neighborhood of η_c in which the CBR-compatible accessibility-critical form is expected.

Both must be fixed before adjudication.

D_crit defines the domain over which baseline-class behavior counts against the instantiated canonical model. U(η_c) defines the local region in which a non-baseline deviation must appear to count as CBR-compatible.

This distinction prevents two errors.

A deviation outside U(η_c) may be scientifically interesting, but it is not automatically a CBR-compatible result.

Baseline behavior outside the declared D_crit does not by itself trigger strong-null failure.

The critical domain and neighborhood are adjudication objects, not interpretive afterthoughts.

7.9 Detectability-valid accessibility regime

Strong-null failure requires not only valid η calibration, but also a detectability-valid accessibility regime.

A regime is detectability-valid when the experiment has sufficient sensitivity across D_crit to detect the declared minimum deviation δ_min after nuisance and calibration uncertainty are included.

Thus, the test must establish:

η values adequately cover D_crit;

uncertainty in η is small enough to assign data to the declared domain;

nuisance uncertainty does not swamp δ_min;

sampling density is sufficient near U(η_c);

visibility precision is sufficient to distinguish V_obs(η) from 𝔅_SQM + 𝒩 by δ_min;

and rival diagnostics are adequate to rule out ordinary artifacts.

If these conditions are not met, baseline-class behavior does not falsify the instantiated model. The result is inconclusive because the experiment lacked the declared detectability.

This point is essential. Strong-null failure is severe only because it applies under valid detectability conditions.

7.10 Separation from ordinary effects

η calibration must be separated from ordinary effects that could masquerade as accessibility dependence.

At minimum, the calibration protocol must distinguish η from:

ordinary decoherence;

detector drift;

phase noise;

postselection effects;

source instability;

environmental leakage;

record-readout inefficiency;

timing jitter;

and data-binning artifacts.

The reason is simple: η is supposed to measure accessible which-path information, not generic degradation of interference or apparatus performance.

If η cannot be separated from ordinary nuisance effects, then the model cannot be adjudicated in that implementation. The correct verdict is inconclusive, not failure and not support.

7.11 Binding accessibility rule

After data interpretation begins, canonical CBR may not:

redefine η;

infer η from V_obs(η);

change the η estimator;

move η_c without predeclared penalty;

alter D_crit;

alter U(η_c);

change η binning or sampling rules in a result-dependent way;

or reinterpret ordinary nuisance effects as accessibility structure.

Any such change is a modified execution tuple.

The original instantiated model either survives, fails, or remains unadjudicated under the declared accessibility lock.

8. Baseline, Nuisance, and Rival Locks

8.1 Purpose

The baseline, nuisance, and rival locks fix the null comparison and the ordinary explanations that must be excluded before a result can be called CBR-compatible.

This section has three functions.

First, it defines the standard quantum baseline class 𝔅_SQM.

Second, it defines the bounded nuisance envelope 𝒩.

Third, it declares the hostile-rival model suite R₁ through R₁₄ and the diagnostics required to exclude them.

The purpose of these locks is:

No redefining standard quantum behavior, expanding ordinary noise, or mistaking artifacts for CBR after empirical information is available.

A non-baseline deviation is not automatically CBR-compatible. It must be outside the declared baseline-plus-nuisance class, occur in the declared critical region, have the declared accessibility-critical form, survive hostile-rival exclusion, and replicate.

Conversely, baseline-class behavior under detectability-valid conditions is not merely uninteresting. Under the strong-null rule, it entails failure of the instantiated canonical CBR model.

8.2 Baseline lock

Define:

𝔅_SQM = declared standard quantum baseline class

The baseline class contains the standard quantum prediction for the declared context, including the declared treatment of ordinary decoherence, apparatus imperfection, finite visibility, and known platform effects.

Define:

V_SQM(η) = standard quantum baseline visibility curve

V_SQM(η) is the primary baseline comparator for V_obs(η).

The exact form of V_SQM(η) must be fixed before adjudication. If the canonical comparator is V_SQM(η) = 1 − η, that form must be stated. If a platform-specific baseline is used, its derivation, calibration, free parameters, and allowed uncertainty must be declared before data interpretation.

The baseline lock prevents the model from revising “what standard quantum mechanics predicted” after the result.

8.3 Baseline-validity conditions

A baseline is valid only if:

the standard quantum comparator is derived or declared before testing;

ordinary decoherence and apparatus effects included in 𝔅_SQM are specified;

any platform-specific parameters are calibrated independently or predeclared;

baseline uncertainty is propagated into 𝒩;

and the baseline does not absorb result-dependent features after data.

If the baseline cannot be fixed, the test cannot trigger strong-null failure. The result is inconclusive because the null was not sufficiently specified.

8.4 Nuisance lock

Define:

V_null(η) = V_SQM(η) + ν(η), with ν ∈ 𝒩

where 𝒩 is the bounded nuisance envelope.

𝒩 contains allowed non-CBR deviations from ideal standard baseline behavior. It accounts for ordinary experimental imperfection, finite sampling, calibration uncertainty, and platform-specific limitations.

The nuisance envelope must be fixed before adjudication. It may be conservative, but it may not be result-dependent. A deviation counts as outside the null only if it exceeds the declared baseline-plus-nuisance envelope by more than δ_min under the pre-registered statistical rule.

This lock protects both sides.

It prevents CBR from calling every ordinary artifact a signal.

It also prevents critics from expanding “noise” after the fact to absorb any possible deviation.

8.5 Nuisance contents and boundedness

At minimum, 𝒩 must declare how it treats:

detector inefficiency;

phase drift;

finite visibility loss;

source instability;

environmental leakage;

timing jitter;

imperfect erasure;

finite-sample uncertainty;

η-calibration uncertainty;

background counts;

alignment drift;

thermal or mechanical instability;

data acquisition noise;

record-readout inefficiency;

and binning or interpolation uncertainty in η.

For each nuisance source, the paper must specify whether it is directly measured, bounded by calibration, absorbed into a conservative envelope, excluded by design, or treated as an inconclusive-test condition if uncontrolled.

The nuisance class must be finite, bounded, and declared. An open-ended nuisance class cannot support strong-null adjudication because it can absorb any result.

8.6 Nuisance-bound certificate

The execution standard requires a nuisance-bound certificate.

For each nuisance source, the certificate must state:

the source;

the measurement or calibration method;

the bound or uncertainty model;

the rule for propagation into ν(η);

whether the source affects η, V_obs(η), V_SQM(η), or more than one;

and the condition under which the source invalidates the test rather than merely enlarging 𝒩.

The combined nuisance envelope may be expressed as an interval, function class, confidence band, credible band, or deterministic bound. The form must be declared before adjudication.

A result is outside the null only when:

V_obs(η) ∉ 𝔅_SQM + 𝒩

by more than δ_min in the declared critical region and under the pre-registered statistical rule.

8.7 Proposition 6 — Null Fixity

Claim.
𝔅_SQM + 𝒩 is fixed before adjudication.

Assumptions.
The standard baseline V_SQM(η), nuisance sources, nuisance bounds, nuisance propagation rules, rival diagnostics, and statistical threshold δ_min are declared before data interpretation.

Proof sketch.
Because V_SQM(η) is fixed and 𝒩 is constructed from predeclared nuisance sources and bounds, the null class 𝔅_SQM + 𝒩 is determined before adjudication. Any later expansion of 𝒩, alteration of V_SQM(η), or revision of nuisance propagation changes the null class and therefore changes the execution tuple.

Execution consequence.
A result is adjudicable only against the predeclared null. If the null must be revised after data, the original test becomes unadjudicated or the revised model must be treated as a new execution tuple.

8.8 Rival-model lock

The hostile-rival suite defines ordinary or non-CBR explanations that must be excluded before a non-baseline deviation can be treated as CBR-compatible.

The rival suite must be declared before testing.

At minimum, the declared hostile rivals are:

R₁ = ordinary decoherence with imperfect erasure.

R₂ = detector-efficiency drift.

R₃ = phase-noise visibility loss.

R₄ = postselection bias.

R₅ = environmental leakage.

R₆ = miscalibrated η.

R₇ = source instability.

R₈ = data-binning artifact.

R₉ = timing jitter.

R₁₀ = memory effects in the record system.

R₁₁ = detector dead-time artifact.

R₁₂ = uncontrolled mode mismatch.

R₁₃ = thermal or mechanical drift.

R₁₄ = analysis-choice artifact.

The list may be expanded before adjudication if the platform requires additional rivals. It may not be expanded or contracted after data in a result-dependent way while preserving the same test.

8.9 Rival-exclusion certificate

A hostile-rival list is insufficient by itself. The paper must also declare a rival-exclusion certificate.

For each rival Rᵢ, the certificate must state:

the rival mechanism;

the observable or diagnostic used to test it;

the exclusion threshold;

whether exclusion is required for CBR-compatible interpretation;

whether failure to exclude makes the result inconclusive;

and whether the rival is already included in 𝒩 or separately diagnosed.

This is necessary because a “rivals considered” list is weaker than a “rivals excluded by declared diagnostics” standard.

A CBR-compatible result requires not merely that rivals were named, but that they were excluded by the predeclared diagnostic standard.

8.10 Rival exclusion standard

A CBR-compatible result must satisfy all of the following:

it occurs in U(η_c);

it has the declared accessibility-critical form;

it exceeds δ_min;

it lies outside 𝔅_SQM + 𝒩;

it survives R₁ through R₁₄ under the rival-exclusion certificate;

and it replicates under the declared replication standard.

This is deliberately stronger than “the data deviate from the baseline.” A deviation may be due to ordinary decoherence, detector drift, phase instability, postselection, environmental leakage, η miscalibration, data binning, or another rival. The execution standard permits CBR-compatible interpretation only after such rivals have been excluded under predeclared diagnostics.

8.11 Binding baseline-nuisance-rival rule

After data interpretation begins, canonical CBR may not:

redefine 𝔅_SQM;

alter V_SQM(η);

expand 𝒩;

add new nuisance allowances;

change nuisance propagation rules;

discard hostile rivals;

weaken rival-exclusion diagnostics;

or reinterpret an identified artifact as a CBR-compatible result.

Any such change creates a modified execution tuple.

Under the baseline, nuisance, and rival locks, a result has only three possible statuses: baseline-class behavior, CBR-compatible non-baseline behavior, or inconclusive behavior. It cannot be moved among these categories by post hoc alteration of the null or rival suite.

9. Statistical and Verdict Locks

9.1 Purpose

The statistical and verdict locks fix the decision rule under which the instantiated canonical CBR model is judged.

The earlier locks determine the tested model, admissible class, burden evaluation, coefficient convention, instantiation, accessibility calibration, standard baseline, nuisance envelope, and hostile-rival suite. Those locks make the model executable. The statistical and verdict locks determine whether the executed model is adjudicated as failed, CBR-compatible, or inconclusive.

The purpose of this section is:

No changing the statistical test, evidential threshold, or verdict interpretation after empirical information is available.

A candidate law is not publicly testable merely because it says that an empirical deviation would be relevant. It becomes publicly testable only when it states in advance:

what counts as baseline-class behavior;

what counts as a CBR-compatible non-baseline result;

what counts as inconclusive;

what sensitivity is required for failure;

what threshold is required for non-baseline interpretation;

and what statistical procedure governs the verdict.

The execution standard therefore requires a pre-registered adjudication rule.

9.2 Adjudication-validity conditions

Before any verdict is assigned, the test must satisfy adjudication-validity conditions.

A test is adjudication-valid only if all required locks are in force:

the model execution tuple is fixed;

𝒜(C) is constructively generated;

the burden evaluation certificate is declared;

α, β, and γ are fixed;

C_DCE is fixed;

η is independently calibrated;

η_c, D_crit, and U(η_c) are fixed;

𝔅_SQM and 𝒩 are fixed;

rival-exclusion diagnostics are declared;

δ_min is pre-registered;

the statistical method is fixed;

and the verdict categories are fixed.

If these conditions are not met, the result is not a failure and not support. It is unadjudicated.

This condition should be stated before the null hypothesis because strong-null failure is meaningful only inside an adjudication-valid test.

9.3 Null hypothesis

The strong-null hypothesis is:

H₀: V(η) ∈ 𝔅_SQM + 𝒩 across D_crit.

This says that the observed visibility behavior remains inside the declared standard quantum baseline class plus the bounded nuisance envelope throughout the experimentally accessible critical accessibility domain.

H₀ is not merely “no CBR signal.” It is a positive baseline-class claim: the data remain adequately described by the predeclared standard comparator and ordinary nuisance structure over the declared test domain.

Under adjudication-valid and detectability-valid conditions, H₀ has a strong consequence. If H₀ holds across D_crit, the instantiated canonical model reaches F₃: failure of the instantiated canonical CBR model.

9.4 CBR-compatible alternative

The CBR-compatible alternative is:

H₁: there exists η ∈ U(η_c) such that V_obs(η) leaves 𝔅_SQM + 𝒩 by more than δ_min with the declared accessibility-critical structure.

This alternative is intentionally narrow.

A result is not CBR-compatible merely because it deviates from the baseline. The deviation must satisfy all of the following:

η is independently calibrated;

the test is adjudication-valid;

the test is detectability-valid;

the deviation occurs in U(η_c);

the deviation exceeds δ_min;

the deviation lies outside 𝔅_SQM + 𝒩;

the deviation has the declared accessibility-critical form;

hostile-rival explanations are excluded;

and the result satisfies the declared replication standard.

This prevents generic anomaly inflation. A CBR-compatible result is not merely an anomaly; it is a structured non-baseline result satisfying the predeclared accessibility, nuisance, rival-exclusion, and replication conditions.

9.5 Statistical threshold δ_min

δ_min is the minimum deviation threshold required for non-baseline interpretation.

δ_min must be declared before testing.

It must exceed the combined uncertainty and nuisance envelope in the relevant domain. A deviation smaller than δ_min may motivate further study, but it cannot count as CBR-compatible under the pre-registered execution standard.

The threshold must be defined relative to the primary observable. If the primary observable is V_obs(η), then δ_min must specify the minimum visibility deviation from 𝔅_SQM + 𝒩 required for adjudication.

Depending on the declared response form, δ_min may be specified as:

an absolute deviation;

a standardized effect size;

a minimum kink magnitude;

a derivative-break threshold;

a lower-bound deviation;

or another predeclared statistic.

The chosen statistic must be fixed before data interpretation.

9.6 Detectability-valid conditions

Adjudication validity and detectability validity are distinct.

Adjudication validity means the execution tuple and decision rule were fixed.

Detectability validity means the experiment was sensitive enough to detect the declared effect if it existed at or above δ_min.

A test is detectability-valid only if:

η calibration is valid;

η values adequately cover D_crit;

sampling density is adequate in U(η_c);

visibility precision is sufficient to resolve δ_min;

nuisance uncertainty does not swamp the detection margin;

statistical power is adequate;

baseline and nuisance classes are fixed;

and rival diagnostics are sufficient.

If detectability validity fails, baseline-class behavior does not entail F₃. The result is inconclusive.

This distinction prevents invalid failure claims. A model is not falsified by an experiment that could not have detected its declared signature.

9.7 Statistical procedure

The statistical procedure must be pre-registered.

At minimum, the pre-registration must declare:

primary observable;

η-calibration method;

η sampling plan;

D_crit;

U(η_c);

δ_min;

sample size;

statistical power;

confidence or credible interval method;

η-scan correction, if applicable;

nuisance propagation method;

rival-exclusion diagnostics;

replication standard;

and verdict categories.

No post hoc switching of inferential method is permitted while preserving the same execution tuple.

If η_c is scanned rather than derived or pre-registered, the scan range and penalty must be declared before analysis. An unpenalized post hoc selection of η_c is inadmissible.

9.8 Proposition 7 — Strong-Null Failure

Claim.
Under adjudication-valid and detectability-valid conditions, baseline-class behavior across D_crit entails F₃: failure of the instantiated canonical CBR model.

Assumptions.
The execution tuple is fixed. η is independently calibrated. 𝔅_SQM + 𝒩 is fixed. D_crit and U(η_c) are declared. δ_min is pre-registered. The test is adjudication-valid and detectability-valid. Rival diagnostics are satisfied. The observed behavior remains inside 𝔅_SQM + 𝒩 across D_crit.

Proof sketch.
The instantiated canonical model asserts empirical exposure in the declared accessibility-critical domain. Under the execution tuple, H₀ represents baseline-class behavior across D_crit, while H₁ represents the declared CBR-compatible non-baseline alternative. If adjudication and detectability conditions hold, then the experiment was both procedurally fixed and sensitive enough to detect the declared CBR-compatible deviation. If the observed behavior nevertheless remains inside the baseline-plus-nuisance class across D_crit, the declared accessibility signature is absent under valid test conditions. By the strong-null failure rule, the instantiated canonical CBR model fails at level F₃.

Execution consequence.
Baseline-class behavior under adjudication-valid and detectability-valid conditions is not merely absence of support. It is failure of the instantiated canonical model.

9.9 Verdict 1: F₃ canonical CBR failure

The verdict is F₃ canonical CBR failure when all of the following hold:

the execution tuple is fixed;

the experiment is adjudication-valid;

the experiment is detectability-valid;

η is independently calibrated;

η_c, D_crit, and U(η_c) are fixed;

𝔅_SQM and 𝒩 are fixed;

δ_min is predeclared;

hostile-rival diagnostics are satisfied;

statistical power is adequate;

and V_obs(η) remains inside 𝔅_SQM + 𝒩 across D_crit.

The verdict is:

F₃ — failure of the instantiated canonical CBR model.

This verdict does not imply that every possible realization-law theory is false. It does not imply that every future CBR variant is false. It means that the locked canonical instantiation failed under its own strong-null rule.

9.10 Verdict 2: CBR-compatible non-baseline result

The verdict is CBR-compatible non-baseline result when all of the following hold:

the execution tuple is fixed;

the experiment is adjudication-valid;

the experiment is detectability-valid;

η is independently calibrated;

the deviation occurs in U(η_c);

the deviation exceeds δ_min;

the deviation has the declared accessibility-critical form;

the deviation lies outside 𝔅_SQM + 𝒩;

hostile-rival explanations are excluded;

and the result satisfies the declared replication standard.

The verdict is:

CBR-compatible non-baseline evidence.

This is not final confirmation. It is a structured survival-and-support result for the instantiated canonical model under the declared execution standard.

The paper should avoid stronger language such as “confirmed CBR” unless a separate, broader confirmation standard is defined across independent implementations.

9.11 Verdict 3: inconclusive or unadjudicated

The verdict is inconclusive when the test fails to satisfy the conditions required for either F₃ failure or CBR-compatible non-baseline interpretation.

Examples include:

incomplete execution tuple;

η calibration failure;

invalid or circular η estimation;

failure to cover D_crit;

insufficient sampling near U(η_c);

nuisance envelope invalid or underbounded;

baseline comparator not fixed;

rival models not excluded;

insufficient statistical power;

failure of replication;

or post hoc changes to the execution tuple.

An inconclusive result is not failure. It is also not support. It means that the canonical model was not adjudicated under the execution standard.

9.12 Verdict exclusivity

The verdict categories are mutually exclusive under a fixed execution tuple.

A result cannot simultaneously count as F₃ failure and CBR-compatible non-baseline evidence.

A result cannot be moved from inconclusive to supportive by post hoc relaxation of the nuisance envelope, rival-exclusion requirement, or replication standard.

A result cannot be moved from failure to survival by redefining η, moving η_c, altering δ_min, or changing the baseline comparator.

This exclusivity is the purpose of the verdict lock. It ensures that empirical interpretation is fixed by the predeclared standard rather than negotiated after data.

9.13 Binding statistical-verdict rule

After data interpretation begins, canonical CBR may not change:

H₀;

H₁;

δ_min;

D_crit;

U(η_c);

the primary observable;

the statistical method;

the η-scan correction;

the power requirement;

the nuisance propagation method;

the rival-exclusion rule;

the replication standard;

or the verdict categories.

Any such change creates a modified execution tuple.

Under the statistical and verdict locks, the original instantiated model either fails, yields a CBR-compatible non-baseline result, or remains inconclusive. It cannot be reclassified by post hoc statistical or interpretive adjustment.

10. Failure Taxonomy and No-Rescue Doctrine

10.1 Purpose

The failure taxonomy and no-rescue doctrine define the consequence of an adjudication result.

The failure taxonomy prevents overclaiming. It distinguishes implementation failure, response-function failure, instantiated-model failure, accessibility-relevance failure, and broad program failure.

The no-rescue doctrine prevents underclaiming. It forbids treating a failed locked model as if it survived by altering the execution tuple after the fact.

The purpose of this section is:

No ambiguous failure claims and no retroactive survival of a modified model as the original model.

10.2 Failure level F₁: implementation failure

F₁ is implementation failure.

F₁ occurs when the experiment fails to satisfy the execution standard sufficiently to adjudicate the model.

Examples include:

η is not independently calibrated;

D_crit is not adequately covered;

visibility precision is insufficient;

the nuisance envelope is not bounded;

the baseline comparator is not fixed;

rival diagnostics are absent;

or the protocol deviates from the locked context.

F₁ does not falsify the instantiated canonical CBR model. It means the test failed to reach adjudication.

The proper verdict is inconclusive.

10.3 Failure level F₂: response-function failure

F₂ is response-function failure.

F₂ occurs when a specific proposed response shape, parametric curve, derivative break, kink structure, or lower-bound deviation form fails, but the broader instantiated canonical model has not been fully adjudicated.

F₂ is narrower than F₃.

For example, if a specific visibility response V_CBR(η) is ruled out but the execution tuple did not bind the entire canonical model to that exact response form, then the failed object is the response function, not the instantiated model as a whole.

To prevent ambiguity, the pre-registration must state whether a response form is illustrative, weak-form, or binding.

If the response form is binding, its failure may imply F₃. If it is not binding, its failure remains F₂.

10.4 Failure level F₃: instantiated canonical CBR failure

F₃ is failure of the instantiated canonical CBR model.

This is the primary invalidation level targeted by the strong-null rule.

F₃ occurs when:

the execution tuple is fixed;

the test is adjudication-valid;

the test is detectability-valid;

η is independently calibrated;

𝔅_SQM + 𝒩 is fixed;

rival diagnostics are satisfied;

and V_obs(η) remains baseline-class across D_crit.

Under these conditions, the declared accessibility signature is absent where the instantiated canonical model required empirical exposure. The model has failed under its own execution standard.

F₃ is stronger than “no support.” It is failure of the locked canonical instantiation.

10.5 Failure level F₄: accessibility-relevance failure

F₄ is accessibility-relevance failure in the tested domain.

F₄ is broader than F₃. It concerns the claim that accessibility is realization-effective across the relevant tested domain.

A single valid F₃ result may not be enough for F₄. F₄ requires a broader pattern: repeated adjudication-valid and detectability-valid tests across relevant implementations showing baseline-class behavior where accessibility-sensitive exposure was required.

F₄ does not necessarily refute every possible realization-law theory. It undermines the accessibility-relevance thesis in the tested domain.

10.6 Failure level F₅: broad CBR program failure

F₅ is broad CBR program failure.

This is the strongest failure level. It would require more than one failed instantiation. It would require a pattern of valid failures, lack of viable canonical revision, and erosion of the formal or empirical basis for CBR as a candidate realization-law program.

F₅ should be used sparingly.

The execution standard does not claim that one failed experiment automatically reaches F₅. Its primary invalidation target is F₃.

This restraint preserves seriousness. It prevents overclaiming while keeping strong-null failure meaningful.

10.7 Main adjudication reach

The direct adjudication reach of this paper is F₃.

The paper defines conditions under which the instantiated canonical CBR model fails.

Repeated F₃ failures across independent implementations may support F₄.

F₅ requires broader theoretical and empirical collapse.

The paper should therefore state:

This execution standard directly adjudicates instantiated canonical CBR. It does not automatically adjudicate every possible CBR modification, every possible realization-law theory, or the entire program in one experiment.

10.8 No-rescue doctrine

The no-rescue doctrine states that a model may not be modified after empirical information is available while claiming that the original model survived.

After data interpretation begins, canonical CBR may not change:

C;

𝒜(C);

𝒞₀(C);

∼ₒₚ;

Ξ_C, Ω_C, Λ_C;

the burden evaluation certificate;

α, β, γ;

η;

η_c;

D_crit;

U(η_c);

δ_min;

𝔅_SQM;

𝒩;

rival exclusions;

statistical procedure;

replication requirement;

or verdict categories.

Changing any of these objects creates a modified execution tuple.

Modified models are allowed. Calling them survival of the failed model is not.

10.9 Modified-model rule

A revised model may be proposed after failure, but it must satisfy three conditions.

First, it must be labeled as a modified model.

Second, it must state which lock changed.

Third, it must provide a new execution tuple before any new adjudication.

A modified model cannot retroactively convert an F₃ failure into survival. It can only propose a future test.

This rule allows scientific revision without permitting post hoc rescue.

10.10 Evidential accounting after revision

The no-rescue doctrine also governs evidential accounting.

If the original model fails at F₃ and a modified model is proposed, the record must state:

the original locked model failed under the declared execution standard;

the modification was introduced after that result;

the modified model requires independent adjudication;

and the failed model’s evidence cannot be counted as support for the modified model unless the modified model had independently predicted the same result under a fixed tuple.

This prevents evidence laundering: treating a result that falsified one model as support for a revised model that was not fixed before the test.

10.11 Binding no-rescue rule

The same instantiated canonical model either survives, fails, or remains unadjudicated under the predeclared rules.

It cannot be redefined into survival after the fact.

This is the binding no-rescue rule.

11. Probability Standing and the Probability-Standing Lock

11.1 Purpose

This section defines the probability-standing condition required for executable CBR.

The purpose is:

No treating probability weighting as a post hoc rescue parameter, and no overstating local quadratic weighting as a derivation of probability from nothing.

The execution standard does not require CBR to derive Hilbert-space geometry, probability theory, or the full Born rule from no assumptions whatsoever. It requires a narrower condition: within standard quantum amplitude structure and canonical admissibility, realization weighting must not remain freely adjustable.

The probability-standing lock therefore fixes what executable CBR may and may not claim about weighting.

11.2 Probability-standing lock

The probability-standing lock has three parts.

First, canonical CBR may assume standard quantum amplitude structure as part of the background formalism.

Second, within that structure, admissible realization weighting must satisfy the canonical constraints of admissible refinement, operational invariance, symmetry, normalization, nontriviality, and regularity.

Third, after data interpretation begins, the model may not alter its weighting rule, admissible refinement rule, or probability-related burden structure to recover agreement with observed outcomes.

This lock prevents probability weighting from becoming a hidden rescue parameter.

11.3 Non-claims

Executable CBR does not claim that probability is derived from nothing.

It does not claim that Hilbert-space geometry is derived from CBR.

It does not claim universal Born-rule closure across every possible admissibility geometry.

It does not claim that every possible realization-law framework must use the canonical CBR admissibility structure.

It does not claim that a local quadratic-weighting result empirically confirms CBR.

It does not claim that frequency data may be fit after the fact by adjusting realization weights.

These non-claims are part of the execution standard. They prevent the probability result from being used more broadly than its premises allow.

11.4 Local uniqueness claim

The probability claim used by executable CBR is:

Given standard quantum amplitude structure and canonical admissibility, admissible refinement, operational invariance, symmetry, normalization, nontriviality, and regularity exclude distinct normalized nonquadratic realization weights.

Equivalently, inside the canonical execution framework, realization weighting is not a free post hoc degree of freedom.

The claim is local in three respects.

It is local to standard quantum amplitude geometry.

It is local to canonical CBR admissibility.

It is local to realization weighting, not to the whole truth of the theory.

This local formulation is stronger than an overbroad claim because it states exactly what is being constrained.

11.5 Correct formulation

The correct formulation is:

The quadratic-weighting result is a local uniqueness result for realization weights inside standard quantum amplitude geometry and canonical admissibility.

It is not:

a derivation of Hilbert-space geometry;

a derivation of probability from no assumptions;

a proof that all possible realization-law frameworks must have the same admissibility structure;

or a substitute for empirical adjudication.

Therefore, even if local quadratic weighting is secured, the instantiated canonical CBR model still faces the strong-null accessibility test. Probability standing supports internal coherence. It does not establish empirical truth.

11.6 Anti-circularity rule

A probability-related structure is inadmissible if it does any of the following:

builds target outcome frequencies directly into 𝒜(C);

uses hidden Born-weight penalties inside Ξ_C, Ω_C, or Λ_C;

defines admissible refinement by simply assuming the desired realization weights rather than by standard amplitude structure and operational refinement constraints;

retunes α, β, or γ to recover target frequencies after observing data;

or treats agreement with ordinary Born statistics as confirmation of the realization law.

The execution standard separates:

standard quantum amplitude geometry;

admissible realization weighting;

empirical outcome frequencies.

Standard amplitude geometry belongs to the background formalism.

Admissible realization weighting is constrained by the local uniqueness result.

Empirical frequencies do not replace the accessibility-signature test.

11.7 Execution role of probability standing

Probability standing enters the execution standard in three places.

First, it constrains admissibility. Channels that smuggle target weights into the selection law fail probabilistic non-insertion.

Second, it constrains burden evaluation. Ξ_C, Ω_C, and Λ_C may not hide probability-fitting terms.

Third, it constrains revision. A failed accessibility-signature test cannot be rescued by changing the realization-weighting rule while claiming the same canonical model survived.

Thus, probability standing is not a decorative appendix. It is part of the no-rescue architecture.

11.8 Binding probability-standing rule

After data interpretation begins, canonical CBR may not:

alter its realization-weighting rule;

redefine admissible refinement;

insert target outcome weights into 𝒜(C);

add probability penalties to Ξ_C, Ω_C, or Λ_C;

retune α, β, or γ to recover frequencies;

or treat local quadratic weighting as empirical confirmation of the whole model.

Any such change is a modified execution tuple or an overclaim.

The original instantiated canonical model must stand or fall under its declared probability standing.

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12. Claims, Non-Claims, and Final Canonical Execution Standard

12.1 Purpose

This section states the final standard.

The paper does not expand CBR. It defines the conditions under which canonical CBR may count as executable, testable, supported, invalidated, or left unadjudicated.

The purpose is:

No expansion by implication, no weakening by ambiguity, and no survival by reinterpretation.

The execution standard is severe by design. It strengthens canonical CBR by fixing the conditions under which it may fail.

12.2 What this paper claims

This paper claims that canonical CBR is executable only when the following are fixed before data interpretation:

the tested canonical object;

the measurement context C;

the construction of 𝒜(C);

the operational quotient ∼ₒₚ;

the burden evaluation procedure;

the coefficient convention;

the delayed-choice record-accessibility instantiation;

the η-calibration method;

η_c, D_crit, and U(η_c);

the standard quantum baseline 𝔅_SQM;

the nuisance envelope 𝒩;

the hostile-rival suite and exclusion diagnostics;

H₀ and H₁;

δ_min;

statistical power and inference method;

replication standard;

verdict categories;

failure taxonomy;

no-rescue rules;

and probability-standing constraints.

The paper also claims that, under adjudication-valid and detectability-valid conditions, baseline-class behavior across D_crit entails F₃: failure of the instantiated canonical CBR model.

This is the central invalidation claim.

12.3 What this paper does not claim

This paper does not claim that CBR is experimentally confirmed.

It does not claim that CBR replaces ordinary quantum mechanics.

It does not claim that CBR proves all rival frameworks false.

It does not claim that CBR derives probability from nothing.

It does not claim that CBR derives Hilbert-space geometry.

It does not claim that CBR solves all of quantum foundations.

It does not claim that one valid F₃ failure destroys every possible realization-law theory.

It does not claim that every future CBR modification is impossible.

It does not claim that an inconclusive test supports CBR.

It does not claim that a CBR-compatible non-baseline result is final confirmation.

It does not claim that canonical CBR can be rescued without declaring a modified model.

These non-claims are not concessions against the theory. They are conditions of scientific discipline.

12.4 The canonical execution standard

The canonical execution standard is:

Canonical CBR is executable only when the full execution tuple is fixed:

(C, 𝒜(C), ℛ_C, α, β, γ, η, η_c, 𝔅_SQM, 𝒩, δ_min, D_crit, U(η_c), H₀, H₁)

and when all locks are in force:

model lock;

admissibility lock;

burden lock;

coefficient lock;

instantiation lock;

accessibility lock;

critical-regime lock;

baseline lock;

nuisance lock;

rival-model lock;

statistical lock;

verdict lock;

failure-level lock;

no-rescue lock;

probability-standing lock.

If the locks are not fixed, the result may motivate future theory or future experiment, but it does not adjudicate the canonical model.

If the locks are fixed, the instantiated model has only three possible adjudication outcomes:

F₃ failure;

CBR-compatible non-baseline evidence;

or inconclusive/unadjudicated result.

No fourth category is permitted in which the model fails under its declared rules but survives by reinterpretation.

12.5 Public adjudication standard

A public canonical CBR test must satisfy twelve requirements.

First, the execution tuple must be declared before data interpretation.

Second, 𝒜(C) must be constructively generated by declared filters and operational quotienting.

Third, Ξ_C, Ω_C, and Λ_C must be evaluable or boundable over declared channel classes.

Fourth, α, β, and γ must be locked.

Fifth, C_DCE and its operational stages must be fixed.

Sixth, η must be independently calibrated.

Seventh, η_c, D_crit, and U(η_c) must be derived, pre-registered, or handled with explicit statistical penalty.

Eighth, 𝔅_SQM and 𝒩 must be fixed.

Ninth, hostile rivals must be declared and diagnostically excluded before positive interpretation.

Tenth, the statistical rule must be pre-registered.

Eleventh, verdict categories must be mutually exclusive.

Twelfth, no-rescue rules must prevent retroactive survival.

These requirements define when canonical CBR is publicly adjudicable.

12.6 Survival, support, and confirmation

The execution standard distinguishes survival, support, and confirmation.

Survival means the instantiated model has not failed under the declared execution standard.

CBR-compatible support means the test produced a structured non-baseline result satisfying the declared accessibility-critical form, nuisance separation, hostile-rival exclusion, and replication standard.

Confirmation is stronger and is not claimed here. Confirmation would require a broader evidential standard across independent implementations, hostile alternatives, and integration with the larger physics context.

A CBR-compatible result is meaningful. It is not final confirmation.

12.7 Failure, revision, and program status

The execution standard also distinguishes failure, revision, and program status.

F₃ failure means the locked instantiated canonical model failed.

Revision means a modified execution tuple is proposed after failure or inconclusive adjudication.

Program-level failure requires a broader pattern of valid failures and lack of viable canonical revision.

A single valid F₃ failure is serious. It invalidates the instantiated canonical model. It does not automatically refute every possible realization-law proposal.

12.8 Final execution principle

The final execution principle is:

Canonical CBR is not executable unless the locks are fixed before data interpretation.

If the locks are fixed, the model becomes publicly adjudicable.

If the locks are not fixed, the result may be interesting but does not decide the canonical model.

If the locks are changed after data, a modified model has been introduced.

This is the central contribution of the paper.

12.9 Conclusion

Constraint-Based Realization is strongest when it accepts public conditions of failure.

The canonical closure paper states the mature CBR law-candidate. The present paper supplies the execution standard required to apply and judge that candidate without post hoc flexibility. It fixes the model, admissible class, burden evaluation, coefficient convention, instantiation, accessibility calibration, critical domain, baseline comparator, nuisance envelope, hostile-rival exclusions, statistical rule, verdict taxonomy, no-rescue doctrine, and probability-standing constraint.

The result is not an expansion of CBR. It is a stricter form of accountability for canonical CBR.

Under this standard, canonical CBR cannot be casually applied, cannot be rescued after failure without revision, and cannot be dismissed as vague if all locks are satisfied.

A canonical realization law becomes scientifically serious not when it avoids failure, but when it states in advance the exact conditions under which it is no longer the law.

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Appendices

The Canonical Execution Standard for Constraint-Based Realization

Constructive Admissibility, Calibrated Accessibility, and Strong-Null Adjudication

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Appendix A — Formal Admissibility Pipeline

A.1 Purpose

This appendix defines the formal admissibility pipeline used to construct the restricted admissible class 𝒜(C). In the canonical execution standard, 𝒜(C) is not an informal collection of possible channels. It is a constructively generated selection domain.

The purpose of this appendix is to make the following condition enforceable:

Canonical CBR is not executable in a context C unless 𝒜(C) is generated by a declared admissibility pipeline before data interpretation.

The admissibility pipeline is:

𝒞₀(C) → admissibility filters → 𝒜(C) → 𝒜(C) ÷ ∼ₒₚ

where 𝒞₀(C) is the initial candidate channel class, 𝒜(C) is the restricted admissible class, and ∼ₒₚ is the operational equivalence relation.

The pipeline must be declared before adjudication. If the pipeline is altered after empirical information is available, the tested object has changed and the original canonical model has not survived. A modified model has been introduced.

A.2 Required input data for C

A context C is a physically specified measurement context. It is not merely an observable label, basis choice, or verbal description of an experiment.

For executable CBR, C must declare all realization-relevant and adjudication-relevant structures. At minimum, C must include:

the prepared quantum system;

the measurement apparatus;

the record subsystem;

the eraser or accessibility-control subsystem, when present;

the uncontrolled environment or nuisance degrees of freedom;

the timing structure;

the measurement interaction;

the record-bearing correlations;

the accessibility structure;

the primary empirical observable;

the η-calibration procedure;

the standard baseline comparator;

the nuisance envelope;

the critical accessibility domain;

the critical neighborhood;

and the pre-registered verdict rule.

For the delayed-choice record-accessibility context C_DCE, the preferred finite-dimensional decomposition is:

ℋ = ℋ_path ⊗ ℋ_record ⊗ ℋ_eraser ⊗ ℋ_environment

where ℋ_path carries the path variable W, ℋ_record carries the record subsystem R, ℋ_eraser carries erasure or accessibility-control degrees of freedom, and ℋ_environment carries uncontrolled environmental or nuisance degrees of freedom.

C is sufficient only if these structures are specified with enough precision to determine admissibility, burden evaluation, η calibration, baseline comparison, and verdict assignment.

A.3 Initial candidate class 𝒞₀(C)

Let 𝒞₀(C) denote the broad starting class of candidate realization channels in context C.

A channel Φ ∈ 𝒞₀(C) is not yet admissible. It is only eligible for admissibility filtering.

The paper or protocol must declare what kinds of objects belong to 𝒞₀(C). Depending on the implementation, these may be:

completely positive trace-preserving maps;

effective operational maps;

context-relative realization maps;

coarse-grained channel classes;

or explicitly defined equivalence classes of candidate realization structures.

The choice must be declared before data interpretation. A candidate type may be excluded from 𝒞₀(C) only for a declared physical, mathematical, or operational reason. It may not be excluded because of the empirical result.

Thus:

Φ ∈ 𝒞₀(C)

does not imply:

Φ ∈ 𝒜(C)

Admissibility is determined only after the declared filters are applied.

A.4 Filter 1 — Dynamical compatibility

A candidate channel Φ passes dynamical compatibility only if it does not covertly replace ordinary quantum dynamics outside realization selection.

CBR is a candidate law of outcome realization. It is not introduced as a replacement for standard quantum evolution, measurement interaction, apparatus dynamics, or ordinary decoherence modeling.

A channel fails dynamical compatibility if it:

changes the declared unitary or open-system evolution;

modifies amplitudes through an undeclared collapse mechanism;

introduces unregistered dynamics outside the execution tuple;

changes the standard baseline V_SQM(η);

or obtains the accessibility response by altering ordinary propagation rather than realization selection.

A channel passes this filter only if it leaves the declared dynamics intact and functions as a candidate realization-selection structure over the physical context already specified.

Failure of this filter is exclusionary.

A.5 Filter 2 — Representational invariance

A candidate channel Φ passes representational invariance only if its operational verdict is invariant under physically irrelevant reformulation of C.

Let 𝒢_rep(C) denote the declared class of representation-preserving transformations of C. These may include path relabeling, basis redescription, equivalent encoding of R, equivalent parametrization of the eraser/control subsystem, or other transformations that preserve the realization-relevant physical context.

A channel fails representational invariance if there exists g ∈ 𝒢_rep(C) such that g preserves the physical context but changes the operational realization verdict.

In schematic form, Φ fails if:

Verdict(Φ, C) ≠ Verdict(gΦg⁻¹, gC)

for a transformation g that is physically representation-preserving.

Representation dependence is exclusionary when it changes the operational verdict. It may be burden-bearing only if the dependence is intermediate, quotientable, and operationally null.

This filter prevents realization selection from depending on notation, labels, or redundant description.

A.6 Filter 3 — Record-structural coherence

A candidate channel Φ passes record-structural coherence only if it respects the declared record-bearing structure of C.

Let W be the outcome-relevant or which-path variable and R the declared record subsystem. The context must state the conditions under which R counts as record-bearing. A formal branch decomposition is not automatically a record-bearing structure.

A channel fails record-structural coherence if it:

ignores the declared record subsystem R;

selects over unsupported formal branch decompositions;

treats non-record-bearing alternatives as physical records;

changes realization verdicts independently of record structure;

or erases the distinction between record formation and arbitrary state decomposition.

A channel may remain admissible with positive Ω_C only if the misalignment is partial and non-fundamental. If it ignores record architecture entirely, exclusion is required.

This filter anchors realization selection in physical record structure while preserving the distinction between record formation and realization.

A.7 Filter 4 — Accessibility consistency

A candidate channel Φ passes accessibility consistency only if it treats accessibility-equivalent contexts equivalently and handles declared accessibility differences coherently.

Two contexts C and C′ are accessibility-equivalent when they have the same record-accessibility structure under the declared η-calibration procedure and preserve all other realization-relevant structures.

A channel fails accessibility consistency if:

C and C′ are accessibility-equivalent;

but Φ assigns different realization verdicts without declared physical distinction.

A channel also fails if it defines accessibility using the same visibility anomaly V_obs(η) that the model is supposed to test.

Accessibility consistency requires that η enter through the declared calibration procedure, not through post hoc interpretation of empirical deviations.

A channel may remain admissible with positive Λ_C only if its accessibility dependence is imperfect but predeclared, operationally meaningful, and separable from nuisance effects.

Circular, arbitrary, or result-dependent accessibility dependence is exclusionary.

A.8 Filter 5 — Probabilistic non-insertion

A candidate channel Φ passes probabilistic non-insertion only if it does not smuggle target probability weighting into the selection law.

A channel fails this filter if it:

builds desired outcome frequencies directly into 𝒜(C);

uses hidden Born-weight penalties inside Ξ_C, Ω_C, or Λ_C;

selects channels by empirical frequency matching;

defines admissible refinement by assuming the desired realization weights rather than by standard amplitude structure and operational refinement constraints;

or tunes realization weights after observing data.

This filter does not deny standard quantum amplitude geometry. It forbids covert insertion of target realization weights into the admissibility or burden machinery.

Failure of probabilistic non-insertion is exclusionary.

A.9 Filter 6 — Admissibility separation

A candidate construction passes admissibility separation only if it preserves operationally distinct candidates until the declared quotient ∼ₒₚ is applied.

A construction fails separation if it prematurely collapses physically distinct candidate verdicts.

Failure examples include:

identifying channels with different realization-relevant consequences;

collapsing Φ_base and Φ_acc before burden evaluation;

defining accessibility-sensitive and baseline-compatible candidates as equivalent without operational justification;

or defining ∼ₒₚ so broadly that empirical distinctions disappear.

Admissibility separation protects the meaning of restricted uniqueness. A uniqueness claim is meaningful only when distinct candidates were not removed by definitional compression before selection.

A.10 Construction of 𝒜(C)

After applying the filters, define:

𝒜(C) = {Φ ∈ 𝒞₀(C) : Φ passes the admissibility pipeline}

Equivalently, schematically:

𝒜(C) = F_sep(F_prob(F_acc(F_rec(F_rep(F_dyn(𝒞₀(C)))))))

where F_dyn, F_rep, F_rec, F_acc, F_prob, and F_sep denote the six filters.

A channel excluded by any filter does not enter minimization.

A channel that passes the filters may still incur positive burden under Ξ_C, Ω_C, or Λ_C. Passing admissibility means eligibility for minimization, not automatic selection.

A.11 Operational equivalence ∼ₒₚ

Define operational equivalence:

Φ ∼ₒₚ Ψ

if no admissible experiment in context C distinguishes Φ and Ψ at the level relevant to realization selection.

The quotient domain is:

𝒜(C) ÷ ∼ₒₚ

The selected object is:

[Φ⋆_C] = argmin{ℛ_C([Φ]) : [Φ] ∈ 𝒜(C) ÷ ∼ₒₚ}

Operational quotienting prevents notational multiplicity from being mistaken for physical multiplicity. It also prevents CBR from claiming representative-level uniqueness where only operational uniqueness is warranted.

The equivalence relation ∼ₒₚ must be declared before adjudication. It may not be broadened after data to hide failure or narrowed after data to manufacture success.

A.12 Non-emptiness condition

For CBR to be executable in C, 𝒜(C) must be nonempty:

𝒜(C) ≠ ∅

For C_DCE, a sufficient non-emptiness condition is the existence of at least one baseline-compatible candidate Φ_base satisfying:

ordinary dynamics are preserved;

representation-preserving transformations do not alter the verdict;

record-bearing structure is respected;

accessibility-equivalent contexts are treated equivalently;

no target probability weighting is inserted;

and operationally distinct candidates are not prematurely collapsed.

This establishes that minimization has a domain. It does not establish which channel is selected.

If 𝒜(C_DCE) = ∅, canonical CBR is not executable in C_DCE.

A.13 Stability conditions

The admissible class must be stable under transformations that should not alter the physical verdict.

At minimum, 𝒜(C) must be stable under:

representation change;

admissible refinement;

admissible coarse-graining;

composition of independent subcontexts;

and operational equivalence.

Stability under representation change means that redescribing the same physical context does not change the admissible verdict space.

Stability under refinement means that admissible subdivision does not introduce hidden weighting or arbitrary verdict changes.

Stability under coarse-graining means that operationally legitimate recombination does not alter realization verdicts arbitrarily.

Stability under composition means that independent contexts combine without spurious cross-context realization effects.

Stability under operational equivalence means that quotienting preserves the physical verdict.

A.14 Admissibility certificate

Every executable CBR test must include an admissibility certificate.

The certificate must declare:

C;

𝒞₀(C);

all six admissibility filters;

the status of each declared channel class;

∼ₒₚ;

𝒜(C) ÷ ∼ₒₚ;

non-emptiness;

stability conditions;

and any exclusionary thresholds.

The certificate must be complete before data interpretation.

A.15 Minimum sufficiency condition

The admissibility construction is sufficient only if all of the following hold:

𝒞₀(C) is declared;

all six admissibility filters are declared;

excluded classes are identified before data;

∼ₒₚ is declared;

𝒜(C) ÷ ∼ₒₚ is constructed;

𝒜(C) ≠ ∅ is shown or justified;

and stability conditions are stated.

A.16 Failure consequence

If the minimum sufficiency condition fails, canonical CBR is not executable in C.

This is not failure of CBR.

It is failure to construct an adjudicable model in that context.

Appendix B — Channel Catalogue and Burden Evaluation

B.1 Purpose

This appendix defines the channel catalogue and burden-evaluation structure for C_DCE.

The purpose is to make the following condition enforceable:

Canonical CBR is not executable in C_DCE unless each declared channel class has a fixed admissibility status, burden status, nuisance status if applicable, and evaluable or boundable burden profile before data interpretation.

The minimum catalogue contains:

Φ_base
Φ_acc
Φ_rep
Φ_rec
Φ_prob
Φ_noise

Additional channel classes may be added before adjudication, but not after data in a result-dependent way.

B.2 Required status categories

Each channel class must be assigned one of four statuses:

admitted;

excluded;

burden-bearing;

or assigned to nuisance modeling.

An admitted channel is eligible for minimization.

An excluded channel does not enter 𝒜(C_DCE).

A burden-bearing channel remains eligible but incurs positive Ξ_C, Ω_C, or Λ_C.

A nuisance-assigned channel belongs to 𝒩 rather than 𝒜(C_DCE).

A channel may not move among these categories after data interpretation begins.

B.3 Φ_base — baseline-compatible candidate

Φ_base is the baseline-compatible candidate channel class.

It represents a candidate that preserves ordinary dynamics, respects representation invariance, tracks record structure, treats accessibility-equivalent contexts equivalently, and contains no hidden probability insertion.

Expected status:

admitted or burden-bearing.

Possible burden profile:

Ξ_C(Φ_base) = 0 or low

Ω_C(Φ_base) = 0 or low

Λ_C(Φ_base) = low if accessibility-equivalent contexts are treated consistently

If Φ_base is selected, the instantiated model does not predict a CBR-specific non-baseline accessibility signature in C_DCE.

B.4 Φ_acc — accessibility-sensitive candidate

Φ_acc is the accessibility-sensitive candidate channel class.

It represents a candidate in which independently calibrated operational accessibility enters realization selection nontrivially.

Expected status:

admitted or burden-bearing, provided accessibility dependence is non-circular and predeclared.

Possible burden profile:

Ξ_C(Φ_acc) = 0 or low if representation-invariant

Ω_C(Φ_acc) = 0 or low if record-coherent

Λ_C(Φ_acc) = low if accessibility dependence is coherent and predeclared

If Φ_acc is selected, the model must state the accessibility-sensitive empirical exposure associated with that selection, including the declared critical regime and failure condition.

B.5 Φ_rep — representation-dependent excluded candidate

Φ_rep is a candidate whose realization verdict changes under physically irrelevant representation change.

Expected status:

excluded, unless representation dependence is merely intermediate and operationally quotientable.

Reason for exclusion:

failure of representational invariance.

Typical violation:

Verdict changes under path relabeling, basis redescription, equivalent record encoding, or equivalent parametrization of the eraser/control system.

Execution consequence:

Φ_rep may not be reintroduced after data to rescue the model.

B.6 Φ_rec — record-incoherent excluded candidate

Φ_rec is a candidate that fails to respect the declared record-bearing structure.

Expected status:

excluded, unless record misalignment is partial and burden-bearing rather than fundamental.

Reason for exclusion:

failure of record-structural coherence.

Typical violation:

ignores R;

selects over unsupported formal branches;

treats arbitrary decompositions as physical records;

or changes verdict independently of W–R record structure.

Execution consequence:

Φ_rec may not be admitted after data to reinterpret a failed result.

B.7 Φ_prob — probability-inserting excluded candidate

Φ_prob is a candidate that inserts target probability weighting into the selection law.

Expected status:

excluded.

Reason for exclusion:

failure of probabilistic non-insertion.

Typical violation:

uses outcome frequencies as a selection criterion;

inserts hidden Born-weight penalties;

tunes realization weights after data;

or defines admissible refinement by assuming the desired realization weights.

Execution consequence:

Probability weighting may not be used as a post hoc rescue mechanism.

B.8 Φ_noise — nuisance-induced effective channel

Φ_noise represents ordinary nuisance behavior.

Expected status:

assigned to 𝒩, not admitted to 𝒜(C_DCE).

Examples include detector inefficiency, phase drift, source instability, environmental leakage, timing jitter, imperfect erasure, dead-time artifacts, mode mismatch, thermal drift, and acquisition artifacts.

Execution consequence:

Φ_noise may explain deviations only through the declared nuisance or rival-model structure. It may not be moved into 𝒜(C_DCE) after data and treated as a realization-law channel.

B.9 Burden evaluation certificate

Every executable CBR test must include a burden evaluation certificate.

For each declared channel class, the certificate must state:

admissibility status;

whether the class is admitted, excluded, burden-bearing, or assigned to 𝒩;

Ξ_C value, bound, or ordinal status;

Ω_C value, bound, or ordinal status;

Λ_C value, bound, or ordinal status;

ℛ_C value, bound, or ordering;

eligibility for minimization;

and whether the declared information is sufficient to determine the selected operational verdict class.

The certificate may use exact values, inequalities, or ordinal rankings. It is sufficient only if it determines the minimizer or declares non-executability.

B.10 Minimum sufficiency condition

The channel catalogue and burden evaluation are sufficient only if every declared channel class has:

admissibility status;

burden status;

nuisance status if applicable;

Ξ_C, Ω_C, and Λ_C evaluation or bound;

ℛ_C ordering or explicit non-executability declaration;

and a fixed eligibility status for minimization.

B.11 Failure consequence

If the relevant admitted channel classes cannot be evaluated, bounded, or ordered sufficiently to determine a selected operational verdict class, the model is not executable in C_DCE.

This is not failure of CBR.

It is failure to instantiate an executable model in the declared context.

Appendix C — η Calibration Protocol

C.1 Purpose

This appendix defines the η-calibration protocol.

The purpose is to enforce the following condition:

Canonical CBR is not adjudicable in C_DCE unless η is calibrated independently of V_obs(η), with declared uncertainty, fixed critical-domain handling, and separation from ordinary nuisance effects.

η is the operational accessibility parameter. It is the empirical bridge between canonical CBR and the accessibility-signature test.

If η is inferred from the same visibility anomaly used to test CBR, the test is circular.

C.2 Definition of η

Define:

η = I_acc(W; R) ÷ H(W)

where W is the which-path variable, R is the record subsystem, I_acc(W; R) is accessible which-path mutual information, and H(W) is the entropy of W.

For binary W with controlled equal path probabilities:

H(W) = 1 bit

so:

η = I_acc(W; R)

when I_acc is measured in bits.

If W is not exactly balanced, H(W) must be estimated or bounded using the declared preparation distribution.

C.3 Declaration of W

The protocol must declare:

whether W is binary or multi-valued;

how W is prepared;

the intended distribution p(W);

how deviations from p(W) are measured;

and whether W is directly labeled, inferred from preparation, or reconstructed from calibration data.

For the simplest C_DCE implementation:

W ∈ {0, 1}

with:

p(W = 0) = p(W = 1) = 1 ÷ 2

unless preparation imbalance is measured and included.

C.4 Declaration of R

The protocol must declare:

the physical subsystem constituting R;

how R becomes correlated with W;

what measurement or retrieval operation accesses R;

what counts as record-bearing;

and how record-readout inefficiency is handled.

R must be distinguished from ℋ_environment. If which-path information leaks into uncontrolled environment rather than declared R, that leakage must be included in 𝒩 or in hostile-rival diagnostics.

C.5 Estimator for I_acc(W; R)

The estimator for I_acc(W; R) must be declared before adjudication.

Acceptable estimator classes include:

direct record-readout mutual information;

retrieval-task success bounds;

tomographic reconstruction with accessible-information optimization;

upper and lower bounds from operational measurement statistics;

or another explicitly defined estimator.

A direct-readout estimator may use:

I(W; R) = Σ_{w,r} p(w,r) log₂[p(w,r) ÷ (p(w)p(r))]

If the readout measurement is declared to be the accessibility-limiting measurement, then this measured mutual information may serve as I_acc(W; R).

If multiple measurement choices are allowed, the protocol must declare whether I_acc is an optimized quantity, a lower bound, an upper bound, or a fixed measurement-specific estimate.

C.6 Bias correction and uncertainty

Finite-sample mutual information estimates are biased.

The protocol must declare:

sample size;

bias-correction method;

uncertainty method;

confidence or credible interval;

calibration drift handling;

and propagation of uncertainty into η.

Let η̂ be the estimate of η. The protocol must report either:

η = η̂ ± Δη

or:

η ∈ [η_low, η_high]

The uncertainty must be propagated into D_crit, U(η_c), and 𝒩.

If η uncertainty prevents assignment of data to the declared critical domain or neighborhood, the result is inconclusive.

C.7 Independence from V_obs(η)

The η estimator must not use V_obs(η) as input.

Allowed:

record-readout calibration;

independent calibration runs;

interleaved calibration trials;

blinded calibration labels;

retrieval tasks independent of visibility deviation;

tomographic or bounded-accessibility estimates.

Not allowed:

estimating η from the magnitude of the visibility anomaly;

choosing η bins after inspecting V_obs(η);

moving η_c to match the observed deviation;

or defining accessibility as whatever parameter makes the data CBR-like.

The independence requirement is mandatory.

C.8 η sampling and binning

The protocol must declare:

η range;

number of η settings;

sampling density near U(η_c);

bin width;

binning rule;

handling of η uncertainty;

and whether bins are fixed before data.

Binning may not be changed after inspecting V_obs(η).

Sampling must cover D_crit sufficiently to support either F₃ failure or CBR-compatible non-baseline interpretation.

C.9 η_c, D_crit, and U(η_c)

η_c must be:

derived from the canonical model;

pre-registered;

or estimated with explicit statistical penalty.

D_crit is the experimentally accessible critical η-domain.

U(η_c) is the declared local neighborhood in which a CBR-compatible accessibility-critical response must occur.

All three must be fixed before adjudication, except under a predeclared penalized estimation rule.

Unpenalized post hoc movement of η_c, D_crit, or U(η_c) is inadmissible.

C.10 Accessibility-validity certificate

Every executable CBR test must include an accessibility-validity certificate.

The certificate must declare:

W;

R;

η estimator;

H(W) method;

I_acc(W; R) method;

bias correction;

η uncertainty;

η binning;

η_c handling;

D_crit;

U(η_c);

independence from V_obs(η);

and separation from nuisance effects.

C.11 Minimum sufficiency condition

η calibration is sufficient only if:

W and R are declared;

I_acc(W; R) estimator is declared;

H(W) is declared or estimated;

uncertainty is quantified;

η is independent of V_obs(η);

η_c, D_crit, and U(η_c) are fixed or penalized under a declared rule;

ordinary nuisance effects are separated, bounded, or declared inconclusive conditions.

C.12 Failure consequence

If η is not independently calibrated, the result is accessibility-invalid and therefore inconclusive.

It cannot count as F₃ failure.

It cannot count as CBR-compatible non-baseline evidence.

Appendix D — Null, Nuisance, and Rival Models

D.1 Purpose

This appendix defines the baseline comparator, nuisance envelope, and hostile-rival model suite.

The purpose is to enforce the following condition:

No result can count as F₃ failure or CBR-compatible evidence unless the null class 𝔅_SQM + 𝒩 and the hostile-rival diagnostics are fixed before adjudication.

A CBR-compatible result requires more than a deviation.

A strong-null failure requires more than absence of visible anomaly.

Both require a fixed null.

D.2 Standard baseline class 𝔅_SQM

Define:

𝔅_SQM = declared standard quantum baseline class

The baseline class must specify:

the model used to derive V_SQM(η);

fixed parameters;

calibrated parameters;

platform effects included in the baseline;

uncertainties propagated into 𝒩;

and effects assigned to hostile-rival diagnostics.

The baseline must be fixed before data interpretation.

D.3 Baseline visibility V_SQM(η)

Define:

V_SQM(η) = standard quantum baseline visibility curve

If the comparator is:

V_SQM(η) = 1 − η

that form must be declared.

If a platform-specific baseline is used, the protocol must declare:

derivation;

parameter values;

calibration method;

uncertainty;

domain;

and any allowed parameter variation.

A baseline with post hoc free parameters is inadmissible.

D.4 Nuisance envelope 𝒩

Define:

V_null(η) = V_SQM(η) + ν(η), with ν ∈ 𝒩

𝒩 is the bounded nuisance envelope.

It must be:

finite;

bounded;

declared;

and propagated into the statistical decision rule.

An open-ended nuisance class is inadmissible because it can absorb any result.

D.5 Required nuisance sources

At minimum, 𝒩 must address:

detector inefficiency;

phase drift;

finite visibility loss;

source instability;

environmental leakage;

timing jitter;

imperfect erasure;

finite-sample uncertainty;

η-calibration uncertainty;

background counts;

alignment drift;

thermal or mechanical instability;

data acquisition noise;

record-readout inefficiency;

binning or interpolation uncertainty in η;

and mode mismatch.

For each source, the protocol must declare whether it is measured, bounded, excluded by design, included in 𝒩, or treated as an inconclusive-test condition if uncontrolled.

D.6 Nuisance-bound certificate

Every adjudication-valid test must include a nuisance-bound certificate.

For each nuisance source, the certificate must state:

source;

measurement or calibration method;

bound or uncertainty model;

propagation into ν(η);

whether it affects η, V_obs(η), V_SQM(η), or multiple quantities;

whether it is additive, multiplicative, correlated, or functional;

and when it invalidates the test rather than merely enlarging 𝒩.

The combined nuisance envelope may be an interval band, function class, confidence band, credible band, or deterministic bound. The form must be fixed before adjudication.

D.7 Null membership

A result is inside the null when:

V_obs(η) ∈ 𝔅_SQM + 𝒩

across the declared domain.

A result is outside the null when:

V_obs(η) ∉ 𝔅_SQM + 𝒩

by more than δ_min under the pre-registered statistical rule.

If null membership is ambiguous because η uncertainty, nuisance uncertainty, or baseline uncertainty is too large, the result is inconclusive.

D.8 Hostile-rival suite

The hostile-rival suite contains ordinary or non-CBR mechanisms that must be excluded before positive interpretation.

The minimum rival suite is:

R₁ = ordinary decoherence with imperfect erasure.

R₂ = detector-efficiency drift.

R₃ = phase-noise visibility loss.

R₄ = postselection bias.

R₅ = environmental leakage.

R₆ = miscalibrated η.

R₇ = source instability.

R₈ = data-binning artifact.

R₉ = timing jitter.

R₁₀ = memory effects in the record system.

R₁₁ = detector dead-time artifact.

R₁₂ = uncontrolled mode mismatch.

R₁₃ = thermal or mechanical drift.

R₁₄ = analysis-choice artifact.

Additional rivals may be added before adjudication if platform-specific risks require them.

D.9 Rival-exclusion certificate

A rival list is insufficient without diagnostics.

For each rival Rᵢ, the protocol must declare:

the rival mechanism;

the observable or diagnostic used to test it;

the exclusion threshold;

whether it is included in 𝒩 or separately diagnosed;

whether failure to exclude it makes the result inconclusive;

and whether it can mimic the declared accessibility-critical form.

A result is CBR-compatible only if all required rival diagnostics are satisfied.

D.10 CBR-compatible non-baseline standard

A result is CBR-compatible only if:

η is independently calibrated;

the result occurs in U(η_c);

the deviation exceeds δ_min;

the deviation has the declared accessibility-critical form;

V_obs(η) lies outside 𝔅_SQM + 𝒩;

R₁ through R₁₄ are excluded by diagnostic rules;

and replication satisfies the declared standard.

If any required condition fails, the result is not CBR-compatible.

D.11 Minimum sufficiency condition

The null and rival structure are sufficient only if:

𝔅_SQM is fixed;

V_SQM(η) is fixed;

𝒩 is finite and bounded;

nuisance propagation is declared;

rival diagnostics are declared;

δ_min is defined relative to the null envelope;

and null membership is testable under the declared statistical rule.

D.12 Failure consequence

If the null is not fixed, no result can count as F₃ failure or CBR-compatible non-baseline evidence.

The result is null-invalid and therefore inconclusive.

Appendix E — Pre-Registration Template

E.1 Purpose

This appendix provides the required pre-registration template.

The purpose is to enforce:

A canonical CBR test is not adjudication-valid unless the execution tuple, locks, statistical procedure, verdict rules, and no-rescue declaration are fixed before data interpretation.

The template may be adapted to a laboratory platform, but materially missing fields make the test unadjudicated.

E.2 Model identification

Declare:

protocol title;

model name;

version number;

date;

authors;

laboratory or platform;

whether this is first test, replication, or modified-model test;

whether prior data were used in design;

and where the pre-registration is archived.

Declare the tested model as:

(C, 𝒜(C), ℛ_C, α, β, γ, η, η_c, 𝔅_SQM, 𝒩, δ_min, D_crit, U(η_c), H₀, H₁)

E.3 Context declaration

Declare:

C_DCE;

ℋ_path;

ℋ_record;

ℋ_eraser;

ℋ_environment;

W;

R;

eraser/control subsystem;

environmental or nuisance degrees of freedom;

timing structure;

record formation stage;

accessibility manipulation stage;

η-calibration stage;

visibility readout stage;

and adjudication stage.

E.4 Admissibility declaration

Declare:

𝒞₀(C_DCE);

six admissibility filters;

operational equivalence ∼ₒₚ;

𝒜(C_DCE);

non-emptiness argument;

stability conditions;

and 𝒜(C_DCE) ÷ ∼ₒₚ.

E.5 Channel catalogue

Declare status for:

Φ_base;

Φ_acc;

Φ_rep;

Φ_rec;

Φ_prob;

Φ_noise;

and any additional channel classes.

For each, declare admitted, excluded, burden-bearing, or assigned to 𝒩.

E.6 Burden evaluation

Declare:

Ξ_C codomain;

Ω_C codomain;

Λ_C codomain;

evaluation method;

bounds or ordinal rankings;

exclusion thresholds;

burden evaluation certificate;

and whether the evaluation determines a selected operational verdict class.

E.7 Coefficient convention

Declare:

α;

β;

γ;

normalization rule;

coefficient domain K, if any;

coefficient-insensitivity claim, if any;

and no-refit rule.

E.8 η calibration

Declare:

η = I_acc(W; R) ÷ H(W);

definition of W;

definition of R;

I_acc estimator;

H(W) method;

bias correction;

uncertainty interval;

η binning;

η sampling plan;

independence from V_obs(η);

and accessibility-validity certificate.

E.9 Critical regime

Declare:

η_c;

how η_c is derived, pre-registered, or estimated;

scan range, if any;

scan penalty, if any;

D_crit;

U(η_c);

sampling density near U(η_c);

and critical-regime validity conditions.

E.10 Baseline and nuisance

Declare:

𝔅_SQM;

V_SQM(η);

whether V_SQM(η) = 1 − η or platform-specific;

baseline derivation;

baseline parameters;

baseline uncertainty;

𝒩;

ν(η);

nuisance-bound certificate;

and null-membership rule.

E.11 Rival models

Declare:

R₁ through R₁₄;

additional platform-specific rivals;

diagnostic for each rival;

exclusion threshold for each rival;

whether failure to exclude makes the result inconclusive;

and whether each rival is part of 𝒩 or separately tested.

E.12 Statistical procedure

Declare:

primary observable;

secondary observables;

sample size;

statistical power;

δ_min;

minimum detectable effect;

confidence or credible interval method;

model-comparison method, if any;

η-scan correction;

multiple-testing correction;

nuisance propagation;

stopping rule;

blinding procedure, if any;

and data-exclusion criteria.

E.13 Verdict rules

Declare the three possible verdicts.

F₃ failure occurs if the test is adjudication-valid, detectability-valid, η is independently calibrated, the null is fixed, rival diagnostics are satisfied, and V_obs(η) remains inside 𝔅_SQM + 𝒩 across D_crit.

CBR-compatible non-baseline evidence occurs if the test is adjudication-valid, detectability-valid, η is independently calibrated, the deviation occurs in U(η_c), exceeds δ_min, has the declared accessibility-critical form, lies outside 𝔅_SQM + 𝒩, survives hostile rivals, and satisfies replication.

Inconclusive occurs if any required execution, calibration, detectability, nuisance, rival-exclusion, replication, or statistical condition fails.

E.14 Replication standard

Declare:

whether replication is required;

whether replication must be independent;

whether replication must be blinded;

whether the same execution tuple must be used;

what implementation variation is allowed;

and what counts as replication failure.

If replication is required but not yet performed, the result must be labeled provisional.

E.15 No-rescue declaration

Declare that after data interpretation begins, the model may not change:

C;

𝒜(C);

𝒞₀(C);

∼ₒₚ;

Ξ_C, Ω_C, Λ_C;

burden evaluation certificate;

α, β, γ;

η;

η_c;

D_crit;

U(η_c);

δ_min;

𝔅_SQM;

𝒩;

rival exclusions;

statistical procedure;

replication requirement;

verdict categories;

or probability-standing constraints.

Any change creates a modified execution tuple.

E.16 Transparency declaration

Declare:

what data will be recorded;

what data will be released;

what analysis code will be released;

what calibration files will be released;

what exclusions are allowed;

where pre-registration is stored;

and how deviations from pre-registration will be reported.

A deviation from pre-registration does not automatically invalidate the experiment, but it may change the result from adjudicated to inconclusive.

E.17 Final pre-registration statement

The pre-registration should end with:

This test adjudicates only the instantiated canonical CBR model defined by the execution tuple declared above. If any locked element is changed after data interpretation begins, the resulting model is a modified model and the original test no longer counts as survival of the original canonical instantiation. Under adjudication-valid and detectability-valid conditions, baseline-class behavior across D_crit entails F₃ failure. A CBR-compatible non-baseline result requires the declared accessibility-critical form, independent η calibration, nuisance separation, hostile-rival exclusion, and replication. An inconclusive result is neither support nor failure.

E.18 Minimum sufficiency condition

A pre-registration is sufficient only if it fixes:

execution tuple;

admissibility construction;

channel catalogue;

burden evaluation;

coefficient convention;

η calibration;

critical regime;

baseline and nuisance;

rival diagnostics;

statistical rule;

verdict categories;

failure taxonomy;

and no-rescue declaration.

E.19 Failure consequence

If pre-registration is absent or materially incomplete, the result is not adjudication-valid.

It cannot yield F₃ failure.

It cannot yield CBR-compatible non-baseline evidence.

Appendix F — Reviewer Audit Instrument

F.1 Purpose

This appendix provides a structured audit instrument for reviewers.

The purpose is to determine whether a proposed canonical CBR test is:

not executable;

executable but unadjudicated;

adjudication-valid;

detectability-valid;

F₃ failure;

CBR-compatible non-baseline evidence;

or inconclusive.

F.2 Audit status labels

Each audit item receives one status:

Satisfied = 2

Partially satisfied = 1

Not satisfied = 0

Not applicable = allowed only with written justification

A partially satisfied essential item is treated as not satisfied for purposes of executability, adjudication validity, detectability validity, or positive interpretation unless the protocol explains why partial satisfaction is sufficient.

F.3 Executability threshold

A test reaches the executable threshold only if the following essential items are satisfied:

model lock;

admissibility lock;

burden evaluation lock;

coefficient lock;

instantiation lock;

channel catalogue;

and no-rescue declaration.

If any essential item fails, the model is not executable.

F.4 Adjudication-valid threshold

A test reaches the adjudication-valid threshold only if it is executable and the following are satisfied:

η calibration;

critical-regime declaration;

baseline lock;

nuisance lock;

rival-model declaration;

statistical lock;

verdict lock;

failure taxonomy;

and pre-registration.

If any essential item fails, the result is unadjudicated or inconclusive.

F.5 Detectability-valid threshold

A test reaches the detectability-valid threshold only if it is adjudication-valid and the following are satisfied:

η coverage of D_crit;

sampling density near U(η_c);

visibility precision sufficient for δ_min;

nuisance uncertainty below detection margin;

statistical power;

rival diagnostics adequate for interpretation;

and replication standard declared.

If detectability validity fails, baseline-class behavior cannot yield F₃ failure.

F.6 Positive-interpretation threshold

A result reaches the positive-interpretation threshold only if:

the test is adjudication-valid;

the test is detectability-valid;

η is independently calibrated;

V_obs(η) leaves 𝔅_SQM + 𝒩 in U(η_c);

the deviation exceeds δ_min;

the deviation has the declared accessibility-critical form;

hostile rivals are excluded;

and replication is satisfied or the result is explicitly labeled provisional.

If any required condition fails, the result is not CBR-compatible evidence.

F.7 Reviewer checklist

Reviewers should assess the following.

Has the execution tuple been declared?

Has 𝒞₀(C) been declared?

Have all six admissibility filters been declared?

Is 𝒜(C) nonempty?

Is ∼ₒₚ defined?

Is 𝒜(C) ÷ ∼ₒₚ constructed?

Are Ξ_C, Ω_C, and Λ_C evaluable or boundable?

Are α, β, and γ fixed?

Is C_DCE specified?

Are W and R defined?

Is η independently calibrated?

Are η_c, D_crit, and U(η_c) fixed?

Is 𝔅_SQM declared?

Is 𝒩 finite and bounded?

Are R₁ through R₁₄ declared?

Are rival diagnostics declared?

Are H₀ and H₁ fixed?

Is δ_min fixed?

Is statistical power declared?

Are verdict categories mutually exclusive?

Are F₁ through F₅ defined?

Are no-rescue rules enforced?

Is probability standing local and non-rescuing?

F.8 Audit consequence

If all essential items are satisfied, the proposed test is executable under the canonical execution standard.

If model, admissibility, burden, coefficient, or instantiation essentials are missing, the model is not executable.

If calibration, baseline, nuisance, rival, statistical, or verdict essentials are missing, the test is not adjudication-valid.

If detectability essentials are missing, the result is inconclusive.

If positive-interpretation essentials are missing, the result is not CBR-compatible evidence.

Appendix G — Canonical CBR Adjudication Algorithm

G.1 Purpose

This appendix converts the execution standard into a verdict algorithm.

The algorithm assigns one of four statuses:

not executable;

inconclusive or unadjudicated;

F₃ failure;

CBR-compatible non-baseline evidence.

No other verdict category is permitted under a fixed execution tuple.

G.2 Algorithm

Step 1 — Check model lock.
Is the full execution tuple declared?

If no: not executable.

If yes: continue.

Step 2 — Check admissibility construction.
Is 𝒜(C) constructively generated from 𝒞₀(C), filters, and ∼ₒₚ?

If no: not executable.

If yes: continue.

Step 3 — Check burden evaluation.
Are Ξ_C, Ω_C, and Λ_C evaluable or boundable over declared channel classes?

If no: not executable.

If yes: continue.

Step 4 — Check coefficient lock.
Are α, β, and γ fixed?

If no: not executable.

If yes: continue.

Step 5 — Check instantiation.
Is C_DCE fixed with operational stages, Hilbert-space decomposition, W, R, and channel catalogue?

If no: not executable.

If yes: continue.

Step 6 — Check η calibration.
Is η independently calibrated as I_acc(W; R) ÷ H(W), with uncertainty?

If no: inconclusive.

If yes: continue.

Step 7 — Check critical-regime lock.
Are η_c, D_crit, and U(η_c) derived, pre-registered, or penalized under a declared rule?

If no: inconclusive.

If yes: continue.

Step 8 — Check null.
Are 𝔅_SQM, V_SQM(η), and 𝒩 fixed and bounded?

If no: inconclusive.

If yes: continue.

Step 9 — Check rival suite.
Are R₁ through R₁₄ declared with diagnostics?

If no: inconclusive for positive interpretation.

If yes: continue.

Step 10 — Check statistical lock.
Are H₀, H₁, δ_min, statistical method, power, scan correction, and verdict categories fixed?

If no: inconclusive.

If yes: continue.

Step 11 — Check detectability validity.
Could the experiment detect the declared effect at or above δ_min across D_crit?

If no: inconclusive.

If yes: continue.

Step 12 — Evaluate H₀.
Does V_obs(η) remain inside 𝔅_SQM + 𝒩 across D_crit?

If yes: F₃ failure.

If no: continue.

Step 13 — Evaluate H₁.
Does V_obs(η) leave 𝔅_SQM + 𝒩 in U(η_c), exceed δ_min, have the declared accessibility-critical form, survive hostile-rival exclusion, and satisfy replication?

If yes: CBR-compatible non-baseline evidence.

If no: inconclusive.

G.3 Verdict definitions

Not executable.
The model locks are incomplete. The canonical model has not been instantiated sufficiently to be tested.

Inconclusive or unadjudicated.
The model is executable, but calibration, null, detectability, rival exclusion, replication, or statistical conditions are insufficient for failure or positive interpretation.

F₃ failure.
The model is executable, adjudication-valid, detectability-valid, and V_obs(η) remains inside 𝔅_SQM + 𝒩 across D_crit.

CBR-compatible non-baseline evidence.
The model is executable, adjudication-valid, detectability-valid, and the declared accessibility-critical deviation appears in U(η_c), exceeds δ_min, lies outside 𝔅_SQM + 𝒩, survives hostile rivals, and satisfies replication.

G.4 Final algorithmic rule

The adjudication algorithm is binding for the instantiated canonical model.

A result may not be moved from one verdict category to another by changing the execution tuple after data interpretation begins.

If a locked object is changed, the result belongs to a modified model and requires new adjudication.