Locked-Dossier Standard for Testing Canonical CBR in a Delayed-Choice Record-Accessibility Interferometer

May 2

Abstract

Constraint-Based Realization (CBR) treats quantum outcome realization as a constrained selection problem within a fixed measurement context, rather than as probability assignment or decoherence alone. Within the CBR program, delayed-choice record-accessibility interferometry supplies a natural empirical arena: the accessibility of which-path records is varied, accessibility is quantified by η = I(W; R_acc) / H(W), and the visibility function V(η) is tested for a registered non-baseline accessibility-sensitive feature. This paper does not report a completed experimental implementation. It defines the locked-dossier standard under which a C_DCE instantiation of canonical CBR becomes test-ready, verdict-competent, and genuinely exposed to strong-null failure.

The controlling doctrine is that a CBR platform instantiation is identical to its pre-comparison registry. A valid C_DCE dossier must therefore fix, before comparison with V_obs(η), the platform context C_DCE, the constructive admissibility pipeline 𝒜₀(C_DCE) → F₁…F_n → 𝒜(C_DCE), the operational quotient 𝒜(C_DCE)/≃_C, the realization-burden functional ℛ_C = αΞ_C + βΩ_C + γΛ_C, the independently calibrated accessibility parameter η, the critical accessibility value η_c or interval I_c, the baseline ℬ, the nuisance class 𝓝, the nuisance envelope B_𝓝, the detectability threshold ε_detect, the statistical analysis plan, the validity gates, and the verdict rule. Any post-comparison alteration of these objects creates a successor model, not a rescue of the registered instantiation.

The paper formalizes the audit machinery required for such a dossier: registration certificates, traceability entries, admissibility and exclusion certificates, quotient-stable selection, computable burden terms, coefficient-fixation rules, independent η calibration, derivation of η_c or I_c from burden geometry, baseline exhaustion, nuisance-envelope non-expansion, power and control requirements, single-pass adjudication, no-rescue discipline, successor-model quarantine, and failure jurisdiction. These conditions separate four verdicts: survival, failure, inconclusive result, and successor-model registration. In particular, if V_obs(η) remains inside B_𝓝 across the registered critical region under valid calibration, baseline, nuisance, sampling, power, control, and detectability conditions, then the registered C_DCE instantiation fails.

The contribution is procedural and evidentiary. It does not establish CBR as the final law of quantum outcome realization, and it does not supply completed platform-specific calibration values. Instead, it specifies the conditions under which the already-proposed CBR delayed-choice record-accessibility test can become a locked, reproducible, non-circular, and falsifiable empirical object. The result is a standard for converting CBR’s empirical proposal into an auditable test: one in which survival cannot be claimed by ambiguity, failure cannot be evaded by reinterpretation, and successor models cannot retroactively rescue the registered instantiation.

1. Purpose, Scope, and Registered Target

This manuscript registers a test object, not a research posture. Its purpose is to specify one platform-specific instantiation of canonical Constraint-Based Realization in a delayed-choice record-accessibility interferometric context C_DCE and to expose that registered instantiation to a defined empirical verdict.

The registered C_DCE instantiation is the only object adjudicated by this dossier. CBR as a broader law-form program is not directly confirmed or disconfirmed here except through explicitly stated bridge claims. The manuscript therefore does not ask whether CBR is metaphysically attractive, interpretively useful, or broadly plausible. It asks whether one fixed platform instantiation can be constructed, certified, traced, computed, compared, and, under valid conditions, allowed to fail.

The governing doctrine is: A CBR platform instantiation is identical to its pre-comparison registry.

The registered object is not “CBR plus whatever revisions are needed after data are observed.” It is the fixed dossier object consisting of C_DCE, 𝒜(C_DCE), ≃_C, ℛ_C, η, η_c or I_c, ℬ, 𝓝, B_𝓝, ε_detect, the statistical test, the verdict rule, and the jurisdiction of failure. Any post-comparison change to these objects creates a successor model, not a rescue of the registered instantiation.

1.1 Purpose

The purpose of this paper is to register one executable CBR instantiation in C_DCE.

The registered instantiation must specify, before comparison with V_obs(η):

the exact platform context C_DCE;
the initial candidate class 𝒜₀(C_DCE);
the admissibility filters F₁…F_n;
the resulting admissible class 𝒜(C_DCE);
the operational equivalence relation ≃_C;
the quotient class 𝒜(C_DCE)/≃_C;
the realization-burden functional ℛ_C;
the burden terms Ξ_C, Ω_C, Λ_C;
the fixed coefficients α, β, γ;
the selected minimizing class [Φ∗_C];
the accessibility parameter η;
the critical accessibility value η_c or interval I_c;
the registered CBR prediction V_CBR(η);
the baseline prediction V_ℬ(η);
the baseline ℬ;
the nuisance class 𝓝;
the nuisance envelope B_𝓝;
the minimum detectable deviation ε_detect;
the statistical comparison rule;
the validity gates;
the verdict taxonomy;
the no-rescue rule;
the jurisdiction of failure.

The purpose is not merely to name these objects. Each verdict-relevant object must be fixed by a registration certificate and traceability entry specifying what it is, how it is constructed or calibrated, what uncertainty or tolerance it carries, how it enters the test, what role it plays in the verdict, and what follows if it is changed after comparison.

1.2 Non-claims

This paper does not claim that CBR is proven true. It does not claim that all alternatives are false. It does not claim that all quantum measurement problems are solved. It does not claim that one failed platform instantiation destroys the broader realization-law thesis.

The paper separates four levels of claim.

First, nature-claims concern what reality actually does. This manuscript does not establish a nature-claim. CBR proposes, but does not establish here, that outcome realization may be governed by constrained selection.

Second, law-form claims concern what a non-circular realization law must specify. At this level, the claim is that a serious realization law must fix its admissible candidates, selection rule, operational equivalence relation, probability discipline, baseline separation, and failure conditions before outcome comparison.

Third, platform-instantiation claims concern this specific C_DCE model. At this level, the claim is that the registered C_DCE instantiation predicts a specific accessibility-sensitive behavior in V(η), relative to ℬ and B_𝓝, under the stated calibration, validity, and detectability conditions.

Fourth, failure claims concern what an adverse result defeats. Failure of the registered C_DCE instantiation defeats that instantiation. It does not automatically defeat every CBR representation, every possible realization-law model, or the broader distinction between probability assignment and outcome realization.

No argument in this dossier may move between these levels without an explicit bridge premise.

1.3 Procedural Phases

The dossier is governed by three phases.

Pre-comparison phase.
All verdict-relevant objects are fixed, certified, and traceable. This includes C_DCE, 𝒜₀(C_DCE), F₁…F_n, 𝒜(C_DCE), ≃_C, ℛ_C, η, η_c or I_c, ℬ, 𝓝, B_𝓝, ε_detect, the statistical test, validity gates, and verdict rule.

Comparison phase.
The observed visibility curve V_obs(η) is evaluated against V_CBR(η), V_ℬ(η), and B_𝓝 using only the registered statistical test and validity gates.

Post-comparison phase.
Only verdict assignment is permitted. Any change to a registered object after comparison creates a successor model. Post-comparison alteration cannot count as survival of the registered instantiation.

This phase structure is part of the empirical discipline of the dossier. It prevents the tested object from being redefined during or after comparison.

1.4 Target of Failure

The object exposed to empirical failure is:

the registered C_DCE instantiation of canonical CBR.

Not all CBR.
Not all possible realization-law models.
Not the measurement problem as such.
Not the distinction between probability and realization.
The registered C_DCE instantiation.

The failure condition has the following governing form:

If V_obs(η) remains inside B_𝓝 across I_c under valid η-calibration, baseline-validation, nuisance-validation, sampling, and detectability conditions, then the registered C_DCE instantiation fails.

The result is survival only if the registered CBR signature appears outside the validated nuisance envelope in the registered critical region under valid test conditions.

The result is failure if the observed visibility remains inside the registered baseline-plus-nuisance envelope across I_c under valid sensitivity conditions.

The result is inconclusive if one or more validity gates fail, η calibration is invalid, the nuisance envelope is not validated, the baseline is not certified, I_c is insufficiently sampled, or ε_detect is not achieved.

The result is successor-model registration if any verdict-relevant object is changed after comparison with V_obs(η).

This target discipline protects the paper in both directions. It prevents a surviving result from being overstated as proof of all CBR, and it prevents a failed result from being overstated as refutation of every possible realization-law thesis.

2. The Registry Identity Principle

The controlling doctrine of this manuscript is the Registry Identity Principle: A CBR platform instantiation is identical to its pre-comparison registry.

The registry is not a list of preferences. It is not a preliminary description. It is not a flexible model family. It is the tested object.

A platform instantiation that can alter its admissible class, burden functional, accessibility calibration, critical interval, baseline, nuisance envelope, statistical test, or verdict rule after observing V_obs(η) is not a locked empirical object. It is an adaptive framework. The present dossier instead registers a fixed object whose evidentiary status depends on the impossibility of post-comparison rescue.

Definition 2.1 — Registered CBR Platform Instantiation

A registered CBR platform instantiation for C_DCE is the ordered object consisting of:

C_DCE, 𝒜₀(C_DCE), F₁…F_n, 𝒜(C_DCE), ≃_C, 𝒜(C_DCE)/≃_C, ℛ_C, Ξ_C, Ω_C, Λ_C, α, β, γ, [Φ∗_C], η, η_c or I_c, V_CBR(η), V_ℬ(η), ℬ, 𝓝, B_𝓝, ε_detect, the statistical test, the validity gates, the verdict rule, the no-rescue rule, and the jurisdiction of failure.

The instantiation is registered only when these objects are fixed before comparison with V_obs(η), and when every verdict-relevant object has both a registration certificate and a traceability entry.

Definition 2.2 — Registration Certificate

A registration certificate for an object O in the C_DCE dossier is a pre-comparison record specifying:

the formal definition of O;
the operational role of O in the instantiation;
the construction, calibration, or theoretical source of O;
the uncertainty, tolerance, or permitted range associated with O;
the dependencies of O on other registered objects;
the lock condition for O;
the role of O in the statistical or verdict rule;
the consequence of changing O after comparison.

An object is not considered fixed merely because it is named. It is fixed only when its registration certificate supplies enough information for an independent evaluator to determine whether the object was used consistently in the test.

Definition 2.3 — Traceability Entry

A traceability entry for a registered object O is the audit record connecting:

definition → source → construction/calibration → uncertainty/tolerance → lock condition → test role → verdict consequence.

Every verdict-relevant object must be traceable from its formal definition to its role in survival, failure, inconclusive result, or successor-model registration.

If O affects admissibility, burden evaluation, η calibration, η_c or I_c, baseline construction, nuisance-envelope construction, ε_detect, statistical comparison, or verdict assignment, then O must have a traceability entry before comparison.

Definition 2.4 — Validity Gate

A validity gate is a pre-registered condition that must be satisfied before survival or failure can be assigned.

Validity gates include, where applicable:

η-calibration validity;
baseline-validation validity;
nuisance-envelope validation;
detector-stability validity;
phase-control validity;
timing-jitter validity;
sampling sufficiency;
I_c coverage;
ε_detect achievement;
statistical-test applicability.

Failure of a validity gate prevents a survival or failure verdict unless the gate failure itself constitutes violation of a registered platform condition. In ordinary cases, validity-gate failure yields an inconclusive result rather than confirmation or defeat of the registered C_DCE instantiation.

Definition 2.5 — Model Identity and Implementation Tolerance

The identity of the registered C_DCE instantiation is fixed by the registered objects. The experimental implementation is accepted only if the realized apparatus, calibration, and data-acquisition procedure remain within the registered tolerances.

Implementation deviations inside registered tolerances do not change the model identity. Implementation deviations outside registered tolerances trigger either an inconclusive result or successor-model registration, depending on the verdict rule.

This distinction prevents the dossier from becoming either too rigid or too permissive. The model is not invalidated by ordinary calibrated tolerances, but it also cannot absorb unregistered deviations after comparison.

Proposition 2.1 — Registry Completeness Condition

A C_DCE instantiation is not test-ready unless every verdict-relevant object has a registration certificate and traceability entry.

Proof sketch. A verdict-relevant object affects whether the result counts as survival, failure, inconclusive, or successor-model registration. If such an object lacks a certificate or traceability entry, then its definition, tolerance, calibration source, lock condition, or verdict role can remain underdetermined. An underdetermined verdict-relevant object permits post-comparison reinterpretation. Therefore the instantiation is not locked and cannot be test-ready until every verdict-relevant object is certified and traceable.

2.1 Registered Objects

The registry must include the following certified and traceable objects.

First, C_DCE fixes the delayed-choice record-accessibility interferometric platform. Its certificate must specify the source preparation, path degree of freedom, which-path variable W, interferometer geometry, record architecture, accessible record register R_acc, inaccessible or environmental record register R_env, delayed-choice operation, erasure operation, detector model, calibration procedure, noise model, validity gates, and context-boundary rule.

Second, 𝒜₀(C_DCE) fixes the initial candidate class. Its certificate must specify the broad class of candidate realization channels or instruments Φ compatible with the declared system, record, environment, and detector registers.

Third, F₁…F_n fix the admissibility filters. Each filter must have a certificate stating its criterion, physical justification, required input data, admissibility consequence, and exclusion consequence.

Fourth, 𝒜(C_DCE) is the admissible class generated by the registered filter pipeline:

𝒜(C_DCE) = F_n ∘ … ∘ F₁[𝒜₀(C_DCE)].

Its certificate must identify the surviving candidate families and the basis on which they survived the filter sequence.

Fifth, ≃_C fixes operational equivalence. Its certificate must specify the registered observables, experimental-resolution threshold, nuisance tolerance, and operational distinguishability metric or pseudometric used to identify duplicates.

Sixth, 𝒜(C_DCE)/≃_C fixes the quotient class of operationally distinct admissible candidates.

Seventh, ℛ_C fixes the realization-burden functional. In canonical registered form:

ℛ_C(Φ) = αΞ_C(Φ) + βΩ_C(Φ) + γΛ_C(Φ).

ℛ_C is not a probability distribution. It is not decoherence renamed. It is not a post hoc score. It is the registered burden ordering over already admissible candidates.

Eighth, Ξ_C, Ω_C, Λ_C must be operationally defined or bounded in C_DCE. Ξ_C measures invariance or representation burden. Ω_C measures record-structure burden. Λ_C measures accessibility-consistency burden.

Ninth, α, β, γ are fixed coefficients. Their certificate must state whether they are fixed by symmetry, normalization, independent calibration, or a registered robustness class. They may not be tuned to fit V_obs(η).

Tenth, [Φ∗_C] is the selected operational equivalence class satisfying:

[Φ∗C] ∈ argmin{[Φ] ∈ 𝒜(C_DCE)/≃_C} ℛ_C([Φ]).

Eleventh, η is the accessibility parameter:

η = I(W; R_acc) / H(W).

η measures normalized accessible which-path information and must be calibrated independently of V_obs(η).

Twelfth, η_c or I_c fixes the critical accessibility region. In the interval form:

I_c = {η : Δℛ_C(η) ≤ δ_C},

where Δℛ_C(η) is the burden gap between competing admissible equivalence classes and δ_C is the registered burden-gap tolerance.

Thirteenth, V_CBR(η) is the registered CBR visibility prediction.

Fourteenth, V_ℬ(η) is the visibility predicted by the baseline ℬ.

Fifteenth, ℬ is the standard quantum/decoherence/detector/noise baseline. It must include standard quantum prediction, platform-specific decoherence, detector inefficiency, dark counts, phase drift, timing jitter, mode mismatch, finite sampling noise, environmental coupling, calibration uncertainty, and data-processing uncertainty.

Sixteenth, 𝓝 is the nuisance class and B_𝓝 is the registered nuisance envelope around V_ℬ(η). B_𝓝 cannot be widened after comparison to rescue the registered C_DCE instantiation.

Seventeenth, ε_detect is the minimum detectable deviation required to distinguish the registered CBR signature from the baseline-plus-nuisance envelope.

Eighteenth, the statistical test fixes the method of comparison between V_obs(η), V_CBR(η), and B_𝓝.

Nineteenth, the validity gates fix the preconditions for assigning survival or failure.

Twentieth, the verdict rule fixes the conditions for survival, failure, inconclusive result, and successor-model registration.

Twenty-first, the no-rescue rule forbids post-comparison alteration of registered objects as a rescue of the same instantiation.

Twenty-second, the jurisdiction of failure states what a failure defeats and what it does not automatically defeat.

2.2 Lock Rule

After comparison with observed data, changing any registered object creates a successor model.

This applies to C_DCE, 𝒜₀(C_DCE), F₁…F_n, 𝒜(C_DCE), ≃_C, 𝒜(C_DCE)/≃_C, ℛ_C, Ξ_C, Ω_C, Λ_C, α, β, γ, [Φ∗_C], η, η_c or I_c, V_CBR(η), V_ℬ(η), ℬ, 𝓝, B_𝓝, ε_detect, the statistical test, validity gates, the verdict rule, the no-rescue rule, and the jurisdiction of failure.

The lock rule is necessary because each of these objects can otherwise become a site of post hoc rescue. A failed prediction could be avoided by expanding 𝒜(C_DCE), redefining ≃_C, changing ℛ_C, retuning α, β, γ, recalibrating η from V_obs(η), shifting I_c, weakening ℬ, widening B_𝓝, raising ε_detect, changing validity gates, or modifying the verdict rule. Such changes may generate a scientifically meaningful successor model. They cannot count as survival of the registered instantiation.

Proposition 2.2 — No-Rescue by Redefinition

If a registered C_DCE instantiation is compared with V_obs(η), and any registered object is then altered to avoid failure or produce agreement, the altered object is not the original registered instantiation.

Proof sketch. By the Registry Identity Principle, the instantiation is identical to its ordered pre-comparison registry. Altering a constitutive element changes the ordered object. Therefore the altered model is a successor model. It may be evaluated in a later registration, but it cannot rescue the original registered instantiation.

Proposition 2.3 — Verdict Requires Validity

Survival or failure may be assigned only if the registered validity gates are satisfied.

Proof sketch. The verdict rule compares V_obs(η) to V_CBR(η), V_ℬ(η), and B_𝓝 under registered calibration, baseline, nuisance, sampling, and detectability conditions. If a validity gate fails, then the comparison does not instantiate the registered test. The result may reveal an implementation failure or motivate a successor model, but it cannot establish survival or failure of the registered C_DCE instantiation unless the verdict rule explicitly defines that gate failure as itself decisive.

3. Exact Platform Context C_DCE

C_DCE defines the physical arena of the registered test. It is not a generic delayed-choice interferometer and not an informal experimental description. It is the certified platform context from which the candidate class, admissibility filters, record architecture, accessibility calibration, baseline, nuisance envelope, validity gates, and verdict rule obtain their meaning.

A vague C_DCE would make the entire dossier unstable. If the platform context can be expanded after observing V_obs(η), then unregistered degrees of freedom, detector behaviors, environmental couplings, or data-processing choices could be invoked to reinterpret the result. This section therefore fixes not only what C_DCE includes, but also what cannot be introduced later without successor-model registration.

Definition 3.1 — Platform Context C_DCE

C_DCE is the delayed-choice record-accessibility interferometric context consisting of the following certified and traceable components:

source preparation;
system Hilbert space and path degree of freedom;
which-path variable W;
interferometer geometry;
phase-control mechanism;
record-generating subsystem;
accessible record register R_acc;
inaccessible or environmental record register R_env;
delayed-choice operation;
erasure or record-access manipulation operation;
detector model;
coincidence-counting rule;
visibility-estimation rule;
η-calibration procedure;
baseline-calibration procedure;
noise and drift model;
nuisance-validity gates;
data-validity gates;
statistical comparison protocol;
implementation tolerances;
context-boundary rule.

Each component must have a registration certificate and traceability entry. Where exact numerical values are platform-specific, the certificate must identify the independent calibration source or registered design specification from which the value is obtained.

[To be fixed before comparison: exact source-preparation specification.]

[To be fixed before comparison: declared Hilbert-space and register decomposition.]

[To be fixed before comparison: detector-efficiency tolerance and detector-response model.]

[To be supplied from independent platform calibration: phase-drift, timing-jitter, dark-count, and mode-mismatch models.]

3.1 System, Path, and Which-Path Variable

The system component of C_DCE must specify the physical carrier, the preparation procedure, the path degree of freedom, and the operational meaning of W. The variable W is the which-path variable whose accessible information is quantified by:

η = I(W; R_acc) / H(W).

W must be defined by the platform architecture and calibration procedure before visibility comparison. It cannot be redefined because a different which-path partition improves agreement with V_obs(η).

The definition of W is verdict-relevant. If W is not fixed, then η is not fixed. If η is not fixed, then Λ_C is not auditable. If Λ_C is not auditable, then ℛ_C is not fully computable. If ℛ_C is not fully computable, then η_c or I_c cannot be derived from burden geometry. Thus W is not a minor experimental detail; it is a constitutive object in the registered instantiation.

3.2 Record Architecture

C_DCE must specify the record architecture before comparison. At minimum, the architecture must distinguish:

R_acc, the accessible record register used for η calibration;
R_env, the inaccessible or environmental record register;
detector records, the final measurement records used to estimate V(η) and related observables.

The accessible/inaccessible split must be fixed independently of V_obs(η). A record cannot be reclassified after comparison to shift η, alter Λ_C, modify I_c, or reinterpret the visibility curve. Such reclassification changes C_DCE and therefore creates a successor model.

The registration certificate for the record architecture must state:

what physical subsystem realizes R_acc;
what physical subsystem realizes R_env;
how record accessibility is controlled or varied;
what data are used to estimate I(W; R_acc);
what data are forbidden from η calibration;
how detector records are separated from accessibility-calibration records;
what implementation tolerances govern the accessible/inaccessible split.

[To be supplied from independent platform calibration: η uncertainty model for R_acc.]

3.3 Delayed-Choice and Erasure Operations

The delayed-choice and erasure operations must be specified as physical operations within C_DCE. Their certificates must state which control settings modify record accessibility, which registers they act on, how they are timed relative to source preparation and detection, how they enter ℬ, and how implementation tolerances are assessed.

These operations generate the η-sweep. They do not provide a post hoc interpretive degree of freedom. The dossier must therefore fix:

the delayed-choice control variable;
the erasure or record-access manipulation procedure;
the timing relationship between choice, record formation, and detection;
the allowed operating range;
the calibration source for that range;
the implementation tolerance for each control operation;
the validity gates for excluding unstable runs.

[To be fixed before comparison: delayed-choice timing tolerance.]

[To be fixed before comparison: erasure-operation fidelity or record-access manipulation tolerance.]

3.4 Visibility and Coincidence Procedure

C_DCE must specify how V(η) is estimated from detector data. This includes the coincidence-counting rule, detector-window criteria, phase-scanning procedure, binning or continuous-estimation method, visibility estimator, outlier rule, exclusion rule, and uncertainty estimator.

[To be fixed before comparison: visibility estimator.]

[To be fixed before comparison: coincidence-window definition.]

[To be fixed before comparison: η-binning rule or continuous-estimation rule.]

[To be fixed before comparison: outlier and exclusion criteria.]

The visibility-estimation procedure is part of C_DCE. It cannot be changed after observing V_obs(η) to sharpen, suppress, relocate, or reinterpret the registered signature.

3.5 Model Identity and Implementation Tolerance

The registered model identity is fixed by C_DCE and the other registered objects. The physical implementation is accepted as an implementation of the registered model only if it remains within the registered tolerances.

An implementation deviation inside tolerance is absorbed by the registered uncertainty, nuisance, or calibration model. An implementation deviation outside tolerance does not automatically falsify CBR. It means the test did not instantiate the registered C_DCE model as certified. Depending on the verdict rule, the result is inconclusive or requires successor-model registration.

This distinction is necessary because no physical implementation is exact in the mathematical sense. The dossier therefore fixes both the model identity and the tolerances under which an experiment counts as implementing that identity.

3.6 Context Boundary Rule

Any degree of freedom, control operation, environmental coupling, detector behavior, calibration procedure, or data-processing operation not included in the certified C_DCE registry is unavailable for post-comparison explanation of V_obs(η), except by successor-model registration.

This rule does not deny that the real platform may contain unmodeled features. Rather, it fixes the evidentiary identity of this instantiation. If an unregistered feature later proves relevant, the correct procedure is not to retrofit the registered model. The correct procedure is to assign the verdict permitted by the validity gates and, if warranted, register a successor model with the expanded context.

Lemma 3.1 — Context Fixity

If C_DCE is fixed by registration certificates and traceability entries before comparison, then later disagreement between V_obs(η) and the registered prediction cannot be repaired by redefining the platform context while preserving the identity of the original instantiation.

Proof sketch. C_DCE is a constitutive element of the registered platform instantiation. By the Registry Identity Principle, changing a constitutive element changes the registered object. Therefore post-comparison context modification creates a successor model rather than a rescue of the tested instantiation.

Proposition 3.1 — Boundary-Limited Explanation

No unregistered platform feature may be used to explain agreement or disagreement between V_obs(η) and the registered prediction without successor-model registration.

Proof sketch. The registered test is defined over C_DCE. A platform feature outside C_DCE is outside the certified context. Introducing it after comparison changes the context, and therefore changes the registered object. Such a change may be scientifically appropriate in a successor model, but it cannot alter the verdict for the original instantiation.

4. Constructive Generation of 𝒜(C_DCE)

The admissible class 𝒜(C_DCE) is constructed, not assumed. Its construction is one of the principal safeguards against vagueness, circularity, hidden probability engineering, and post hoc rescue.

The construction follows the registered pipeline:

𝒜₀(C_DCE) → F₁…F_n → 𝒜(C_DCE) → 𝒜(C_DCE)/≃_C.

The initial class 𝒜₀(C_DCE) defines the broad candidate domain. The filters F₁…F_n determine which candidates are admissible. The quotient relation ≃_C identifies operational duplicates. Only after these steps may ℛ_C rank the surviving operational equivalence classes.

A candidate class is not admissible merely because it is mathematically describable. It is admissible only if it survives the registered filter pipeline and receives an admissibility certificate before comparison.

No candidate may enter 𝒜(C_DCE) because it explains the observed data.

4.1 Burdened Inclusion and Exclusion

Inclusion and exclusion are both burdened.

A candidate cannot be admitted casually, because admission affects the minimization domain of ℛ_C. A candidate also cannot be excluded silently, because exclusion can artificially shape the admissible class. Therefore every platform-relevant candidate family must receive either an admissibility certificate or an exclusion certificate before comparison.

Silent omission is not permitted for verdict-relevant candidates.

This rule protects 𝒜(C_DCE) against two opposite abuses: overexpansion after comparison and selective narrowing before comparison. A fair referee must be able to audit not only what was admitted, but why relevant nearby alternatives were excluded.

4.2 Initial Class 𝒜₀(C_DCE)

𝒜₀(C_DCE) is the broad class of candidate realization channels or instruments Φ compatible with the declared system, record, environment, and detector registers of C_DCE.

At this stage, 𝒜₀(C_DCE) is intentionally broad. It includes candidate CPTP maps or quantum instruments acting on the declared degrees of freedom, subject to the initial platform specification. It is not yet the admissible class. It is the pre-filter candidate domain.

The certificate for 𝒜₀(C_DCE) must specify:

the mathematical representation of Φ;
whether candidates are channels, instruments, or a registered mixture of both;
the system, record, environment, and detector registers on which Φ acts;
the allowed dependence of Φ on η;
the excluded forms of dependence, including dependence on V_obs(η) or realized detector outcomes;
the relation between 𝒜₀(C_DCE) and the platform context C_DCE;
the traceability of 𝒜₀(C_DCE) to C_DCE.

[To be fixed before comparison: exact mathematical representation of candidate channels or instruments in 𝒜₀(C_DCE).]

[To be fixed before comparison: declared register structure on which Φ acts.]

4.3 Admissibility Filters

The admissible class is generated by applying registered filters:

𝒜(C_DCE) = F_n ∘ … ∘ F₁[𝒜₀(C_DCE)].

Each filter F_i must have a registration certificate stating its criterion, physical or operational basis, required inputs, uncertainty or tolerance, admissibility consequence, exclusion consequence, and traceability to C_DCE.

The following filters are required unless replaced by a stronger registered condition.

F₁ Physical admissibility.
A candidate Φ must be a valid quantum channel or instrument in the declared platform representation. In the channel case, Φ must be completely positive and trace preserving. In the instrument case, the registered components must be physically valid and sum to the declared non-selective channel.

F₂ Context compatibility.
Φ must act only on the degrees of freedom declared in C_DCE. A candidate that depends on unregistered registers, unmodeled controls, undeclared environmental couplings, or undeclared detector behavior is not admissible in this instantiation.

F₃ Born compatibility.
Φ must preserve the Born-compatible marginal statistics required by the preparation and measurement context. This filter prevents 𝒜(C_DCE) from becoming a hidden probability-engineering device. CBR may rank admissible candidates, but it may not smuggle a rival probability rule into admissibility.

F₄ Causal admissibility.
Φ cannot depend on future outcome information, realized detector events, or the observed visibility curve. This excludes candidates whose membership depends on what they are later used to explain.

F₅ Record compatibility.
Φ must respect the declared record architecture of C_DCE, including W, R_acc, R_env, detector records, delayed-choice operations, and erasure or accessibility-control operations.

F₆ Accessibility compatibility.
Φ may depend on η only as independently calibrated through:

η = I(W; R_acc) / H(W).

Φ may not depend on η as inferred from V_obs(η), nor may η be redefined after comparison to improve agreement between V_CBR(η) and V_obs(η).

F₇ Decoherence separation.
Φ cannot merely reproduce the non-selective decoherence baseline unless it is classified as baseline-equivalent. This filter protects the distinction between CBR selection and ordinary decoherence. A candidate that collapses into ℬ without producing an operationally distinguishable accessibility-sensitive prediction is not a distinct CBR candidate for purposes of this registered test.

F₈ Calibration compatibility.
Φ must remain inside registered calibration tolerances for detector response, phase stability, timing, mode overlap, environmental coupling, source stability, and any additional platform-specific parameter included in C_DCE.

[To be fixed before comparison: full calibration-tolerance list and numerical bounds.]

F₉ No post hoc admission.
No candidate may be admitted to 𝒜(C_DCE) because it explains V_obs(η). A candidate proposed after comparison may define a successor model, but it does not belong to the admissible class of this registered instantiation.

4.4 Admissibility and Exclusion Certificates

The filter pipeline must produce two audit records.

First, an admissibility certificate must be supplied for each surviving candidate family or generated candidate class. The certificate must state:

the candidate family;
the representation of Φ;
which filters F₁…F_n it satisfies;
the evidence or construction showing satisfaction;
any uncertainty or tolerance associated with satisfaction;
the operational role of the candidate in 𝒜(C_DCE);
whether it survives as distinct after quotienting by ≃_C;
the traceability of the candidate to C_DCE and the relevant filters.

Second, an exclusion certificate must be supplied for each platform-relevant rejected candidate family. The certificate must state:

the rejected candidate family;
the filter or filters that exclude it;
the reason for exclusion;
whether exclusion is physical, causal, operational, calibration-based, Born-compatibility-based, record-compatibility-based, accessibility-based, decoherence-separation-based, or post hoc;
whether the rejected candidate may be considered only in a successor model;
the traceability of the exclusion to a registered filter or context boundary.

The purpose of exclusion certificates is not to enumerate every mathematically imaginable map. It is to prevent selective silence about relevant rival candidates. A skeptical referee should be able to see not only what was admitted, but also why significant nearby alternatives were excluded.

[To be fixed before comparison: list of platform-relevant candidate families requiring admissibility or exclusion certificates.]

4.5 Independence Lemma

Lemma 4.1 — Outcome-Independence of 𝒜(C_DCE).
Membership in 𝒜(C_DCE) is fixed without reference to the realized detector outcome or the observed visibility curve V_obs(η).

Proof sketch. By construction, 𝒜(C_DCE) is generated by applying F₁…F_n to 𝒜₀(C_DCE). Each filter is certified and traceable before comparison and defined by physical, causal, operational, calibration, Born-compatibility, record-compatibility, or accessibility-compatibility constraints. F₄ excludes dependence on future outcome information. F₆ excludes η definitions inferred from V_obs(η). F₉ excludes post hoc admission based on explanatory fit. Therefore membership in 𝒜(C_DCE) is independent of the realized detector outcome and observed visibility curve.

Proposition 4.1 — Non-Circular Admissibility

If 𝒜(C_DCE) is generated by the registered filter pipeline 𝒜₀(C_DCE) → F₁…F_n → 𝒜(C_DCE), and no filter depends on V_obs(η), then admissibility is non-circular with respect to the empirical comparison.

Proof sketch. Circularity would require candidate membership to depend on the data the candidate is later used to explain. The filter pipeline fixes membership before comparison and excludes post hoc admission. Therefore the observed data do not determine admissibility.

Proposition 4.2 — Burdened Exclusion

If a platform-relevant candidate family is excluded from 𝒜(C_DCE), then its exclusion is valid only if the dossier supplies an exclusion certificate traceable to a registered filter or context boundary.

Proof sketch. Exclusion changes the minimization domain of ℛ_C. If exclusion is not certified, then the admissible class may be silently narrowed in a way that affects [Φ∗_C]. Certification ensures that exclusion is governed by registered physical, causal, operational, calibration, Born-compatibility, record-compatibility, accessibility, or decoherence-separation constraints rather than by preference for a desired verdict.

4.6 Relation to Burden Evaluation

Only candidates in 𝒜(C_DCE) are eligible for burden evaluation under ℛ_C. The burden functional does not create admissibility. It ranks already admissible candidates.

This order is essential:

𝒜₀(C_DCE) → F₁…F_n → 𝒜(C_DCE) → 𝒜(C_DCE)/≃_C → ℛ_C → [Φ∗_C].

If ℛ_C were allowed to admit candidates, then burden minimization could become a disguised post hoc selection device. In this dossier, admissibility is fixed before burden evaluation, burden evaluation is fixed before comparison with V_obs(η), and any post-comparison change to the admissible domain creates a successor model.

5. Operational Equivalence and Quotienting

Canonical CBR selects among operationally distinct admissible candidates. It does not claim to distinguish candidates that differ only by representation while agreeing on every registered observable of C_DCE. The operational equivalence relation ≃_C prevents artificial uniqueness by identifying candidates that have no registered experimental distinction in the platform.

The quotient structure is also part of the failure discipline. If the selected class [Φ∗_C] fails under the registered verdict rule, failure cannot be avoided by replacing Φ∗_C with another representative of the same class.

5.1 Registered Observables

Let 𝒪_C denote the registered observable set of C_DCE. At minimum, 𝒪_C includes:

detector probabilities;
coincidence counts;
V(η);
phase-dependent fringe structure;
which-path record statistics;
η-calibration statistics;
baseline-relevant nuisance observables;
any additional platform observables declared before comparison.

[To be fixed before comparison: complete registered observable set 𝒪_C.]

The observable set 𝒪_C must be certified, traceable, and fixed before comparison. Adding or removing observables after comparison changes ≃_C and therefore creates a successor model.

5.2 Operational Distinguishability Pseudometric

Operational equivalence must be auditable. The dossier therefore registers an operational distinguishability pseudometric d_C over 𝒜(C_DCE).

A general form is:

d_C(Φ₁, Φ₂) = sup_{O ∈ 𝒪_C} D_O(P_{Φ₁}, P_{Φ₂}),

where 𝒪_C is the registered observable set, P_{Φ_i} is the prediction induced by Φ_i over the registered observable O, and D_O is the registered distinguishability measure for that observable.

The threshold τ_C denotes the registered operational-resolution tolerance.

[To be fixed before comparison: exact operational distinguishability pseudometric d_C.]

[To be fixed before comparison: registered operational-resolution threshold τ_C.]

[To be fixed before comparison: observable-specific distinguishability measures D_O.]

The certificate for d_C must state its definition, observable inputs, nuisance dependencies, uncertainty treatment, tolerance threshold, and verdict role. The traceability entry must show how d_C connects the platform observables 𝒪_C to quotient membership in 𝒜(C_DCE)/≃_C.

Definition 5.1 — Operational Equivalence in C_DCE

For Φ₁, Φ₂ ∈ 𝒜(C_DCE), define:

Φ₁ ≃_C Φ₂

if and only if:

d_C(Φ₁, Φ₂) ≤ τ_C.

Thus two candidates are operationally equivalent when their maximum registered distinguishability over 𝒪_C falls within the certified experimental-resolution threshold.

This definition replaces informal indistinguishability with a registered criterion. It prevents ≃_C from being adjusted after comparison to merge inconvenient failures or split convenient successes.

5.3 The Quotient Class

The quotient class:

𝒜(C_DCE)/≃_C

is the class of operationally distinct admissible candidates. Its elements are equivalence classes [Φ].

The registered selection rule is:

[Φ∗C] ∈ argmin{[Φ] ∈ 𝒜(C_DCE)/≃_C} ℛ_C([Φ]).

This formulation prevents representational overclaiming. CBR does not require that one microscopic representative Φ be uniquely selected when all representatives in [Φ] agree on the registered observables within τ_C. The meaningful selection target is the operational equivalence class [Φ∗_C].

5.4 Compatibility of ℛ_C with Quotienting

For burden minimization to be well-defined over 𝒜(C_DCE)/≃_C, ℛ_C must be quotient-compatible.

The strongest condition is quotient invariance:

If Φ₁ ≃_C Φ₂, then ℛ_C(Φ₁) = ℛ_C(Φ₂).

If exact equality is unavailable because of representative-level computational differences, the dossier must register a representative-selection or class-evaluation rule before comparison.

[To be fixed before comparison: proof of quotient invariance or registered representative-evaluation rule for ℛ_C([Φ]).]

This requirement prevents representational artifacts from determining [Φ∗_C]. It also clarifies the role of Ξ_C: the invariance or representation burden term must penalize dependence on arbitrary representation choices rather than physically registered distinctions.

Lemma 5.1 — Quotient Selection Avoids Representational Overclaiming

If Φ₁ ≃_C Φ₂, then selecting Φ₁ rather than Φ₂ has no registered operational meaning in C_DCE. Therefore the meaningful selection target is [Φ], not an arbitrary representative.

Proof sketch. By definition, Φ₁ ≃_C Φ₂ implies d_C(Φ₁, Φ₂) ≤ τ_C. Therefore no registered observable in 𝒪_C distinguishes them beyond certified resolution. A claim of unique selection between Φ₁ and Φ₂ would exceed the operational content of the platform. Selection of [Φ] preserves the registered experimental meaning.

Proposition 5.1 — Quotient-Stable Failure

If [Φ∗_C] generates the registered prediction V_CBR(η), and V_obs(η) remains inside B_𝓝 across I_c under valid η-calibration, baseline-validation, nuisance-validation, sampling, and detectability conditions, then replacing Φ∗_C with another representative of [Φ∗_C] cannot avoid failure.

Proof sketch. All representatives of [Φ∗_C] are equivalent under ≃_C and therefore agree over the registered observables within τ_C. The failure condition is defined over those observables, including V(η), the baseline envelope B_𝓝, and the registered critical interval I_c. Representative substitution cannot change the verdict without changing ≃_C, d_C, τ_C, 𝒪_C, or the registered prediction rule. Any such change creates a successor model.

Proposition 5.2 — Quotient Manipulation Creates a Successor Model

If ≃_C, 𝒪_C, d_C, τ_C, observable-specific distinguishability measures, nuisance tolerances, or the quotient-evaluation rule are changed after comparison with V_obs(η), then the resulting model is a successor model.

Proof sketch. The quotient structure determines which candidates count as operationally distinct and therefore determines the domain over which ℛ_C selects [Φ∗_C]. Changing the quotient structure changes the selection domain or the interpretation of the selected class. By the Registry Identity Principle, this changes the registered object and cannot rescue the original instantiation.

5.5 Relation to Failure Jurisdiction

The quotient structure fixes the jurisdiction of failure at the level of operational equivalence classes. If the selected class [Φ∗_C] fails under the registered strong-null rule, then the registered C_DCE instantiation fails. Failure cannot be avoided by shifting to another representative in [Φ∗_C], because the representatives are equivalent by construction.

A post-comparison change to ≃_C, 𝒪_C, d_C, τ_C, nuisance tolerances, or the quotient-evaluation rule creates a successor model. It cannot rescue the registered instantiation.

Operational quotienting therefore serves two roles. It prevents artificial uniqueness, and it prevents post hoc equivalence manipulation. It ensures that the selected object is neither more precise than the platform can justify nor more flexible than the verdict rule permits.

6. Exact Burden Functional ℛ_C

The realization-burden functional ℛ_C is the technical center of the registered C_DCE instantiation. It is the registered ordering rule applied only after the admissible class has already been constructed and quotient-identified:

𝒜₀(C_DCE) → F₁…F_n → 𝒜(C_DCE) → 𝒜(C_DCE)/≃_C → ℛ_C → [Φ∗_C].

ℛ_C does not create admissibility. It does not alter Born probabilities. It is not a probability distribution, not decoherence renamed, and not a post hoc score assigned after V_obs(η) is known. It is the pre-comparison burden ordering over already admissible operational equivalence classes.

The canonical registered form is:

ℛ_C(Φ) = αΞ_C(Φ) + βΩ_C(Φ) + γΛ_C(Φ).

Because selection is made over operational equivalence classes, the operative form is:

ℛ_C([Φ]) = αΞ_C([Φ]) + βΩ_C([Φ]) + γΛ_C([Φ]),

where [Φ] ∈ 𝒜(C_DCE)/≃_C.

A third party must be able to compute or bound ℛ_C([Φ]) from the registered inputs. If ℛ_C cannot be evaluated from the locked registry, then the C_DCE instantiation is not test-ready.

Definition 6.1 — Admissible Burden-Term Family

A burden term T_C ∈ {Ξ_C, Ω_C, Λ_C} belongs to an admissible burden-term family only if it satisfies the following conditions before comparison:

Nonnegativity: T_C([Φ]) ≥ 0 unless a signed structure is explicitly certified.
Normalization: T_C is placed on a registered scale comparable to the other burden terms.
Quotient-compatibility: if Φ₁ ≃_C Φ₂, then T_C(Φ₁) and T_C(Φ₂) agree within the registered quotient tolerance, or the dossier supplies a certified class-evaluation rule.
Platform computability: T_C is computable or bounded from registered C_DCE inputs.
Calibration traceability: all empirical inputs to T_C trace to independent platform calibration, not to V_obs(η).
Uncertainty boundedness: T_C has a registered uncertainty or tolerance model.
No visibility leakage: T_C cannot use V_obs(η), post-comparison residuals, or observed baseline disagreement as an input.
Failure relevance: the dossier states how failure to compute T_C affects the verdict.

This definition prevents ℛ_C from being an unconstrained symbolic placeholder. Each term must belong to a declared admissible formula family, not merely be named.

Definition 6.2 — Burden Evaluation Certificate

A burden evaluation certificate for ℛ_C specifies:

the exact mathematical or algorithmic definition of Ξ_C, Ω_C, and Λ_C;
the admissible formula family for each term;
the registered inputs required to evaluate each term;
the calibration source for those inputs;
the uncertainty or tolerance model for each term;
the normalization rule for each term;
the coefficient rule for α, β, and γ;
the quotient-compatibility rule over 𝒜(C_DCE)/≃_C;
the computational procedure for evaluating ℛ_C([Φ]);
the consequence of modifying any burden term after comparison.

ℛ_C is fixed only when its certificate allows an independent evaluator to compute or bound ℛ_C([Φ]) for every registered admissible equivalence class.

6.1 Ξ_C — Invariance or Representation Burden

Ξ_C measures the burden associated with dependence on arbitrary representation choices rather than registered physical distinctions in C_DCE. Its role is to penalize candidate structure that changes under transformations that should not alter the operational content of the platform.

An admissible Ξ_C family must be a nonnegative, normalized, quotient-compatible functional over registered representation transformations. It must be evaluated using the registered observable set 𝒪_C, the operational distinguishability structure d_C, and the resolution threshold τ_C.

A certified form may be:

Ξ_C([Φ]) = N_Ξ⁻¹ · R_Ξ([Φ]),

where R_Ξ([Φ]) is the registered invariance residual and N_Ξ is the registered normalization rule or constant.

The certificate for Ξ_C must specify:

the representation transformations treated as non-physical or gauge-like in C_DCE;
the observable set over which invariance is tested;
the distinguishability criterion used to compare transformed and untransformed candidates;
the uncertainty tolerance for residual representation dependence;
the normalization rule;
the consequence if Ξ_C cannot be computed.

[To be fixed before comparison: registered representation-transformation class for Ξ_C.]

[To be fixed before comparison: exact invariance residual R_Ξ.]

[To be fixed before comparison: normalization constant or normalization rule N_Ξ.]

Ξ_C cannot be altered after comparison to make a preferred candidate appear less burdensome. Such alteration changes ℛ_C and therefore creates a successor model.

6.2 Ω_C — Record-Structure Burden

Ω_C measures the burden associated with record formation, record stability, and detector-level registration in C_DCE. It evaluates whether a candidate Φ is compatible with the registered record architecture: W, R_acc, R_env, delayed-choice operations, erasure or accessibility-control operations, and final detector records.

An admissible Ω_C family must be a nonnegative, normalized, quotient-compatible functional over the certified record architecture. It must evaluate record compatibility using registered record-calibration data, not by inferring record structure from V_obs(η).

A certified form may be:

Ω_C([Φ]) = N_Ω⁻¹ · R_Ω([Φ]),

where R_Ω([Φ]) is the registered record-structure residual and N_Ω is the registered normalization rule or constant.

The certificate for Ω_C must specify:

which record-formation constraints are evaluated;
which record-stability constraints are evaluated;
which detector-registration constraints are evaluated;
how Φ acts on W, R_acc, R_env, and detector records;
whether Ω_C is computed analytically, estimated from calibration, or bounded by simulation;
how record-calibration uncertainty propagates into Ω_C;
how baseline-equivalent candidates are classified.

[To be fixed before comparison: record-structure residual R_Ω.]

[To be supplied from independent platform calibration: record-stability uncertainty model.]

[To be fixed before comparison: normalization constant or normalization rule N_Ω.]

Ω_C is not a decoherence functional. It may use decoherence-related calibration quantities where they belong to the platform record model or baseline ℬ, but it cannot collapse CBR selection into the non-selective decoherence baseline. If a candidate has no operational distinction from ℬ, it must be classified as baseline-equivalent under the admissibility and quotienting rules.

6.3 Λ_C — Accessibility-Consistency Burden

Λ_C measures the burden associated with consistency between candidate realization structure and the independently calibrated accessibility parameter η. It connects ℛ_C to the record-accessibility structure of C_DCE.

The registered accessibility parameter is:

η = I(W; R_acc) / H(W),

where W is the which-path variable and R_acc is the accessible record register. η measures normalized accessible which-path information and must be calibrated independently of V_obs(η).

An admissible Λ_C family must be a nonnegative, normalized, quotient-compatible, η-dependent functional whose η-dependence is fixed by independent accessibility calibration. It may not use visibility behavior to infer accessibility.

A certified form may be:

Λ_C([Φ]; η) = N_Λ⁻¹ · R_Λ([Φ]; η),

where R_Λ([Φ]; η) is the registered accessibility-consistency residual and N_Λ is the registered normalization rule or constant.

The certificate for Λ_C must specify:

how Φ depends on η;
how η enters Λ_C;
how Λ_C is evaluated across the registered η-sweep;
how η uncertainty enters the burden;
how Λ_C contributes to Δℛ_C(η);
how Λ_C participates in deriving η_c or I_c;
which calibration data are allowed;
which data are forbidden.

[To be fixed before comparison: accessibility-consistency residual R_Λ.]

[To be supplied from independent platform calibration: η uncertainty model.]

[To be fixed before comparison: normalization constant or normalization rule N_Λ.]

Λ_C cannot be retuned after V_obs(η) is known. It cannot be used to move η_c or I_c into a favorable region after comparison. Any such modification creates a successor model.

6.4 Normalization

Each burden term must be normalized before coefficient application. Normalization prevents α, β, and γ from secretly carrying the substantive burden structure.

The normalization certificate must specify:

whether Ξ_C, Ω_C, and Λ_C are dimensionless;
the expected range of each term;
the normalization rule or constant for each term;
how uncertainty in normalization is propagated;
whether normalization depends on independent platform calibration;
whether normalization can affect the identity of [Φ∗_C].

[To be fixed before comparison: numerical or rule-based normalization for Ξ_C, Ω_C, and Λ_C.]

Normalization cannot be adjusted after observing V_obs(η). If normalization is changed after comparison, ℛ_C changes, and the modified model is a successor model.

6.5 Uncertainty Propagation

The registered C_DCE instantiation must propagate uncertainty through each burden term and through ℛ_C as a whole. Calibration uncertainty, detector uncertainty, η uncertainty, nuisance uncertainty, and numerical approximation error may all affect burden ordering.

For each [Φ] ∈ 𝒜(C_DCE)/≃_C, the dossier must compute or bound:

Ξ_C([Φ]) ± σ_Ξ([Φ]),
Ω_C([Φ]) ± σ_Ω([Φ]),
Λ_C([Φ]) ± σ_Λ([Φ]),
ℛ_C([Φ]) ± σ_ℛ([Φ]).

The uncertainty method must be fixed before comparison and must state whether uncertainty is treated by intervals, covariance propagation, bootstrap calibration, Bayesian calibration, worst-case bounding, or another registered method.

[To be fixed before comparison: uncertainty-propagation method for ℛ_C.]

[To be fixed before comparison: numerical tolerance for burden comparison.]

[To be supplied from independent platform calibration: covariance or interval model for Ξ_C, Ω_C, and Λ_C inputs.]

Uncertainty may produce:

a certified unique minimizing class;
a certified near-degenerate minimizer set;
an unresolved burden ordering.

The dossier must state before comparison how each case affects the prediction and verdict.

Proposition 6.1 — ℛ_C Well-Definedness

ℛ_C is well-defined over 𝒜(C_DCE)/≃_C only if Ξ_C, Ω_C, and Λ_C are quotient-compatible, normalized, uncertainty-bounded, and computable or bounded from registered inputs.

Proof sketch. ℛ_C assigns burden values to operational equivalence classes. If any term depends on representative choice, lacks normalization, lacks an uncertainty model, or cannot be computed from registered inputs, then ℛ_C([Φ]) is not an auditable class-level quantity. Therefore minimization over 𝒜(C_DCE)/≃_C is not well-defined.

Proposition 6.2 — Burden Evaluation Does Not Create Admissibility

Only candidates in 𝒜(C_DCE)/≃_C may be evaluated under ℛ_C for purposes of selection.

Proof sketch. The registered construction order places admissibility before burden evaluation. If ℛ_C could admit candidates, then the ranking rule would alter its own domain. That would collapse admissibility and selection into a single adjustable procedure. The registry forbids this.

Proposition 6.3 — No Hidden Probability Engineering Through ℛ_C

If Born compatibility is enforced at the admissibility stage and ℛ_C ranks only already admissible candidates, then ℛ_C cannot function as a hidden replacement for Born probabilities unless the registered burden terms or coefficients explicitly violate Born compatibility.

Proof sketch. Born-compatible marginal statistics are fixed before ℛ_C is applied. ℛ_C selects among admissible candidates; it does not assign outcome probabilities. Any attempt to use ℛ_C to alter Born marginals violates the admissibility structure or creates a successor model.

7. Coefficient Fixation

The coefficients α, β, and γ determine how Ξ_C, Ω_C, and Λ_C are combined. Because coefficient choice can affect [Φ∗_C], η_c, I_c, and V_CBR(η), coefficient fixation is verdict-relevant. The coefficients are therefore certified registry objects, not adjustable fitting parameters.

They must be fixed before comparison with V_obs(η). They may not be selected to fit the observed visibility curve, force η_c into a desired region, rescue a null result, or hide non-Born probability weights inside ℛ_C.

Definition 7.1 — Coefficient Certificate

A coefficient certificate for α, β, and γ specifies:

the numerical values or registered coefficient domain;
the rule by which the values or domain are fixed;
sign restrictions;
normalization relationship to Ξ_C, Ω_C, and Λ_C;
sensitivity of [Φ∗_C] to coefficient variation;
sensitivity of η_c or I_c to coefficient variation;
coefficient uncertainty;
the coefficient-domain verdict rule, if a domain is registered;
the consequence of coefficient modification after comparison.

[To be fixed before comparison: registered numerical values or permitted domain for α, β, and γ.]

[To be fixed before comparison: sign and normalization constraints on α, β, and γ.]

Because Ξ_C, Ω_C, and Λ_C are burden terms, the default registered expectation is α, β, γ ≥ 0. Any negative or signed coefficient requires a separate certificate explaining its physical role and why it does not convert ℛ_C into a reward functional or hidden probability rule.

7.1 Permitted Coefficient Rules

The coefficients may be fixed only by rules that do not use V_obs(η). Permitted rules include:

Symmetry.
Coefficients may be fixed by a declared symmetry among burden terms.
Dimensional normalization.
Coefficients may be fixed after each burden term is normalized to a common dimensionless scale.
Independent calibration.
Coefficients may be fixed using calibration data independent of the observed visibility curve.
Pre-registered robustness class.
The dossier may register a coefficient domain and require the minimizer, critical region, or predicted signature to be stable over that domain.
Declared sensitivity domain.
Coefficients may be fixed by declaring the sensitivity regime in which the platform has discriminating power, provided the rule is fixed before comparison.

[To be fixed before comparison: whether coefficients are point-fixed or domain-fixed.]

[To be fixed before comparison: robustness criterion over the coefficient domain, if domain-fixed.]

7.2 Forbidden Coefficient Rules

The coefficients may not be fixed by:

fitting V_obs(η);
selecting values after outcome comparison;
forcing η_c or I_c into a favorable region;
rescuing a null result;
hiding non-Born probability weights;
weakening baseline contrast after the fact;
widening or narrowing V_CBR(η) after observing V_obs(η).

These are not merely bad practices. They are identity-changing operations. Any such change modifies ℛ_C and creates a successor model.

7.3 Coefficient Robustness and Verdict Assignment

If the dossier registers a coefficient domain rather than a single coefficient triple, it must specify whether the prediction is required to hold:

for all triples in the domain;
for a registered subset defined before comparison;
for a nominal triple with uncertainty bounds;
under a worst-case certified robustness rule;
under a best-case rule, if explicitly justified and certified.

The verdict rule must be tied to this choice. A signature appearing only for a post hoc-selected coefficient triple cannot count as survival. A null result cannot be avoided by retreating to a different coefficient triple unless that rule was registered before comparison.

[To be fixed before comparison: coefficient-domain verdict rule.]

[To be fixed before comparison: coefficient sensitivity analysis plan.]

Proposition 7.1 — No Coefficient Tuning

If α, β, or γ are selected or modified using V_obs(η), post-comparison residuals, or observed baseline disagreement, then the resulting burden functional is not the registered ℛ_C.

Proof sketch. α, β, and γ are constitutive elements of ℛ_C. If they are selected using the data they are meant to help predict or test, the burden ordering becomes data-dependent. That violates the Registry Identity Principle and creates a successor model.

7.4 Successor-Model Rule

Changing α, β, or γ after comparison creates a successor model.

This applies whether the change is numerical, rule-based, normalization-based, or domain-based. A revised coefficient choice may be scientifically motivated by failure, but it cannot rescue the registered C_DCE instantiation.

8. Selection Algorithm and Reproducibility

The registered C_DCE instantiation must be reproducible. A third party should be able to begin with the certified registry, construct 𝒜(C_DCE), quotient by ≃_C, compute ℛ_C, identify [Φ∗_C], derive V_CBR(η), derive η_c or I_c, and apply the registered comparison rule without adding interpretive choices after the fact.

The selection algorithm is therefore not explanatory decoration. It is a verdict-relevant registered object.

Definition 8.1 — Reproducible Selection Procedure

A reproducible selection procedure is a pre-comparison algorithm that maps the certified registry to:

𝒜(C_DCE);
𝒜(C_DCE)/≃_C;
burden values ℛ_C([Φ]);
selected class [Φ∗_C] or certified minimizer set;
V_CBR(η);
η_c or I_c;
uncertainty report;
audit log.

The procedure must specify its inputs, steps, uncertainty handling, tie rule, output objects, failure modes, and consequence if modified after comparison.

[To be fixed before comparison: exact selection algorithm.]

[To be fixed before comparison: software, pseudocode, or mathematical procedure used to compute [Φ∗_C].]

8.1 Registered Algorithm

The registered selection algorithm is:

Fix C_DCE by registration certificates and traceability entries.
Generate 𝒜₀(C_DCE).
Apply admissibility filters F₁…F_n.
Construct 𝒜(C_DCE).
Assign admissibility and exclusion certificates.
Define ≃_C using 𝒪_C, d_C, and τ_C.
Construct 𝒜(C_DCE)/≃_C.
Evaluate Ξ_C([Φ]), Ω_C([Φ]), and Λ_C([Φ]) for each [Φ].
Propagate uncertainty through each burden term.
Compute ℛ_C([Φ]) = αΞ_C([Φ]) + βΩ_C([Φ]) + γΛ_C([Φ]).
Identify the minimizer set M_C = argmin ℛ_C([Φ]).
Produce a minimizer certificate.
Apply the registered tie or degeneracy rule if needed.
Derive V_CBR(η).
Derive η_c or I_c from Δℛ_C(η).
Lock the prediction before comparison with V_obs(η).
Compare to V_obs(η) only after registry lock.

No step may be reordered after comparison.

Definition 8.2 — Minimizer Certificate

A minimizer certificate is the audit record for the selected burden-minimizing class. It must state:

the selected class [Φ∗_C] or certified minimizer set M_C;
all competing classes considered;
the burden value or burden interval for each relevant class;
the burden gap to the nearest competitor;
uncertainty intervals;
whether the minimizer is unique, near-degenerate, or unresolved;
the tie or degeneracy rule applied;
the consequence for V_CBR(η);
the consequence for η_c or I_c;
the consequence if minimization cannot be certified.

[To be fixed before comparison: minimizer-certification format.]

[To be fixed before comparison: burden-gap threshold for certified minimizer uniqueness.]

The selected class [Φ∗_C] is not considered registered until the minimizer certificate is complete.

8.2 Pseudocode

A reproducibility appendix should include pseudocode of the following form:

Input:
  Registered C_DCE
  Registered 𝒜₀(C_DCE)
  Registered filters F₁…F_n
  Registered ≃_C via 𝒪_C, d_C, τ_C
  Registered Ξ_C, Ω_C, Λ_C
  Registered α, β, γ
  Registered η calibration
  Registered uncertainty model

Procedure:
  1. Construct 𝒜(C_DCE) = F_n ∘ … ∘ F₁[𝒜₀(C_DCE)]
  2. Certify admitted and excluded candidate families
  3. Form quotient 𝒜(C_DCE)/≃_C
  4. For each [Φ] in 𝒜(C_DCE)/≃_C:
       compute Ξ_C([Φ])
       compute Ω_C([Φ])
       compute Λ_C([Φ])
       propagate uncertainty
       compute ℛ_C([Φ])
  5. Identify minimizer set M_C = argmin ℛ_C([Φ])
  6. Produce minimizer certificate
  7. Apply registered tie/degeneracy rule
  8. Output [Φ∗_C] or registered minimizer set
  9. Derive V_CBR(η)
 10. Derive η_c or I_c
 11. Lock prediction and comparison rule

Output:
  [Φ∗_C] or M_C
  V_CBR(η)
  η_c or I_c
  Δℛ_C(η)
  minimizer certificate
  uncertainty report
  audit log

[To be fixed before comparison: exact pseudocode or executable workflow.]

8.3 Tie, Degeneracy, and Non-Uniqueness

If multiple operational equivalence classes minimize ℛ_C within registered uncertainty, the dossier must specify the consequence before comparison.

Permitted options include:

a registered tie-breaking rule independent of V_obs(η);
a set-valued prediction V_CBR(η);
a declared near-degenerate critical interval;
an inconclusive selection outcome;
successor-model registration if the degeneracy reveals under-specification.

A tie cannot be resolved after observing which candidate better fits V_obs(η).

[To be fixed before comparison: tie or degeneracy rule.]

8.4 Reproducibility Package

A 10/10 dossier should include:

mathematical definitions used in the selection algorithm;
pseudocode or executable notebook;
registered input files or symbolic input registry;
calibration-input interface;
uncertainty-propagation routine;
burden-evaluation output;
minimizer certificate;
η_c or I_c derivation;
audit log.

[To be supplied before comparison: reproducibility appendix or computational notebook.]

Proposition 8.1 — Reproducibility Prevents Algorithmic Rescue

If the selection algorithm is fixed before comparison, then a failed registered prediction cannot be rescued by changing the computation procedure while preserving the identity of the original instantiation.

Proof sketch. The algorithm maps the registered objects to [Φ∗_C], V_CBR(η), and η_c or I_c. Changing the algorithm may change those outputs. Since the algorithm is registered and verdict-relevant, modifying it after comparison creates a successor model.

9. Independent Accessibility Calibration

The accessibility parameter η is the empirical bridge between the record architecture of C_DCE and the registered CBR prediction. It must be calibrated independently, certified before comparison, and insulated from the observed visibility curve.

The registered definition is:

η = I(W; R_acc) / H(W).

η measures normalized accessible which-path information. It is an input to the registered prediction, not an interpretation extracted from V_obs(η).

Definition 9.1 — No-Visibility-Leakage Rule

No information derived from V_obs(η), post-comparison residuals, or observed disagreement with V_ℬ(η) may enter:

η;
ℛ_C;
Ξ_C, Ω_C, or Λ_C;
α, β, or γ;
η_c or I_c;
δ_C;
V_CBR(η);
ℬ;
𝓝;
B_𝓝;
ε_detect;
the statistical test;
the verdict rule.

This rule forbids both direct and indirect leakage. A quantity is not independent merely because V_obs(η) is not named explicitly. If visibility-derived information affects its construction after comparison, the registered object has changed and the result is a successor model.

9.1 Definition of W and R_acc

W and R_acc are certified components of C_DCE.

The certificate for W must specify:

the physical path degree of freedom;
the operational encoding of path alternatives;
the probability model for W;
the entropy estimator for H(W);
the calibration data used to estimate W statistics.

The certificate for R_acc must specify:

the physical subsystem or record channel constituting the accessible record;
the accessibility-control operation;
the data used to estimate the joint distribution of W and R_acc;
the distinction between R_acc, R_env, and detector records;
the implementation tolerance for accessibility control.

[To be fixed before comparison: operational definition of W.]

[To be fixed before comparison: physical and statistical definition of R_acc.]

9.2 Mutual Information Estimation

For discrete registered variables:

I(W; R_acc) = Σ_{w,r} p(w,r) log[p(w,r)/(p(w)p(r))],

and:

H(W) = −Σ_w p(w) log p(w).

If W or R_acc is continuous, coarse-grained, or estimated through proxies, the dossier must register the estimator, binning rule, bias correction, finite-sample treatment, and uncertainty model before comparison.

[To be fixed before comparison: mutual-information estimator.]

[To be fixed before comparison: entropy estimator for H(W).]

[To be fixed before comparison: finite-sample correction or bias treatment.]

η is invalid if H(W) is zero, if the estimator fails its validity gate, or if the accessibility data cannot be separated from the visibility comparison.

9.3 Calibration Data Allowed and Forbidden

Allowed η-calibration data include:

independently collected record-accessibility calibration data;
source and path calibration data;
registered record-channel calibration data;
detector-independent accessibility measurements, where available;
platform calibration data certified before comparison.

Forbidden η-calibration data include:

V_obs(η);
post-comparison visibility deviations;
data selected because it shifts η_c or I_c favorably;
detector-fringe behavior used to infer accessibility after the fact;
any calibration rule chosen after observing the visibility curve.

The governing rule is:

η must be calibrated independently of V_obs(η).

9.4 η-Sweep and Calibration Map

Let u denote the registered accessibility-control setting. The dossier must provide a certified calibration map:

u ↦ η(u),

including uncertainty:

η(u) ± σ_η(u).

The calibration map must be obtained independently of V_obs(η). It must state whether η is monotonic in u, whether non-monotonicity is allowed, and how repeated calibration measurements are combined.

[To be fixed before comparison: accessibility-control setting u.]

[To be supplied from independent platform calibration: calibration map u ↦ η(u).]

[To be supplied from independent platform calibration: η uncertainty model σ_η(u).]

9.5 η Validity Gates

The registered test requires η validity gates:

valid definition of W;
valid identification of R_acc;
valid estimation of I(W; R_acc);
valid estimation of H(W);
sufficient η resolution across the sweep;
sufficient coverage of η_c or I_c;
independence from V_obs(η);
calibration stability over the data-collection interval.

If an η validity gate fails, the result is inconclusive unless the verdict rule explicitly defines that gate failure as decisive. A failed η calibration cannot be repaired after comparison by redefining W, R_acc, the estimator, or the calibration map.

Proposition 9.1 — Accessibility Calibration Non-Circularity

If η is calibrated using only registered accessibility data independent of V_obs(η), then η is non-circular with respect to the visibility comparison.

Proof sketch. Circularity would require η to be inferred from the visibility curve it is later used to test. Here η is defined from I(W; R_acc) / H(W) using independent calibration. Therefore V_obs(η) does not determine η.

10. Derivation of η_c or I_c from Burden Geometry

The critical accessibility region is not a discretionary window. It is a registered consequence of the burden geometry of the C_DCE instantiation.

The dossier therefore derives η_c or I_c from:

𝒜(C_DCE)/≃_C, ℛ_C, Δℛ_C(η), δ_C, and the independently calibrated η structure.

It does not select η_c or I_c from V_obs(η).

Definition 10.1 — Critical-Region Certificate

A critical-region certificate specifies:

whether the instantiation uses η_c or I_c;
the competing classes involved near the critical region;
the formula or algorithm for Δℛ_C(η);
the registered value or rule for δ_C;
the η calibration and uncertainty model used;
the required η coverage and sampling density;
the connection between the critical region and V_CBR(η);
the consequence if the burden gap never closes;
the consequence if the critical region is too broad to test;
the consequence of modifying the critical region after comparison.

[To be fixed before comparison: critical-region certificate.]

10.1 Burden Functions Over η

For each [Φ] ∈ 𝒜(C_DCE)/≃_C:

ℛ_C([Φ]; η) = αΞ_C([Φ]) + βΩ_C([Φ]) + γΛ_C([Φ]; η).

The η-dependence must be registered before comparison and must use η as calibrated from I(W; R_acc) / H(W). It may not use V_obs(η).

[To be fixed before comparison: η-dependence of Λ_C and any other burden term.]

[To be fixed before comparison: computational grid, continuous method, or analytic method for evaluating ℛ_C([Φ]; η).]

10.2 Burden Gap Δℛ_C(η)

Let [Φ₁(η)] denote the lowest-burden class at η, and let [Φ₂(η)] denote the lowest-burden competitor not operationally equivalent to [Φ₁(η)]. Then:

Δℛ_C(η) = ℛ_C([Φ₂(η)]; η) − ℛ_C([Φ₁(η)]; η).

If uncertainty produces interval-valued burdens, the dossier must specify whether Δℛ_C(η) is evaluated by nominal values, conservative lower bounds, overlap criteria, or another registered rule.

[To be fixed before comparison: burden-gap computation rule.]

[To be fixed before comparison: treatment of uncertainty in Δℛ_C(η).]

Δℛ_C(η) is computed from the registered burden functional and admissible quotient class. It is not inferred from the observed visibility curve.

10.3 Critical Accessibility Value η_c

If the registered burden geometry produces a distinct ordering transition, η_c is the point at which the minimizing operational equivalence class changes:

[Φ∗_C(η⁻)] ≠ [Φ∗_C(η⁺)].

The certificate for η_c must state:

the competing classes involved;
the burden terms responsible for the transition;
the uncertainty in η_c;
the calibration data used to locate η_c;
the relation between η_c and V_CBR(η);
the validity gates required for testing near η_c.

[To be fixed before comparison: η_c derivation, if a point critical value is used.]

η_c cannot be shifted after observing V_obs(η).

10.4 Critical Accessibility Interval I_c

If a point η_c is too sharp relative to uncertainty, finite sampling, or near-degenerate burden geometry, the dossier must use:

I_c = {η : Δℛ_C(η) ≤ δ_C},

where δ_C is the registered burden-gap tolerance.

δ_C must be fixed before comparison. It may be determined by burden uncertainty, calibration uncertainty, sensitivity requirements, or a registered robustness criterion, but it may not be chosen after observing V_obs(η).

[To be fixed before comparison: registered numerical value or rule for δ_C.]

[To be fixed before comparison: derivation of I_c from Δℛ_C(η).]

[To be supplied from independent platform calibration: η-resolution and coverage model for I_c.]

The interval I_c is not a region where the data look interesting. It is the region where the registered burden geometry makes competing admissible equivalence classes close enough, by the δ_C criterion, to generate the registered accessibility-sensitive prediction.

10.5 If the Burden Gap Never Closes

The dossier must specify what follows if Δℛ_C(η) never falls below δ_C across the registered η-sweep.

Permitted outcomes include:

no critical-region prediction for this platform;
an inconclusive platform instantiation;
a registered smooth prediction without critical behavior;
successor-model registration if the absence of a critical region contradicts the intended test object.

This condition must be specified before comparison. The absence of a critical region cannot be repaired after V_obs(η) is known by redefining δ_C or broadening the η-sweep.

[To be fixed before comparison: verdict consequence if Δℛ_C(η) never closes.]

10.6 If the Critical Region Is Too Broad to Test

The dossier must also specify what follows if I_c is so broad that the predicted signature is not empirically discriminating.

Permitted outcomes include:

inconclusive test readiness;
required platform refinement before testing;
registered weak-discrimination status;
successor-model registration.

A critical interval that cannot support a discriminating visibility test cannot be used to claim survival. It may at most support an inconclusive result or motivate a better platform instantiation.

[To be fixed before comparison: maximum admissible width or discriminability criterion for I_c.]

10.7 Relation to V_CBR(η)

The critical region matters only if it connects to a registered visibility prediction. The dossier must specify how [Φ∗_C(η)] generates V_CBR(η), and how changes or near-degeneracies in [Φ∗_C(η)] produce the registered feature.

The prediction must state:

whether the expected feature is a kink, slope change, bounded non-baseline deviation, transition in visibility response, or another registered structure;
the region in which it must occur;
the minimum detectable deviation ε_detect;
how the feature is separated from V_ℬ(η) and B_𝓝;
how uncertainty in η_c or I_c propagates into V_CBR(η).

[To be fixed before comparison: registered form of V_CBR(η).]

[To be fixed before comparison: signature type expected within η_c or I_c.]

[To be fixed before comparison: registered numerical value of ε_detect.]

Proposition 10.1 — Critical-Region Non-Circularity

If η_c or I_c is derived from 𝒜(C_DCE)/≃_C, ℛ_C, Δℛ_C(η), δ_C, and independent η calibration before comparison, then the critical region is non-circular with respect to V_obs(η).

Proof sketch. The critical region is computed from registered pre-comparison objects. None of those objects may depend on V_obs(η). Therefore the observed visibility curve does not determine the critical region.

Proposition 10.2 — Strong-Null Failure for the Registered Critical Region

Proof sketch. The registered instantiation predicts an accessibility-sensitive feature in V_CBR(η) within the registered critical region, with detectable separation from the baseline-plus-nuisance envelope. If all validity gates are satisfied and V_obs(η) remains inside B_𝓝 across I_c, the registered feature is absent. Since I_c, B_𝓝, ε_detect, and the statistical test are fixed before comparison, the absence defeats the registered instantiation.

Theorem 10.1 — Test-Readiness of the Burden-to-Critical-Region Chain

The registered C_DCE instantiation has a non-circular, test-ready burden-to-critical-region chain only if:

𝒜(C_DCE)/≃_C is certified;
ℛ_C is well-defined over 𝒜(C_DCE)/≃_C;
Ξ_C, Ω_C, and Λ_C belong to admissible burden-term families;
α, β, and γ are fixed before comparison;
[Φ∗_C] or the minimizer set is certified;
η is independently calibrated;
Δℛ_C(η) is computable or bounded;
η_c or I_c is derived from burden geometry;
V_CBR(η) is registered before comparison;
the critical-region certificate is complete.

If any of these conditions fail, the instantiation is not test-ready. It may be incomplete, inconclusive, or require successor-model registration, but it cannot be treated as a locked empirical test of the registered C_DCE instantiation.

Proof sketch. The burden-to-critical-region chain connects admissibility, quotienting, burden computation, accessibility calibration, critical-region derivation, and visibility prediction. If any link is missing or data-dependent, the registered prediction is either underdetermined or circular. If all links are certified before comparison, then the critical region and prediction are fixed independently of V_obs(η), and the instantiation is test-ready.

10.8 Inconclusive and Successor-Model Cases

The result is inconclusive if:

η calibration fails;
I_c is not adequately sampled;
δ_C is not registered;
Δℛ_C(η) cannot be computed or bounded;
burden uncertainty overwhelms the critical-region derivation;
the burden gap never closes and no consequence is registered;
I_c is too broad to discriminate;
B_𝓝 is not validated;
ε_detect is not achieved;
the statistical test is not applicable.

The result is successor-model registration if, after comparison, the dossier changes η_c, I_c, δ_C, Δℛ_C(η), η calibration, ℛ_C, V_CBR(η), B_𝓝, ε_detect, or the verdict rule.

The registered critical region is part of the model’s identity. It is not an adjustable window.

11. Baseline ℬ and Nuisance Envelope B_𝓝

The registered C_DCE instantiation must be tested against the strongest relevant standard account available for the platform, not against an idealized or weakened comparator. The baseline ℬ is therefore not standard quantum mechanics in abstraction. It is the registered standard quantum/decoherence/detector/noise model for the actual delayed-choice record-accessibility interferometric context C_DCE.

The function of ℬ is to specify the visibility behavior expected from the platform without the registered CBR accessibility-sensitive contribution. The function of 𝓝 is to collect all registered non-CBR effects capable of affecting V(η). The function of B_𝓝 is to define the allowed visibility envelope around V_ℬ(η) under those registered nuisance effects.

A CBR signature is evidentially meaningful only if it escapes the full baseline-plus-nuisance account. It is not enough for V_CBR(η), or V_obs(η), to differ from the central baseline curve V_ℬ(η). The registered CBR feature must be separated from the entire nuisance envelope B_𝓝 by at least ε_detect in the registered signature region R_sig ⊆ I_c.

The baseline and nuisance construction must be fixed before comparison with V_obs(η). Neither ℬ nor B_𝓝 may be weakened, narrowed, widened, shifted, or reinterpreted after observing the data.

Definition 11.1 — Baseline Certificate

A baseline certificate for ℬ specifies, before comparison:

the standard quantum prediction used for C_DCE;
the platform-specific decoherence model;
the detector model;
the noise and drift model;
the calibration inputs;
the uncertainty model;
the resulting baseline visibility prediction V_ℬ(η);
the baseline-validation gates;
the traceability of each baseline component to C_DCE;
the relationship between ℬ and the nuisance class 𝓝;
the consequence if ℬ fails validation.

The baseline certificate must be complete before V_obs(η) is compared against V_CBR(η).

Definition 11.2 — Baseline Exhaustion Requirement

Before a CBR deviation can be considered evidential, every registered standard quantum, decoherence, detector, calibration, environmental, finite-sampling, data-processing, and nuisance explanation capable of producing an apparent feature in V(η) at scale ≥ ε_detect must be included in ℬ or 𝓝.

This requirement does not demand metaphysical exhaustion of every imaginable effect. It demands platform-level exhaustion of all standard explanations that are known, calibratable, or reasonably modelable within C_DCE at the registered sensitivity scale.

If a standard platform effect capable of producing a feature at or above ε_detect is omitted from ℬ or 𝓝, survival cannot be assigned. The result is inconclusive or requires successor-model registration with an expanded baseline.

11.1 Baseline ℬ

The baseline ℬ includes all registered standard effects relevant to V(η), including:

standard quantum prediction;
platform-specific decoherence;
detector inefficiency;
dark counts;
phase drift;
timing jitter;
mode mismatch;
finite sampling noise;
environmental coupling;
calibration uncertainty;
data-processing uncertainty.

The baseline prediction is:

V_ℬ(η).

V_ℬ(η) must be computed or bounded from registered platform inputs. It may depend on independently calibrated η, but it may not be fitted to observed CBR-test residuals after comparison.

[To be fixed before comparison: registered standard quantum prediction for C_DCE.]

[To be fixed before comparison: platform-specific decoherence model.]

[To be fixed before comparison: detector-efficiency model.]

[To be fixed before comparison: dark-count model.]

[To be fixed before comparison: phase-drift model.]

[To be fixed before comparison: timing-jitter model.]

[To be fixed before comparison: mode-mismatch model.]

[To be fixed before comparison: finite-sampling model.]

[To be fixed before comparison: environmental-coupling model.]

[To be fixed before comparison: calibration-uncertainty model.]

[To be fixed before comparison: data-processing uncertainty model.]

The baseline must be strong enough that an apparent CBR deviation cannot be obtained merely by comparison against an artificially clean, incomplete, or underpowered standard model.

Proposition 11.1 — No Straw-Baseline Condition

A registered C_DCE test is not evidentially valid unless ℬ includes all platform-relevant standard quantum, decoherence, detector, calibration, environmental, finite-sampling, and data-processing effects capable of affecting V(η) at or above the registered sensitivity scale.

Proof sketch. The registered CBR signature is defined as a non-baseline accessibility-sensitive feature in V(η). If ℬ omits platform-relevant standard effects, an apparent deviation may be attributable to ordinary platform physics rather than to the registered CBR instantiation. Therefore a weak baseline cannot support survival. The baseline must be strong enough to absorb all registered non-CBR effects within B_𝓝.

Proposition 11.2 — Baseline Exhaustion Condition

If a known or calibratable standard effect capable of producing a visibility feature of size ≥ ε_detect is omitted from ℬ or 𝓝, then the registered C_DCE test is not competent to assign survival.

Proof sketch. Survival requires that the observed feature not be explainable by the baseline-plus-nuisance model. If a standard effect capable of producing such a feature is omitted, the exclusion of that explanation is not registered. The observed feature may therefore be ordinary platform behavior. Survival is not warranted.

11.2 Nuisance Class 𝓝

The nuisance class 𝓝 contains all registered non-CBR effects that can affect V(η) in C_DCE. It includes platform deviations, calibration imperfections, detector effects, drift processes, finite-sample effects, and data-processing uncertainties not treated as part of the central baseline curve V_ℬ(η).

A nuisance certificate must specify:

each nuisance source;
the physical or statistical origin of the nuisance;
the calibration source for its allowed range;
its effect on V(η);
whether it is treated analytically, experimentally, statistically, or by simulation;
its uncertainty model;
its interaction with other nuisance sources;
its role in B_𝓝;
the consequence if the nuisance source fails validation.

[To be fixed before comparison: complete nuisance class 𝓝.]

[To be fixed before comparison: allowed range for each nuisance parameter.]

[To be fixed before comparison: dependence structure among nuisance parameters.]

No nuisance source may be added after observing V_obs(η) to explain away a failed or successful result. A newly discovered nuisance may justify an inconclusive verdict or successor-model registration, but it cannot retroactively alter the registered nuisance class.

11.3 Nuisance Envelope B_𝓝

B_𝓝 is the registered nuisance envelope around V_ℬ(η). It defines the visibility values or visibility curves compatible with ℬ under the registered nuisance class 𝓝.

A general interval form is:

B_𝓝(η) = [V_ℬ(η) − b_𝓝⁻(η), V_ℬ(η) + b_𝓝⁺(η)],

where b_𝓝⁻(η) and b_𝓝⁺(η) are registered lower and upper nuisance bounds.

If a symmetric envelope is justified, the dossier may use:

B_𝓝(η) = {v : |v − V_ℬ(η)| ≤ b_𝓝(η)}.

The envelope construction must specify:

whether B_𝓝 is analytic, simulation-based, calibration-based, empirical, worst-case, confidence-based, or hybrid;
the confidence or coverage rule, if statistical;
the treatment of correlated nuisance sources;
the treatment of η uncertainty;
the treatment of detector and phase uncertainty;
the relationship between B_𝓝 and ε_detect;
the validation procedure for B_𝓝.

[To be fixed before comparison: exact construction rule for B_𝓝.]

[To be fixed before comparison: coverage or confidence rule for B_𝓝, if statistical.]

[To be fixed before comparison: treatment of correlated nuisance sources.]

[To be fixed before comparison: treatment of η uncertainty inside B_𝓝.]

B_𝓝 is not an adjustable safety margin. It is a registered object.

11.4 Envelope Non-Expansion and Non-Overlap

B_𝓝 cannot be widened after observing V_obs(η) to rescue the registered C_DCE instantiation.

This prohibition includes:

adding nuisance sources after comparison;
increasing nuisance parameter ranges after comparison;
changing the confidence rule after comparison;
changing the treatment of correlated nuisance sources after comparison;
changing the η uncertainty model after comparison;
expanding detector or calibration tolerances after comparison;
redefining V_ℬ(η) after comparison.

The registered CBR signature must also satisfy an envelope non-overlap condition:

The predicted feature V_CBR(η) must lie outside B_𝓝 by at least ε_detect over the registered signature region R_sig ⊆ I_c, according to the registered statistical criterion.

Equivalently, CBR does not earn a survival verdict merely by differing from the central baseline curve V_ℬ(η). It must differ from the entire registered baseline-plus-nuisance envelope.

[To be fixed before comparison: non-overlap criterion between V_CBR(η) and B_𝓝.]

[To be fixed before comparison: signature region R_sig ⊆ I_c.]

11.5 Baseline and Nuisance Validation Gates

Before survival or failure can be assigned, ℬ and B_𝓝 must satisfy registered validation gates. These include:

validation of V_ℬ(η) outside the critical region where applicable;
detector-model validation;
dark-count validation;
phase-stability validation;
timing-jitter validation;
mode-overlap validation;
finite-sample adequacy;
nuisance-range validation;
calibration-stability validation;
data-processing validation.

[To be fixed before comparison: baseline-validation gates.]

[To be fixed before comparison: nuisance-validation gates.]

If ℬ or B_𝓝 fails validation, the result is inconclusive unless the verdict rule explicitly treats that failure as decisive. A failed baseline validation cannot be repaired after comparison by weakening ℬ or widening B_𝓝.

Proposition 11.3 — Baseline-Envelope Fixity

If ℬ or B_𝓝 is changed after comparison with V_obs(η), then the resulting comparison is not a verdict on the registered C_DCE instantiation.

Proof sketch. The registered verdict depends on whether V_obs(η) lies inside or outside B_𝓝 relative to V_ℬ(η). Changing ℬ or B_𝓝 changes the comparison target. By the Registry Identity Principle, this changes the registered object and creates a successor model.

12. Registered CBR Prediction

The registered CBR prediction is the empirical center of the dossier. It states what the C_DCE instantiation predicts for the observable V(η), where the prediction must occur, what feature counts as the predicted signature, how large the feature must be, and how the feature is separated from the baseline-plus-nuisance envelope.

The prediction is not a general claim that CBR may produce some deviation somewhere. It is a registered platform-instantiation claim about V(η) in the critical accessibility region η_c or I_c.

Definition 12.1 — Prediction Certificate

A prediction certificate for V_CBR(η) specifies, before comparison:

the selected operational equivalence class [Φ∗_C] or registered minimizer set;
the procedure by which [Φ∗_C] generates V_CBR(η);
the critical region η_c or I_c;
the signature region R_sig ⊆ I_c;
the signature type;
the minimum detectable deviation ε_detect;
the non-overlap criterion relative to B_𝓝;
the relationship between V_CBR(η), V_ℬ(η), and B_𝓝;
the uncertainty in V_CBR(η);
the statistical test used to compare prediction and data;
the survival condition;
the failure condition;
the consequence of modifying the prediction after comparison.

The registered prediction is fixed only when this certificate is complete.

12.1 Observable

The observable is:

V(η),

the interference visibility as a function of the independently calibrated accessibility parameter:

η = I(W; R_acc) / H(W).

V(η) must be estimated using the registered visibility estimator and η-calibration procedure. The visibility estimator cannot be changed after observing the data to favor CBR.

[To be fixed before comparison: registered visibility estimator.]

[To be fixed before comparison: uncertainty model for V_obs(η).]

12.2 Signature Region

The relevant region is η_c or I_c, derived from burden geometry:

I_c = {η : Δℛ_C(η) ≤ δ_C},

or, if a point transition is registered, η_c is the accessibility value at which the minimizing class changes.

The prediction certificate may further identify a signature region:

R_sig ⊆ I_c,

where the registered feature is expected to appear and where non-overlap with B_𝓝 is evaluated.

Neither I_c nor R_sig may be selected from V_obs(η). They must be derived from 𝒜(C_DCE)/≃_C, ℛ_C, Δℛ_C(η), δ_C, and independent η calibration.

[To be fixed before comparison: certified η_c or I_c.]

[To be fixed before comparison: registered signature region R_sig ⊆ I_c.]

[To be fixed before comparison: required η coverage inside R_sig and I_c.]

12.3 Signature Type

The registered signature must be specified before comparison as one of the following or as another explicitly certified feature:

kink in V(η);
slope discontinuity;
bounded non-baseline deviation;
transition in visibility response;
localized deviation pattern;
other pre-registered accessibility-sensitive feature.

The signature certificate must specify the mathematical or statistical criterion by which the feature is detected. A qualitative statement that “CBR predicts a change near accessibility” is insufficient.

[To be fixed before comparison: exact signature type.]

[To be fixed before comparison: mathematical or statistical detection criterion for the signature.]

12.4 Minimum Detectable Deviation ε_detect

The minimum effect size is:

ε_detect.

ε_detect is the registered minimum detectable deviation required for the platform to distinguish V_CBR(η) from B_𝓝 within R_sig ⊆ I_c. It must be fixed before comparison and tied to statistical power, nuisance-envelope width, visibility uncertainty, and η uncertainty.

[To be fixed before comparison: registered numerical value of ε_detect.]

[To be fixed before comparison: derivation of ε_detect from platform sensitivity.]

[To be fixed before comparison: relationship between ε_detect and B_𝓝.]

ε_detect cannot be lowered after a weak deviation is observed or raised after a null result is observed. Any post-comparison change creates a successor model.

12.5 Envelope Non-Overlap Criterion

Survival requires non-overlap between the registered CBR signature and the entire baseline-plus-nuisance envelope.

A sufficient registered condition has the form:

dist(V_CBR(η), B_𝓝(η)) ≥ ε_detect for η ∈ R_sig,

where dist denotes the registered distance from the CBR prediction to the nuisance envelope. If the prediction or envelope is interval-valued, the dossier must specify whether non-overlap is evaluated by worst-case separation, confidence-band exclusion, likelihood comparison, or another registered criterion.

[To be fixed before comparison: distance or separation rule between V_CBR(η) and B_𝓝.]

[To be fixed before comparison: non-overlap rule for interval-valued predictions or envelopes.]

CBR does not survive merely because V_obs(η) differs from V_ℬ(η). It survives only if the observed feature satisfies the registered signature criterion outside B_𝓝 by at least ε_detect under valid test conditions.

12.6 Registered Prediction Statement

The registered C_DCE instantiation predicts a non-baseline accessibility-sensitive feature in V(η) within R_sig ⊆ I_c exceeding ε_detect after nuisance-envelope correction.

More explicitly:

There exists a registered region R_sig ⊆ I_c such that V_CBR(η) is separated from B_𝓝 by at least ε_detect according to the registered non-overlap criterion, and the observed data must display the registered signature in that region for survival to be assigned.

If the prediction is set-valued because the minimizer is degenerate, the prediction certificate must specify set-valued survival and failure conditions before comparison.

[To be fixed before comparison: rule for set-valued V_CBR(η), if applicable.]

12.7 No Prediction Fitting

V_CBR(η) cannot be fitted to V_obs(η). The prediction is generated from [Φ∗_C], ℛ_C, η calibration, and the registered critical-region derivation before comparison.

Post-comparison changes to V_CBR(η), signature type, R_sig, ε_detect, non-overlap criterion, or prediction certificate create a successor model.

Proposition 12.1 — Prediction Independence

If V_CBR(η) is generated from the registered minimizer [Φ∗_C], independently calibrated η, and pre-comparison burden geometry, then V_CBR(η) is independent of V_obs(η).

Proof sketch. The prediction is computed from registered objects fixed before comparison. The no-visibility-leakage rule excludes V_obs(η), post-comparison residuals, and observed baseline disagreement from entering [Φ∗_C], η, η_c, I_c, R_sig, ε_detect, or V_CBR(η). Therefore the observed visibility curve does not determine the prediction.

Proposition 12.2 — Non-Overlap Requirement for Survival

A registered C_DCE instantiation cannot receive a survival verdict unless the registered signature is observed outside B_𝓝 by at least ε_detect in R_sig ⊆ I_c under valid test conditions.

Proof sketch. The baseline-plus-nuisance envelope represents all registered non-CBR explanations for V(η). If the observed feature remains inside B_𝓝, it is compatible with the registered standard account. If the feature does not exceed ε_detect, the platform lacks registered sensitivity to distinguish it. Therefore survival requires both envelope escape and detectable separation.

13. Statistical Analysis and Validity Gates

The statistical analysis plan determines how V_obs(η) is compared to V_CBR(η), V_ℬ(η), and B_𝓝. It is therefore a verdict-relevant registered object. It must be fixed before comparison and cannot be selected after observing the data because it favors CBR.

The analysis plan must enforce a model-comparison hierarchy. The final CBR comparison is permitted only after the platform, calibration, baseline, nuisance envelope, and power requirements have been validated.

Definition 13.1 — Statistical Analysis Certificate

A statistical analysis certificate specifies, before comparison:

the visibility estimator;
the η-binning or continuous-estimation rule;
the sample-size requirement;
the required number and placement of η points inside I_c and R_sig;
the statistical test;
the confidence, credibility, or error-control threshold;
the treatment of multiple comparisons, if applicable;
the uncertainty model;
the outlier rule;
the exclusion rule;
the blinding and unblinding procedure;
the model-comparison hierarchy;
the validity gates;
the verdict mapping.

[To be fixed before comparison: complete statistical analysis certificate.]

13.1 Model-Comparison Hierarchy

The registered comparison proceeds in the following order:

validate implementation of C_DCE within registered tolerances;
validate independent η calibration;
validate the baseline ℬ;
validate the nuisance class 𝓝 and envelope B_𝓝;
confirm statistical power and ε_detect sensitivity;
confirm required η coverage inside I_c and R_sig;
evaluate V_obs(η) against the registered CBR prediction and baseline envelope;
assign survival, failure, inconclusive result, or successor-model registration.

No later stage may be used to repair failure at an earlier stage. A visible deviation from V_ℬ(η) cannot count as survival if η calibration failed, if B_𝓝 was not validated, or if the platform lacked power to distinguish ε_detect.

[To be fixed before comparison: full ordered model-comparison hierarchy.]

13.2 Visibility Estimator

The visibility estimator must be defined before comparison. The certificate must state how V_obs(η) is computed from detector records, including phase dependence, fringe fitting, coincidence counts, uncertainty estimates, and any binning or smoothing.

[To be fixed before comparison: exact visibility estimator.]

[To be fixed before comparison: uncertainty estimator for V_obs(η).]

[To be fixed before comparison: fringe-fitting or phase-estimation procedure.]

The estimator cannot be altered after observing the visibility curve to amplify or suppress the registered signature.

13.3 η-Binning and Critical-Region Coverage

The analysis plan must state how η values are binned or treated continuously. It must also specify the minimum coverage of I_c and R_sig required to assign survival or failure.

[To be fixed before comparison: η-binning rule or continuous-analysis rule.]

[To be fixed before comparison: required number of η points inside I_c.]

[To be fixed before comparison: required number of η points inside R_sig.]

[To be fixed before comparison: required distribution of η points inside I_c and R_sig.]

[To be fixed before comparison: rule for handling η uncertainty in bin assignment.]

If I_c or R_sig is not adequately sampled, the result is inconclusive unless the verdict rule explicitly states otherwise.

13.4 Sample Size and Sensitivity

The test must specify the sample size required to detect ε_detect under the registered nuisance and uncertainty model. This requirement must be tied to the power analysis in Section 14.

[To be fixed before comparison: sample-size requirement.]

[To be fixed before comparison: minimum detectable visibility deviation under the registered analysis.]

[To be fixed before comparison: sampling sufficiency criterion.]

If the sample size or sensitivity is insufficient, failure cannot be assigned merely because the signature was not observed. The result is inconclusive.

13.5 Statistical Test

The statistical test must be fixed before comparison. It must specify whether the comparison is based on confidence bands, hypothesis testing, model comparison, likelihood ratios, Bayesian evidence, interval exclusion, worst-case envelope testing, or another registered method.

[To be fixed before comparison: statistical test.]

[To be fixed before comparison: confidence, credibility, or error-control threshold.]

[To be fixed before comparison: treatment of multiple comparisons, if applicable.]

The test must compare V_obs(η) to the registered objects. It may not be selected after observing which method makes CBR appear stronger.

13.6 Outlier, Exclusion, and Data-Quality Rules

Outlier and exclusion rules must be registered before comparison. They must state:

what counts as an outlier;
what data may be excluded;
what detector or calibration failure triggers exclusion;
whether exclusions are applied before or after blinding;
how exclusions are logged;
how exclusions affect validity gates.

[To be fixed before comparison: outlier rule.]

[To be fixed before comparison: exclusion rule.]

[To be fixed before comparison: data-quality logging procedure.]

No data point may be excluded because it weakens the CBR signature unless the exclusion is required by a registered rule independent of the desired verdict.

13.7 Blinding and Unblinding Procedure

The dossier should specify a blinding procedure sufficient to prevent post hoc adjustment of η calibration, baseline construction, nuisance modeling, statistical analysis, or verdict mapping.

[To be fixed before comparison: blinding procedure.]

[To be fixed before comparison: unblinding sequence.]

At minimum, the analysis plan must state when V_obs(η) becomes available to the evaluator and which registry objects must be locked before unblinding.

13.8 Validity Gates

Survival or failure may be assigned only if the registered validity gates are satisfied. These include:

implementation validity;
η-calibration validity;
baseline-validation validity;
nuisance-envelope validation;
detector-stability validity;
phase-control validity;
timing-jitter validity;
sample-size sufficiency;
I_c coverage;
R_sig coverage;
ε_detect achievement;
statistical-test applicability;
data-quality compliance;
blinding-lock compliance.

[To be fixed before comparison: full list of validity gates.]

[To be fixed before comparison: pass/fail criteria for each validity gate.]

Failure of a validity gate produces an inconclusive result unless the verdict rule explicitly defines the gate failure as decisive.

Definition 13.2 — Single-Pass Adjudication Rule

The registered C_DCE test is adjudicated once, using the locked registry, in the registered order. No repeated reclassification is permitted after observing the verdict.

After adjudication, the assigned result may be reported as survival, failure, inconclusive result, or successor-model registration. Re-running the adjudication with altered analysis choices, widened nuisance envelopes, modified controls, changed thresholds, revised R_sig, altered η calibration, or changed statistical tests creates a successor model or exploratory analysis. It does not revise the original verdict.

Proposition 13.1 — No Post Hoc Analysis Choice

No statistical, binning, exclusion, blinding, validity-gate, or model-comparison choice may be selected after observing V_obs(η) because it favors CBR.

Proof sketch. Such choices affect whether V_obs(η) is classified as survival, failure, or inconclusive. If chosen after comparison, they make the verdict depend on post-comparison analysis selection. That changes the registered test and creates a successor model.

Proposition 13.2 — Ordered Comparison Requirement

The registered CBR prediction may be tested only after implementation validity, η calibration, baseline validation, nuisance-envelope validation, power, and critical-region coverage have been certified.

Proof sketch. The CBR comparison depends on these prior objects. If any prior object is invalid, the final comparison no longer tests the registered C_DCE instantiation. The model-comparison hierarchy therefore prevents a final visibility pattern from overriding failed preconditions.

14. Simulation and Power Analysis

The registered C_DCE dossier must show that the experiment can decide the registered claim. A platform instantiation that declares a prediction but lacks sufficient sensitivity to distinguish that prediction from ℬ and B_𝓝 is not test-ready.

Simulation and power analysis certify whether the registered platform has the capacity to distinguish V_CBR(η) from V_ℬ(η) plus nuisance effects within R_sig ⊆ I_c.

Definition 14.1 — Power Certificate

A power certificate specifies, before comparison:

simulated or analytic V_ℬ(η);
simulated or analytic V_CBR(η);
nuisance envelope B_𝓝;
expected deviation size;
η uncertainty;
detector noise;
finite-sample effects;
coefficient robustness;
nuisance variation;
false-positive risk;
false-negative risk;
negative-control behavior;
positive-control or sensitivity-control behavior;
baseline-control behavior;
required sample size;
required η coverage;
the sensitivity condition required for survival or failure.

[To be fixed before comparison: complete power certificate.]

14.1 Simulated Baseline V_ℬ(η)

The simulation must include V_ℬ(η) under the full registered baseline ℬ. This includes standard quantum prediction, platform-specific decoherence, detector inefficiency, dark counts, phase drift, timing jitter, mode mismatch, finite sampling noise, environmental coupling, calibration uncertainty, and data-processing uncertainty.

[To be fixed before comparison: baseline simulation procedure.]

[To be fixed before comparison: baseline simulation inputs.]

14.2 Simulated CBR Prediction V_CBR(η)

The simulation must include V_CBR(η) as generated from [Φ∗_C], ℛ_C, η calibration, and the registered critical region. It may not be fitted to V_obs(η).

[To be fixed before comparison: CBR-prediction simulation procedure.]

[To be fixed before comparison: CBR-prediction simulation inputs.]

14.3 Nuisance Envelope Simulation

The simulation must propagate the registered nuisance class 𝓝 into B_𝓝. It must state how nuisance parameters are sampled, bounded, correlated, or varied.

[To be fixed before comparison: nuisance simulation procedure.]

[To be fixed before comparison: treatment of correlated nuisance variation.]

[To be fixed before comparison: confidence or coverage rule for simulated B_𝓝.]

14.4 Negative, Positive, and Baseline Controls

A verdict-competent dossier must include controls.

Negative controls test regions or configurations where the registered CBR signature should not appear. These may include regions outside I_c or R_sig, control phases, or baseline-dominant settings.

Positive controls or sensitivity controls demonstrate that the platform could detect a feature of size ε_detect if such a feature were present. These may be simulated injections, calibration injections, synthetic-data tests, or registered platform perturbations that do not use V_obs(η) to tune the result.

Baseline controls test whether ℬ and B_𝓝 correctly capture standard platform behavior in regimes where CBR does not predict the registered signature.

[To be fixed before comparison: negative-control design.]

[To be fixed before comparison: positive-control or sensitivity-control design.]

[To be fixed before comparison: baseline-control design.]

If controls fail, survival or failure cannot be assigned unless the verdict rule explicitly defines the control failure as decisive.

14.5 Detectability and ε_detect

The power analysis must show whether the registered signature exceeds ε_detect under the declared sampling and nuisance conditions. It must specify the minimum platform sensitivity needed to distinguish V_CBR(η) from B_𝓝 in R_sig ⊆ I_c.

[To be fixed before comparison: detectability criterion.]

[To be fixed before comparison: required sample size for ε_detect.]

[To be fixed before comparison: required η coverage for ε_detect.]

If the predicted signature is not detectable at ε_detect under the registered design, the test is not capable of assigning failure. The result may be inconclusive or require platform refinement.

14.6 Robustness Analysis

The simulation must evaluate robustness to:

η uncertainty;
detector noise;
finite sample effects;
coefficient variation within the registered coefficient rule;
nuisance variation;
baseline uncertainty;
phase drift;
timing jitter;
mode mismatch;
calibration uncertainty.

[To be fixed before comparison: robustness-analysis plan.]

[To be fixed before comparison: coefficient robustness simulation plan.]

14.7 False Positive and False Negative Risk

The power certificate must state how false positive and false negative risks are controlled.

A false positive occurs when baseline-plus-nuisance behavior is misclassified as survival of the registered CBR signature.

A false negative occurs when the registered CBR signature is present but the experiment lacks sufficient sensitivity, sampling, or critical-region coverage to detect it.

[To be fixed before comparison: false-positive risk criterion.]

[To be fixed before comparison: false-negative risk criterion.]

[To be fixed before comparison: simulation or analytic method for estimating these risks.]

Proposition 14.1 — Power Requirement for Failure

Failure may be assigned only if the registered experiment has sufficient power to detect the registered signature at or above ε_detect across the required portion of R_sig ⊆ I_c.

Proof sketch. Failure means the predicted feature is absent under valid conditions. If the platform lacks sufficient sensitivity, the absence of an observed feature may reflect inadequate power rather than failure of the registered instantiation. Therefore power is a precondition for assigning failure.

Proposition 14.2 — Power Requirement for Survival

Survival may be assigned only if the observed feature exceeds B_𝓝 and ε_detect under a statistical procedure with controlled false-positive risk.

Proof sketch. Survival means the observed feature is not explained by the baseline-plus-nuisance envelope. If false-positive risk is uncontrolled, a nuisance fluctuation could be misclassified as survival. Therefore survival requires envelope escape, detectability, and false-positive control.

Theorem 14.1 — Verdict Competence

A registered C_DCE test is competent to assign survival or failure only if, before unblinding:

C_DCE implementation validity is satisfied;
η calibration is valid and independent of V_obs(η);
ℬ is validated;
𝓝 and B_𝓝 are validated;
I_c and R_sig are adequately sampled;
ε_detect is achieved;
positive or sensitivity controls show the platform could detect the registered feature;
negative controls do not show spurious registered-signature behavior;
baseline controls support the registered standard model;
the statistical test is applicable.

If these conditions are not satisfied, the result is inconclusive unless the verdict rule explicitly defines a specific failure of competence as decisive.

Proof sketch. Survival and failure both require that the observed visibility behavior be interpretable relative to the registered prediction, baseline, nuisance envelope, and detectability threshold. If the platform cannot validate those objects or demonstrate power to discriminate the registered signature, then the visibility comparison does not adjudicate the registered instantiation. Verdict competence is therefore a precondition for survival or failure.

Corollary 14.1 — No Survival Without Baseline Exhaustion

If ℬ or 𝓝 omits a known or calibratable standard explanation capable of producing the observed feature at scale ≥ ε_detect, survival cannot be assigned.

Corollary 14.2 — No Failure Without Power

If the platform lacks power to detect the registered signature at ε_detect across R_sig ⊆ I_c, failure cannot be assigned.

Corollary 14.3 — No Verdict Without Valid η Calibration

If η is not validly calibrated independently of V_obs(η), neither survival nor failure can be assigned.

Corollary 14.4 — No Successor Rescue

If a successor model is introduced after comparison, it cannot alter the verdict assigned to the original registered C_DCE instantiation.

15. Verdict Rule

The verdict rule is the final registered mapping from observed data to outcome classification. It must be impossible to misread. The registered C_DCE instantiation admits four possible verdict categories:

survival;
failure;
inconclusive result;
successor-model registration.

No fifth category is available after comparison. In particular, “CBR survives by reinterpretation” is not a verdict category.

Definition 15.1 — Verdict Certificate

A verdict certificate specifies:

the survival condition;
the failure condition;
the inconclusive conditions;
the successor-model conditions;
the validity gates required before survival or failure;
the role of ε_detect;
the role of B_𝓝;
the role of I_c and R_sig;
the statistical threshold;
the control requirements;
the jurisdiction of failure;
the successor-model quarantine rule;
the single-pass adjudication rule;
the exploratory-analysis quarantine rule;
the holdout, replication, or independent-test requirement for successor models.

[To be fixed before comparison: complete verdict certificate.]

15.1 Adjudication Table

The verdict is assigned according to the following registered checklist.

Survival requires all of the following:

registry locked before comparison;
valid C_DCE implementation;
valid independent η calibration;
validated ℬ;
validated 𝓝 and B_𝓝;
baseline exhaustion satisfied;
I_c and R_sig adequately sampled;
ε_detect achieved;
positive or sensitivity controls passed;
negative controls passed;
baseline controls passed;
statistical test applicable;
false-positive risk controlled;
V_obs(η) displays the registered CBR signature outside B_𝓝 by at least ε_detect in R_sig ⊆ I_c.

Failure requires all of the following:

registry locked before comparison;
valid C_DCE implementation;
valid independent η calibration;
validated ℬ;
validated 𝓝 and B_𝓝;
baseline exhaustion satisfied;
I_c and R_sig adequately sampled;
ε_detect achieved;
positive or sensitivity controls passed;
negative controls passed;
baseline controls passed;
statistical test applicable;
false-negative risk controlled;
V_obs(η) remains inside B_𝓝 across the required portion of R_sig ⊆ I_c.

Inconclusive result applies if any required validity, power, control, calibration, baseline, nuisance, sampling, or statistical condition required for survival or failure is not satisfied.

Successor-model registration applies if any verdict-relevant registered object is changed after comparison.

This table is part of the registered verdict rule. It cannot be revised after comparison.

15.2 Formal Adjudication Flow

The registered adjudication proceeds in the following order:

Are all registry objects locked?
Are C_DCE implementation tolerances satisfied?
Is η validly calibrated independently of V_obs(η)?
Are ℬ, 𝓝, and B_𝓝 validated?
Is baseline exhaustion satisfied?
Are I_c and R_sig adequately sampled?
Is ε_detect achieved?
Do positive or sensitivity controls pass?
Do negative controls pass?
Do baseline controls pass?
Is the statistical test applicable?
Does V_obs(η) escape B_𝓝 by at least ε_detect in R_sig?
If yes, assign survival.
If no, and all failure-competence conditions are satisfied, assign failure.
If any adjudication prerequisite fails, assign inconclusive.
If any registered object is changed after comparison, assign successor-model registration.

This flow is single-pass. The verdict is assigned once using the locked registry and registered order.

15.3 Survival

The registered C_DCE instantiation survives if, and only if, all registered validity gates are satisfied, the test is verdict-competent, and V_obs(η) displays the registered CBR signature outside B_𝓝 within R_sig ⊆ I_c with deviation at least ε_detect under the registered statistical test.

Survival requires:

valid implementation of C_DCE;
valid η calibration;
validated ℬ;
validated 𝓝 and B_𝓝;
baseline exhaustion;
adequate sampling of I_c and R_sig;
achieved ε_detect;
passed positive or sensitivity controls;
passed negative controls;
passed baseline controls;
controlled false-positive risk;
observed envelope escape by at least ε_detect;
satisfaction of the registered signature criterion.

Survival is a platform-instantiation verdict. It does not establish that CBR is the final law of outcome realization. It means only that the registered C_DCE instantiation was not defeated and produced the registered non-baseline accessibility-sensitive feature under valid conditions.

15.4 Failure

The registered C_DCE instantiation fails if, and only if, the test is verdict-competent, all registered validity gates required for failure are satisfied, and:

V_obs(η) remains inside B_𝓝 across the required portion of R_sig ⊆ I_c

under valid η-calibration, baseline-validation, nuisance-validation, sampling, power, control, and detectability conditions.

Failure requires:

valid implementation of C_DCE;
valid independent η calibration;
validated ℬ;
validated 𝓝 and B_𝓝;
baseline exhaustion;
adequate sampling of I_c and R_sig;
achieved ε_detect;
passed positive or sensitivity controls showing the platform could detect the registered feature;
passed negative controls showing no spurious signature behavior;
passed baseline controls;
controlled false-negative risk;
absence of the registered feature outside B_𝓝.

Failure defeats the registered C_DCE instantiation. It does not automatically defeat all CBR representations or the broader realization-law thesis.

15.5 Inconclusive Result

The result is inconclusive if survival or failure cannot be assigned because one or more required conditions fail. Inconclusive cases include:

invalid C_DCE implementation;
invalid η calibration;
invalid baseline validation;
invalid nuisance envelope;
baseline exhaustion not satisfied;
insufficient sample size;
insufficient η coverage inside I_c or R_sig;
failure to achieve ε_detect;
detector instability;
phase-control instability;
unvalidated timing jitter;
failed negative controls;
failed positive or sensitivity controls;
failed baseline controls;
failed blinding or analysis-lock procedure;
unresolved burden ordering;
noncomputable or uncertified V_CBR(η);
statistical-test inapplicability.

An inconclusive result is not survival. It is not failure. It means the registered test did not validly adjudicate the registered instantiation.

15.6 Successor-Model Registration

Any post-comparison alteration to a verdict-relevant object creates a successor model. This includes changes to:

C_DCE;
𝒜₀(C_DCE);
F₁…F_n;
𝒜(C_DCE);
≃_C;
ℛ_C;
Ξ_C, Ω_C, Λ_C;
α, β, γ;
η;
η_c or I_c;
δ_C;
R_sig;
V_CBR(η);
V_ℬ(η);
ℬ;
𝓝;
B_𝓝;
ε_detect;
statistical test;
controls;
validity gates;
verdict rule.

A successor model may be scientifically useful, but it is not the same registered instantiation.

15.7 Successor-Model Quarantine

A successor model cannot be used to reinterpret the old data as survival of the original registered C_DCE instantiation.

Post-comparison revisions may be reported as exploratory analysis, model diagnosis, or motivation for a new registered instantiation. They may not be treated as confirmation of the original test object unless the original verdict rule explicitly allowed a specific retrospective exploratory category, and even then such a category is non-verdict evidence.

A successor model requires independent registration before it can receive a survival or failure verdict. If it is evaluated on the same data that motivated its construction, the dossier must label that evaluation exploratory unless a valid independent holdout, replication, or pre-registered reuse rule is supplied.

[To be fixed before comparison: successor-model quarantine rule.]

[To be fixed before comparison: whether any exploratory non-verdict category is permitted.]

15.8 Exploratory-Analysis Quarantine

Exploratory analysis after comparison is permitted only as non-verdict analysis. It may identify diagnostic failures, propose alternative baselines, suggest revised nuisance models, motivate a successor CBR instantiation, or reveal platform improvements. It may not be reported as survival, confirmation, or registered evidence for the original C_DCE instantiation.

Any exploratory result must be labeled as exploratory and separated from the registered verdict.

[To be fixed before comparison: exploratory-analysis labeling rule.]

[To be fixed before comparison: permitted scope of exploratory post-comparison analysis.]

15.9 Holdout, Replication, or Independent-Test Discipline

A successor model constructed after failure or inconclusive adjudication must be tested on one of the following before receiving a survival verdict:

new data collected after successor-model registration;
a pre-registered holdout dataset not used to construct the successor model;
an independently replicated run;
a pre-registered reuse protocol that was fixed before the original comparison.

A successor model cannot learn from a failed or inconclusive dataset and then claim survival on that same dataset unless a valid holdout, replication, or pre-registered reuse rule is supplied.

[To be fixed before comparison: holdout, replication, or independent-test requirement for successor models.]

Proposition 15.1 — Verdict Exclusivity

For a locked C_DCE instantiation, survival, failure, inconclusive result, and successor-model registration are mutually exclusive verdict categories under the registered verdict rule.

Proof sketch. Survival and failure require satisfied validity gates, verdict competence, and opposite outcomes relative to the registered signature and B_𝓝. Inconclusive result applies when validity gates or adjudication conditions fail. Successor-model registration applies when the registered object is changed after comparison. Because these conditions are defined by disjoint verdict rules, the categories are mutually exclusive.

Proposition 15.2 — Failure Jurisdiction

Failure of the registered C_DCE instantiation defeats that instantiation and only that instantiation unless an additional bridge theorem connects the failed instantiation to a broader CBR class.

Proof sketch. The registered test adjudicates the locked C_DCE object. The broader CBR program contains claims at different levels: law-form claims, platform-instantiation claims, and possible nature-claims. A failure at the platform-instantiation level does not automatically propagate upward without a bridge premise. Therefore failure jurisdiction is limited to the registered instantiation unless separately extended.

Proposition 15.3 — Successor Models Do Not Rescue Registered Failure

If a registered C_DCE instantiation fails under the verdict rule, a later successor model cannot convert that failure into survival of the original instantiation.

Proof sketch. A successor model differs from the original registered object by at least one verdict-relevant element. It may explain why the original failed or propose a revised test object. But by the Registry Identity Principle, it is not identical to the original instantiation. Therefore its later adequacy cannot alter the verdict assigned to the original registered model.

Proposition 15.4 — Exploratory Analysis Is Non-Verdict Evidence

Post-comparison exploratory analysis cannot change the verdict assigned to the registered C_DCE instantiation.

Proof sketch. The registered verdict is determined by the locked registry and single-pass adjudication rule. Exploratory analysis occurs after comparison and may use information unavailable at registry lock. It can motivate successor work, but it is not part of the registered evidentiary chain. Therefore it cannot convert failure or inconclusive outcome into survival.

15.10 Final Strong-Null Rule

The strong-null rule for this dossier is:

If V_obs(η) remains inside B_𝓝 across the required portion of R_sig ⊆ I_c under valid η-calibration, baseline-validation, nuisance-validation, sampling, power, control, and detectability conditions, then the registered C_DCE instantiation fails.

This rule is the empirical discipline of the paper. It ensures that the registered model can be defeated by the absence of its declared accessibility-sensitive feature under valid conditions. It also ensures that failure is not assigned when the test itself lacks verdict competence.

The registered instantiation therefore ends in one of four states:

survived, failed, inconclusive, or replaced by a successor model.

No post-comparison rescue is permitted.

16. No-Rescue Doctrine

The registered C_DCE instantiation is identical to its pre-comparison registry. It is not an adaptive framework, a family of possible repairs, or a theory to be reinterpreted after the observed visibility curve is known. Its evidentiary value depends on a fixed relation between registered objects, observed data, and verdict rule.

The no-rescue doctrine is therefore:

A failed registered instantiation may motivate a successor model, but it cannot be retroactively repaired.

A successor model may be scientifically useful. It may reveal a better platform description, a stronger nuisance model, a revised admissibility construction, a corrected accessibility calibration, or a sharper burden functional. But it is not the same registered object. It must be separately registered and separately tested.

Definition 16.1 — Registered Rescue Operation

A rescue operation is any post-comparison modification to a verdict-relevant object made to avoid failure, convert an inconclusive result into survival, reinterpret a null result, recover agreement with V_obs(η), or weaken the strong-null consequence.

Registered rescue operations are forbidden.

They include post-comparison changes to:

C_DCE;
𝒜₀(C_DCE);
filters F₁…F_n;
𝒜(C_DCE);
≃_C;
𝒜(C_DCE)/≃_C;
ℛ_C;
Ξ_C, Ω_C, Λ_C;
α, β, γ;
η;
η_c or I_c;
δ_C;
R_sig;
V_CBR(η);
V_ℬ(η);
ℬ;
𝓝;
B_𝓝;
ε_detect;
statistical test;
validity gates;
controls;
power analysis;
verdict rule;
failure jurisdiction.

Changing any of these after comparison creates a successor model.

16.1 Objects Protected by the No-Rescue Doctrine

Each protected object matters because it contributes to the identity, prediction, comparison, or verdict of the registered test.

C_DCE cannot be expanded after comparison to include new degrees of freedom, environmental couplings, detector behaviors, timing effects, control variables, or data-processing operations.

𝒜₀(C_DCE), F₁…F_n, and 𝒜(C_DCE) cannot be revised after comparison to admit a candidate that explains V_obs(η) or exclude a candidate that threatens the registered prediction.

≃_C and 𝒜(C_DCE)/≃_C cannot be redefined after comparison to merge inconvenient distinctions or split convenient alternatives.

ℛ_C, Ξ_C, Ω_C, Λ_C, and α, β, γ cannot be altered after comparison to change [Φ∗_C], Δℛ_C(η), η_c, I_c, or V_CBR(η).

η, η_c, I_c, and δ_C cannot be shifted after comparison to relocate the accessibility signature into a favorable region of V_obs(η).

ℬ, 𝓝, and B_𝓝 cannot be weakened, expanded, narrowed, or reinterpreted after comparison to manufacture survival or avoid failure.

ε_detect, the statistical test, validity gates, controls, power analysis, and verdict rule cannot be modified after comparison to change the evidentiary classification.

16.2 No-Rescue Matrix

The following matrix states the audit consequence of changing a registered object after comparison.

C_DCE changed.
Why it matters: changes the physical platform being tested.
Verdict consequence: successor model.

𝒜₀(C_DCE), F₁…F_n, or 𝒜(C_DCE) changed.
Why it matters: changes the domain over which CBR selection occurs.
Verdict consequence: successor model.

≃_C or 𝒜(C_DCE)/≃_C changed.
Why it matters: changes which candidates count as operationally distinct.
Verdict consequence: successor model.

ℛ_C changed.
Why it matters: changes the burden ordering over admissible candidates.
Verdict consequence: successor model.

Ξ_C, Ω_C, or Λ_C changed.
Why it matters: changes the internal structure of the realization-burden functional.
Verdict consequence: successor model.

α, β, or γ changed.
Why it matters: changes the relative weighting of burden terms and may change [Φ∗_C].
Verdict consequence: successor model.

η changed.
Why it matters: changes the accessibility calibration and the meaning of V(η).
Verdict consequence: successor model.

η_c, I_c, δ_C, or R_sig changed.
Why it matters: changes the region where the registered signature must occur.
Verdict consequence: successor model.

V_CBR(η) changed.
Why it matters: changes the prediction being tested.
Verdict consequence: successor model.

V_ℬ(η), ℬ, 𝓝, or B_𝓝 changed.
Why it matters: changes the standard comparator or nuisance envelope.
Verdict consequence: successor model.

ε_detect changed.
Why it matters: changes the minimum detectable effect needed for survival or failure.
Verdict consequence: successor model.

Statistical test changed.
Why it matters: changes the rule by which evidence is classified.
Verdict consequence: successor model.

Validity gates or controls changed.
Why it matters: changes whether the experiment is competent to assign a verdict.
Verdict consequence: successor model.

Verdict rule changed.
Why it matters: changes the meaning of survival, failure, inconclusive result, or successor-model registration.
Verdict consequence: successor model.

This matrix is part of the registry. It makes the no-rescue rule mechanically auditable: every protected object has a reason and a consequence.

16.3 Permitted Post-Comparison Work

The no-rescue doctrine does not forbid learning from failure. It forbids treating post-comparison revision as survival of the original registered instantiation.

Permitted post-comparison work includes:

exploratory diagnosis of why the registered instantiation failed or was inconclusive;
identification of omitted nuisance sources;
proposal of a successor baseline ℬ′;
proposal of a successor nuisance envelope B_𝓝′;
refinement of η calibration for a future registration;
construction of a new admissible class 𝒜′(C_DCE);
reformulation of ℛ_C for a successor model;
design of a new platform instantiation;
replication, holdout, or independent testing under a newly registered dossier.

Such work must be labeled as exploratory, diagnostic, or successor-model development. It is not a survival verdict for the original registered C_DCE instantiation.

Definition 16.2 — Successor Model

A successor model is any post-comparison model that differs from the registered C_DCE instantiation in at least one verdict-relevant object.

A successor model must receive a new registry before it can be tested. If it is motivated by the same data that defeated or failed to adjudicate the original model, it cannot claim survival on those same data unless a pre-registered holdout, replication, or reuse rule permits that evaluation.

Proposition 16.1 — No Retroactive Repair

A registered C_DCE instantiation cannot be repaired after comparison while remaining identical to the original registered object.

Proof sketch. By the Registry Identity Principle, the registered instantiation is identical to its pre-comparison registry. A post-comparison modification changes at least one constitutive element of that registry. Therefore the modified object is not the original instantiation. It is a successor model.

Proposition 16.2 — No Rescue by Reclassification

A failed result cannot be reclassified as survival by altering the verdict rule, statistical test, critical region, nuisance envelope, prediction, or validity gates after comparison.

Proof sketch. The verdict is assigned by the locked registry. If a post-comparison change alters the rule under which the result is classified, the adjudicated object has changed. The new classification may apply to a successor model, but it cannot revise the verdict of the original registered instantiation.

16.4 Strong No-Rescue Rule

If the registered C_DCE instantiation fails under the strong-null rule, the failure remains the verdict for that instantiation. Later revisions may explain the failure, motivate successor work, or improve the model class. They cannot convert the failed instantiation into a surviving one.

The doctrine is therefore:

Failure is allowed. Repair is allowed only as successor-model registration. Retroactive rescue is not allowed.

17. Jurisdiction of Failure

The jurisdiction of failure specifies what a failed C_DCE test defeats and what it does not defeat. This section prevents two opposite errors: overclaiming survival and over-destroying failure.

The registered C_DCE test adjudicates one platform-specific instantiation. It does not directly adjudicate all possible CBR representations, all possible accessibility-based CBR models, or the broader realization-law thesis. To extend failure beyond the registered instantiation, an explicit bridge theorem is required.

Definition 17.1 — Failure Jurisdiction

The failure jurisdiction of a registered test is the class of claims defeated by failure under the registered verdict rule.

For this dossier, the direct failure jurisdiction is:

the registered C_DCE instantiation of canonical CBR.

Failure does not automatically propagate beyond this level.

17.1 Failure Defeats

Failure defeats the registered C_DCE instantiation.

Specifically, it defeats the claim that the fixed objects registered in this dossier jointly produce the declared non-baseline accessibility-sensitive feature in V(η) within R_sig ⊆ I_c under valid test conditions.

Thus, if V_obs(η) remains inside B_𝓝 across the required portion of R_sig ⊆ I_c under valid η-calibration, baseline-validation, nuisance-validation, sampling, power, control, and detectability conditions, then the registered C_DCE instantiation fails.

The failed object includes:

the registered C_DCE context;
the registered admissible class 𝒜(C_DCE);
the registered quotient structure 𝒜(C_DCE)/≃_C;
the registered burden functional ℛ_C;
the registered accessibility calibration η;
the registered critical region η_c or I_c;
the registered prediction V_CBR(η);
the registered baseline ℬ;
the registered nuisance envelope B_𝓝;
the registered verdict rule.

17.2 Failure Jurisdiction Ladder

Failure propagates only by justified steps. The jurisdiction ladder is:

Level 1 — Registered C_DCE instantiation.
Directly defeated by failure under the registered strong-null rule.

Level 2 — Accessibility-CBR subclass.
Defeated only if a bridge theorem shows that the failed C_DCE instantiation faithfully represents that accessibility-CBR subclass in the tested domain.

Level 3 — Canonical CBR representation class.
Defeated only if a stronger bridge theorem shows that canonical CBR, as a representation class, entails the failed accessibility structure or an operationally equivalent signature in C_DCE-like domains.

Level 4 — Broader realization-law thesis.
Not defeated by this test alone. A failed C_DCE instantiation does not establish that no law of outcome realization is possible.

Level 5 — Probability/realization distinction.
Not defeated by this test. The conceptual distinction between probability assignment and outcome realization does not stand or fall with one platform instantiation.

This ladder prevents both rhetorical inflation and rhetorical collapse. The test is allowed to be genuinely falsifying at the level it actually registers.

Definition 17.2 — Bridge Theorem

A bridge theorem is a registered result showing that failure of one platform instantiation entails failure of a broader class of models.

A bridge theorem must specify:

the broader class being targeted;
the assumptions connecting that class to C_DCE;
the representation relation between the class and the registered instantiation;
why every model in the broader class would require the failed signature or an operationally equivalent one;
the conditions under which failure propagates;
the limits of propagation.

Without such a bridge theorem, failure remains local to the registered C_DCE instantiation.

Proposition 17.1 — Locality of Platform Failure

Failure of the registered C_DCE instantiation defeats that instantiation and does not automatically defeat broader CBR classes.

Proof sketch. The registered verdict is defined over the objects fixed in the C_DCE registry. Broader CBR classes may differ in platform context, admissible class, burden functional, accessibility structure, empirical signature, or failure rule. Therefore failure of one registered object cannot defeat a broader class unless a bridge theorem shows that the broader class is faithfully represented by that object in the tested domain.

17.3 Failure Does Not Automatically Defeat

Failure of the registered C_DCE instantiation does not automatically defeat:

all CBR representations;
the broader realization-law thesis;
the distinction between probability and realization;
the claim that a non-circular realization law must specify admissibility, selection, equivalence, probability discipline, and failure conditions;
the quantum measurement problem;
all possible outcome-law approaches;
all possible accessibility-based empirical routes.

This restraint is not a retreat from falsifiability. It is jurisdictional precision. The registered model is allowed to fail, but the verdict is not inflated beyond the object actually tested.

17.4 Survival Jurisdiction

Survival is also jurisdiction-limited.

If the registered C_DCE instantiation survives, the result does not prove that CBR is the final law of outcome realization. It shows only that the registered instantiation produced the declared non-baseline accessibility-sensitive feature under valid conditions and was not defeated by the strong-null test.

A survival verdict may strengthen the case for further CBR testing, but it does not establish all CBR representations or the broader nature-claim.

Proposition 17.2 — Symmetry of Jurisdiction

The same jurisdictional discipline that limits failure also limits survival.

Proof sketch. The registered test adjudicates one platform instantiation. If failure cannot automatically defeat all broader CBR claims without a bridge theorem, survival cannot automatically confirm them either. Both verdicts are local unless explicitly connected to broader claims by additional argument.

17.5 Jurisdiction Statement

The jurisdiction of this dossier is therefore:

Survival supports only the registered C_DCE instantiation under the stated conditions. Failure defeats only the registered C_DCE instantiation unless a bridge theorem extends the defeat. Inconclusive result adjudicates neither survival nor failure. Successor-model registration creates a new object requiring separate evaluation.

18. Adversarial Stress Tests

The registered C_DCE dossier is not complete unless it is tested against hostile objections. This section subjects the platform instantiation to adversarial stress tests designed to identify whether the registry blocks the most serious sources of ambiguity, circularity, tuning, overclaiming, and empirical indistinguishability.

Each adversarial test has six elements:

objection;
registry defense;
required certificate;
defeat condition;
inconclusive condition;
successor-model condition.

This structure turns adversarial review into an audit tool. Each objection is either blocked by the registry or assigned a clear verdict consequence.

18.1 Standard Quantum Mechanics Plus Decoherence

Objection.
The observed behavior of V(η) may be fully explained by standard quantum mechanics, platform-specific decoherence, detector effects, and noise.

Registry defense.
The baseline ℬ and nuisance envelope B_𝓝 include standard quantum prediction, decoherence, detector inefficiency, dark counts, phase drift, timing jitter, mode mismatch, finite sampling noise, environmental coupling, calibration uncertainty, and data-processing uncertainty. CBR must produce a registered feature outside B_𝓝 by at least ε_detect.

Required certificate.
Baseline certificate, nuisance certificate, B_𝓝 construction certificate, power certificate.

Defeat condition.
If V_obs(η) remains inside B_𝓝 across R_sig ⊆ I_c under valid conditions, the registered C_DCE instantiation fails.

Inconclusive condition.
If ℬ or B_𝓝 is incomplete, unvalidated, or missing a standard effect capable of producing the observed feature, survival cannot be assigned.

Successor-model condition.
If ℬ or B_𝓝 is expanded after comparison, the expanded object is a successor model.

18.2 Coefficient Tuning

Objection.
The coefficients α, β, and γ could be adjusted to force the desired minimizer, shift η_c or I_c, or recover agreement with V_obs(η).

Registry defense.
α, β, and γ are registered before comparison by a coefficient certificate. They may be fixed by symmetry, dimensional normalization, independent calibration, or a pre-registered robustness class. They may not be fitted to V_obs(η), tuned to force η_c, or changed to rescue a null result.

Required certificate.
Coefficient certificate; coefficient-domain verdict rule, if domain-fixed; coefficient robustness analysis.

Defeat condition.
If the prediction depends on post-comparison coefficient adjustment, the registered instantiation does not survive.

Inconclusive condition.
If coefficient uncertainty prevents a certified minimizer or critical region from being determined, the test is not verdict-competent.

Successor-model condition.
Any post-comparison coefficient revision creates a successor model.

18.3 Arbitrary η_c or I_c

Objection.
The critical accessibility region may be selected after the fact from a visually interesting region of V_obs(η).

Registry defense.
η_c or I_c is derived from burden geometry before comparison. In the interval form:

I_c = {η : Δℛ_C(η) ≤ δ_C}.

Here Δℛ_C(η) is computed from 𝒜(C_DCE)/≃_C and ℛ_C, and δ_C is fixed before comparison.

Required certificate.
Critical-region certificate; δ_C certificate; burden-gap computation certificate; η calibration certificate.

Defeat condition.
If η_c, I_c, δ_C, or R_sig is selected after observing V_obs(η), the registered instantiation is not rescued.

Inconclusive condition.
If Δℛ_C(η) cannot be computed or bounded, or if I_c is too broad to support a discriminating test, the result is inconclusive.

Successor-model condition.
Post-comparison revision of η_c, I_c, δ_C, or R_sig creates a successor model.

18.4 Hidden Probability Engineering

Objection.
ℛ_C might smuggle in non-Born weighting or function as a hidden probability rule.

Registry defense.
Born compatibility is enforced at the admissibility stage. ℛ_C ranks only already admissible candidates in 𝒜(C_DCE)/≃_C. It is not a probability distribution and does not assign outcome probabilities.

Required certificate.
Born-compatibility certificate for admissibility; burden evaluation certificate; coefficient certificate.

Defeat condition.
If ℛ_C, Ξ_C, Ω_C, Λ_C, or α, β, γ alter the registered Born-compatible marginals, the instantiation violates its admissibility discipline and fails as a canonical CBR instantiation.

Inconclusive condition.
If Born compatibility cannot be certified for the admissible class, the test is not ready for verdict assignment.

Successor-model condition.
A revised burden functional that changes probability discipline is a successor model.

18.5 Decoherence Reduction

Objection.
CBR may collapse into ordinary decoherence and fail to add an operationally distinct selection principle.

Registry defense.
The admissibility and quotienting stages classify baseline-equivalent candidates. A candidate that produces no operational distinction from ℬ is not a distinct CBR prediction for this test. The registered instantiation must specify V_CBR(η) and show non-overlap with B_𝓝 by at least ε_detect in R_sig ⊆ I_c.

Required certificate.
Operational-equivalence certificate; baseline certificate; prediction certificate; non-overlap certificate.

Defeat condition.
If V_CBR(η) is operationally indistinguishable from V_ℬ(η) within B_𝓝, then the registered instantiation cannot claim survival.

Inconclusive condition.
If the platform lacks the power to distinguish CBR from ℬ, the test is inconclusive.

Successor-model condition.
A revised prediction that becomes distinguishable only after changing ℛ_C, η, I_c, or B_𝓝 is a successor model.

18.6 Admissibility Manipulation

Objection.
𝒜(C_DCE) may have been constructed to exclude inconvenient candidates or include convenient ones.

Registry defense.
𝒜(C_DCE) is constructed through:

𝒜₀(C_DCE) → F₁…F_n → 𝒜(C_DCE) → 𝒜(C_DCE)/≃_C.

Every platform-relevant candidate family must receive either an admissibility certificate or an exclusion certificate. No candidate may enter 𝒜(C_DCE) because it explains observed data.

Required certificate.
Admissibility certificate; exclusion certificate; filter certificates F₁…F_n.

Defeat condition.
If a verdict-relevant candidate was silently excluded or admitted without certification, survival cannot be assigned.

Inconclusive condition.
If admissibility cannot be reconstructed from registered physical, causal, operational, calibration, Born-compatibility, record-compatibility, and accessibility-compatibility constraints, the test is inconclusive.

Successor-model condition.
Any post-comparison alteration of admissibility produces a successor model.

18.7 Empirical Indistinguishability

Objection.
The registered instantiation may not genuinely differ from the baseline model ℬ in an experimentally detectable way.

Registry defense.
The dossier requires non-overlap between V_CBR(η) and B_𝓝 by at least ε_detect in R_sig ⊆ I_c, supported by power analysis and controls.

Required certificate.
Prediction certificate; non-overlap certificate; power certificate; control certificate.

Defeat condition.
If the registered prediction remains inside B_𝓝 or below ε_detect, survival cannot be assigned.

Inconclusive condition.
If formal separation exists but the platform lacks power to detect it, the result is inconclusive.

Successor-model condition.
A revised distinguishable signature introduced after comparison is a successor model.

18.8 Operational-Equivalence Evasion

Objection.
The quotient relation ≃_C could be used to hide failure by declaring failed candidates operationally equivalent to successful ones.

Registry defense.
≃_C is defined before comparison by the registered observable set 𝒪_C, distinguishability pseudometric d_C, and threshold τ_C. It cannot be altered after comparison.

Required certificate.
Operational-equivalence certificate; 𝒪_C certificate; d_C certificate; τ_C certificate.

Defeat condition.
If post-comparison quotient manipulation is required to avoid failure, the registered instantiation fails or becomes a successor model.

Inconclusive condition.
If ≃_C, d_C, or τ_C is under-specified, the quotient structure is not audit-ready.

Successor-model condition.
Any post-comparison alteration of ≃_C creates a successor model.

18.9 Nuisance-Envelope Inflation

Objection.
B_𝓝 could be widened after the data are seen to avoid failure or narrowed to manufacture survival.

Registry defense.
B_𝓝 is fixed before comparison through a nuisance-envelope certificate. It cannot be widened, narrowed, shifted, or reinterpreted after comparison.

Required certificate.
Nuisance certificate; B_𝓝 construction certificate; nuisance-validation gates.

Defeat condition.
If V_obs(η) remains inside the registered B_𝓝 across R_sig ⊆ I_c under valid conditions, the registered instantiation fails.

Inconclusive condition.
If B_𝓝 is invalid or incomplete, no survival verdict is permitted.

Successor-model condition.
Any post-comparison change to B_𝓝 creates a successor model.

18.10 Overclaiming

Objection.
The dossier may overstate what survival or failure means.

Registry defense.
The paper separates nature-claims, law-form claims, platform-instantiation claims, and failure claims. Survival and failure are jurisdiction-limited.

Required certificate.
Verdict certificate; failure-jurisdiction statement; bridge-theorem statement if broader claims are made.

Defeat condition.
If the manuscript treats survival as proof of all CBR or failure as refutation of all realization-law models, it violates its own claim discipline.

Inconclusive condition.
If the scope of the claim is unclear, the jurisdiction of the verdict is under-specified.

Successor-model condition.
A broader claim requires a separate bridge theorem or successor theoretical registration.

Proposition 18.1 — Adversarial Closure Standard

A registered C_DCE dossier is adversarially closed only if each major route of post hoc rescue, hidden tuning, baseline weakening, nuisance inflation, empirical indistinguishability, and jurisdictional overclaiming is either blocked by the registry or converted into a clear failure, inconclusive, or successor-model condition.

Proof sketch. A locked test is meaningful only if adverse outcomes cannot be absorbed by reinterpretation. The adversarial stress tests identify the principal routes of reinterpretation. If each route is blocked or assigned a verdict consequence, the dossier is adversarially closed for the registered instantiation.

19. Limitations and Successor Work

This dossier registers one platform-specific instantiation of canonical CBR. Its strength is its narrowness. It does not attempt to prove the final truth of CBR, defeat all rival interpretations, or settle the measurement problem in full. It attempts to make one CBR instantiation exact enough to be tested, audited, and possibly defeated.

These limitations do not weaken the dossier. They define the exact object exposed to failure.

A vague test can appear broad but fail to say what would count against it. A locked test is narrower, but its verdict has real content.

19.1 Platform Limitation

This is one platform:

C_DCE.

The results of this dossier apply directly only to the delayed-choice record-accessibility interferometric context registered here. Other platforms may require different admissible classes, accessibility calibrations, burden terms, baselines, nuisance envelopes, and verdict rules.

Survival in C_DCE would motivate further testing. It would not establish all CBR.

Failure in C_DCE would defeat the registered C_DCE instantiation. It would not automatically defeat all possible CBR representations.

19.2 Instantiation Limitation

The exposed object is the registered model, not the total CBR program.

This means:

the registered 𝒜(C_DCE) is the tested admissible class;
the registered ℛ_C is the tested burden functional;
the registered η calibration is the tested accessibility bridge;
the registered I_c or η_c is the tested critical region;
the registered ℬ and B_𝓝 are the tested standard comparator;
the registered verdict rule determines the result.

If any of these are later revised, the revised model is a successor.

19.3 Empirical Route Limitation

η-sensitive testing is one empirical route. It is not the only possible route by which a realization-law program could be exposed to failure.

A failure of the accessibility-sensitive C_DCE instantiation may show that this route, this burden geometry, this platform calibration, or this visibility signature fails. It does not automatically show that no realization-law account could be formulated or tested elsewhere.

19.4 Survival Limitation

If the registered C_DCE instantiation survives, the correct conclusion is limited:

The registered platform produced the declared non-baseline accessibility-sensitive feature in V(η), outside B_𝓝 by at least ε_detect, under valid conditions.

This would be significant. It would justify further replication, broader platform testing, and bridge-theorem development. It would not prove that CBR is the final law of outcome realization.

19.5 Failure Limitation

If the registered C_DCE instantiation fails, the correct conclusion is also limited:

The registered instantiation did not produce its declared accessibility-sensitive feature under valid conditions.

This would defeat the registered C_DCE model. It would not automatically defeat all CBR representations, the broader realization-law thesis, the distinction between probability and realization, or every possible outcome-law approach.

19.6 Successor Work

Successor work may proceed in several ways:

register a revised C_DCE model with modified platform objects;
test a different delayed-choice record-accessibility platform;
develop a bridge theorem connecting C_DCE failure to a broader CBR class;
test a non-DCE platform;
refine η calibration independently of V_obs(η);
refine ℛ_C while preserving pre-comparison fixation;
improve baseline and nuisance modeling;
run replication or holdout tests;
compare CBR against alternative realization-law candidates under the same registry discipline.

All successor work must preserve the central rule:

A new model requires a new registry.

Proposition 19.1 — Modesty Strengthens Falsifiability

Limiting the verdict to the registered C_DCE instantiation strengthens rather than weakens the scientific status of the dossier.

Proof sketch. Overbroad claims make survival and failure ambiguous. A local registered claim specifies exactly what survives or fails. This makes the empirical verdict meaningful and prevents both rhetorical confirmation and rhetorical refutation beyond the tested object.

20. Appendix Architecture for a 10/10 Locked Dossier

The appendices are not supplementary decoration. They are the audit machinery of the locked C_DCE dossier. Each appendix must support reproducibility, traceability, and verdict competence.

A referee should be able to use the appendices to reconstruct the registered object, reproduce the selection procedure, verify the baseline and nuisance envelope, inspect the statistical plan, and determine whether the verdict was assigned according to the locked rule.

Definition 20.1 — Appendix Acceptance Criterion

An appendix is complete only if an independent evaluator can use it to verify the registered object it supports without adding unregistered assumptions.

Each appendix must identify:

the registered objects it supports;
the certificates it contains;
the traceability entries it supplies;
the computations, calibrations, or definitions it fixes;
the unresolved placeholders, if any;
the verdict consequence if the appendix is incomplete.

Appendix A — One-Page Registry

Appendix A is complete only if every registered object appears in one place and links to its certificate.

It must include:

C_DCE;
𝒜₀(C_DCE);
F₁…F_n;
𝒜(C_DCE);
≃_C;
𝒜(C_DCE)/≃_C;
ℛ_C;
Ξ_C, Ω_C, Λ_C;
α, β, γ;
[Φ∗_C];
η;
η_c or I_c;
δ_C;
R_sig;
V_CBR(η);
V_ℬ(η);
ℬ;
𝓝;
B_𝓝;
ε_detect;
statistical test;
controls;
validity gates;
verdict rule;
no-rescue rule;
failure jurisdiction.

Appendix B — Platform and Register Definitions

Appendix B is complete only if a third party can reconstruct C_DCE, W, R_acc, R_env, detector records, and the accessibility-control structure.

It must specify the physical meaning of W and the register structure used to define:

η = I(W; R_acc) / H(W).

Appendix C — Admissibility Construction

Appendix C is complete only if a third party can reconstruct:

𝒜₀(C_DCE) → F₁…F_n → 𝒜(C_DCE).

It must include admissibility certificates and exclusion certificates for platform-relevant candidate families.

Appendix D — Operational Equivalence

Appendix D is complete only if a third party can determine when Φ₁ ≃_C Φ₂.

It must define 𝒪_C, d_C, τ_C, and 𝒜(C_DCE)/≃_C, and it must show how operational duplicates are quotient-identified.

Appendix E — Burden-Term Computation

Appendix E is complete only if a third party can compute or bound:

Ξ_C, Ω_C, Λ_C, and ℛ_C([Φ])

without adding assumptions.

It must include normalization, uncertainty propagation, quotient-compatibility, and burden-gap computation where relevant.

Appendix F — Coefficient Fixation

Appendix F is complete only if α, β, and γ are fixed by a certified rule independent of V_obs(η).

It must specify their values or domain, robustness analysis, and the consequence of coefficient variation.

Appendix G — η Calibration

Appendix G is complete only if η can be computed independently of V_obs(η).

It must include the mutual-information estimator, entropy estimator, calibration map u ↦ η(u), η uncertainty model, validity gates, and independence proof.

Appendix H — η_c / I_c Derivation

Appendix H is complete only if η_c or I_c can be derived from burden geometry.

It must include Δℛ_C(η), δ_C, competing classes near the critical region, uncertainty in the critical region, coverage requirements, and R_sig if distinct from I_c.

Appendix I — Baseline ℬ

Appendix I is complete only if V_ℬ(η) can be computed or bounded from the registered standard model.

It must include standard quantum prediction, platform-specific decoherence, detector inefficiency, dark counts, phase drift, timing jitter, mode mismatch, finite sampling noise, environmental coupling, calibration uncertainty, and data-processing uncertainty.

Appendix J — Nuisance Envelope B_𝓝

Appendix J is complete only if B_𝓝 can be reconstructed and validated.

It must specify 𝓝, nuisance parameter ranges, dependence structure, correlated nuisance treatment, η uncertainty treatment, confidence or coverage rule, and validation gates.

Appendix K — Simulation Protocol

Appendix K is complete only if a third party can reproduce the simulation or analytic workflow for:

V_ℬ(η);
V_CBR(η);
B_𝓝;
power analysis;
controls;
false-positive risk;
false-negative risk.

Appendix L — Statistical Plan

Appendix L is complete only if a third party can reproduce the adjudication of V_obs(η).

It must specify the visibility estimator, η-binning rule, sample size, statistical test, confidence threshold, multiple-comparison treatment, outlier rules, exclusion rules, blinding/unblinding procedure, and validity gates.

Appendix M — Adversarial Rival Analysis

Appendix M is complete only if each major hostile objection is mapped to:

registry defense;
required certificate;
defeat condition;
inconclusive condition;
successor-model condition.

It must include the adversarial stress tests listed in Section 18.

Appendix N — Failure Jurisdiction

Appendix N is complete only if the verdict can be assigned without ambiguity.

It must include the strong-null rule, no-rescue doctrine, successor-model quarantine, exploratory-analysis quarantine, failure jurisdiction ladder, bridge-theorem requirements, adjudication table, and formal adjudication flow.

Theorem 20.1 — Final Completion Criterion

The C_DCE dossier is complete only if every registered object:

appears in the one-page registry;
has a registration certificate;
has a traceability entry;
has an appendix location;
has a verdict consequence if changed;
has no unresolved platform-specific placeholder unless the paper is explicitly framed as a registration standard rather than a completed platform dossier.

If any verdict-relevant object lacks one of these six requirements, the dossier is not a completed locked C_DCE instantiation. It may still function as a registration standard, but it cannot claim to be a completed platform-specific test object.

Proof sketch. A locked dossier is only as complete as its registered objects. If an object is missing from the registry, lacks a certificate, lacks traceability, lacks an appendix location, lacks a change consequence, or remains unresolved while the paper claims completion, then the test cannot be independently audited. Therefore all six requirements are necessary for completion.

Proposition 20.1 — Appendix Sufficiency for Auditability

The appendices are sufficient for auditability only if an independent evaluator can reconstruct the registered C_DCE instantiation and assign the verdict without adding unregistered assumptions.

Proof sketch. The main text states the registry doctrine and verdict logic. The appendices supply the operational, mathematical, calibration, simulation, and statistical details. If any verdict-relevant object is absent from the appendices, the test cannot be independently audited. Therefore appendix completeness is required for a 10/10 locked dossier.

Robert Duran IV