The Jurisdiction of Failure in Quantum Outcome Realization: Constraint-Based Realization and the Law-Form Burden

---

Abstract

This paper develops a jurisdictional framework for evaluating Constraint-Based Realization as a candidate law of quantum outcome realization. It distinguishes four theoretical objects that must not be conflated: the realization-law thesis, the CBR representation class, canonical CBR, and the accessibility-signature instantiation. The realization-law thesis states that if individual outcome realization is treated as a physical event not exhausted by ordinary evolution, probability assignment, observer update, branching description, or non-selective decoherence, then a law-form or law-equivalent burden arises. The CBR representation class formalizes that burden as context-indexed constrained selection from an admissible candidate class. Canonical CBR fixes one member of that class. The accessibility-signature instantiation exposes that member to empirical risk.

The paper’s central claim is not that CBR survives failure. It is that success and failure must be assigned to the correct theoretical object. A validated strong null against a fixed accessibility-sensitive CBR instantiation falsifies that instantiation. It does not automatically falsify canonical CBR as a framework, the CBR representation class, or the broader realization-law thesis unless a bridge theorem shows that the higher-level object entails the excluded consequence. Conversely, the broader realization-law thesis cannot rescue a failed instantiation by post hoc revision, semantic migration, redefinition of η, relocation of η_c, alteration of ℬ, expansion of nuisance bounds, or reinterpretation of failed data as confirmation.

The paper develops seven linked results: a realization-law burden theorem, a representation-class theorem, a canonical-specialization theorem, a jurisdiction-of-failure theorem, a strong-null model-death theorem, a framework-null elevation theorem, and a non-evasion revision theorem. Together, they define a theory of evaluation for realization-law candidates: what a model must specify, when it becomes empirically liable, what a strong null kills, when model failure can become framework failure, and what a successor model must prove after failure.

The result is not a safer CBR, but a more answerable one: a candidate realization-law program in which failure has an address, success has a boundary, and revision has a burden.

---

1. Introduction — The Problem Is Not Survival; It Is Jurisdiction

A theory candidate is not made serious by surviving every possible outcome. It is made serious by specifying which outcomes defeat which commitments.

That is the standard of this paper. The question is not how Constraint-Based Realization can be protected from failure. The question is what any success or failure has authority to decide. A result should not be asked to falsify more than its premises entail, and a theory should not be permitted to survive more than its failed commitments allow. The central problem, therefore, is not survival. It is jurisdiction.

The issue arises because the CBR program contains several distinct theoretical objects. These objects are related, but they are not identical. First, there is the realization-law thesis: the claim that if individual outcome realization is treated as a physical event, then a theory must either specify a law-form for that event or explain why no such law-form is needed. Second, there is the CBR representation class: the structural claim that a disciplined realization law must move from a physically specified context C, to an admissible candidate class 𝒜(C), to a pre-outcome burden ordering ≼_C or realization functional ℛ_C, to a selected realization channel Φ∗_C, modulo operational equivalence ≃_C. Third, there is canonical CBR: a fixed member of that representation class, equipped with restricted admissibility, a canonical burden functional, probability discipline, operational uniqueness, an accessibility parameter η, a critical accessibility regime η_c, a baseline comparator ℬ, and a strong-null verdict rule. Fourth, there is the accessibility-signature instantiation: the specific empirical exposure of canonical CBR in a designated accessibility-sensitive protocol family.

These four objects form a hierarchy:

realization-law thesis → CBR representation class → canonical CBR → accessibility-signature instantiation.

Failure may move upward through this hierarchy only by argument. More precisely, failure can travel upward only through a bridge theorem. A validated strong null against one accessibility-sensitive CBR instantiation would be a serious result. If the context, admissible class, realization functional, accessibility parameter, critical regime, baseline comparator, nuisance envelope, observable burden, tolerance structure, and validity gates were fixed in advance, and if the experiment then produced only baseline-class behavior across the declared critical regime, the instantiated model would be false. That consequence should not be softened. A theory that cannot accept the death of its fixed empirical instantiation is not yet scientifically disciplined.

But the reverse error must also be avoided. The failure of one fixed instantiation does not automatically falsify the broader realization-law thesis. It does not, by itself, show that probability assignment is outcome selection. It does not show that non-selective decoherence is a single-outcome realization law. It does not show that no disciplined law-form for realization can exist. To reach that stronger conclusion, one would need a framework-null argument showing that every admissible implementation of the relevant law-form class entails the excluded empirical consequence. Without such a bridge, the strong null has model-level jurisdiction, not automatic framework-level or thesis-level jurisdiction.

The central principle of this paper is therefore:

A result falsifies only the theoretical object whose fixed commitments entail the failed prediction, and confirms only what its controls establish.

This principle is symmetrical. It prevents defenders of CBR from evading falsification by relocating the target after a failed test. It also prevents critics from assigning a local null result broader destructive force than its premises warrant. A positive result in the accessibility regime would not prove all of CBR, still less the universal truth of the realization-law thesis. It would support only the theoretical commitments actually implicated by the validated test, subject to baseline adequacy, nuisance separation, calibration discipline, and independent replication. Conversely, a negative result would not defeat more than the commitments that generated the failed prediction.

This paper develops a formal adjudication structure for that principle. It asks what theoretical object is under test, what commitments belong to that object, what consequences those commitments entail, and what kind of result is sufficient to defeat them. The inquiry is not merely methodological. It is necessary for any serious realization-law program. Without such distinctions, empirical failure becomes ambiguous: a defender may claim that nothing important failed, while a critic may claim that everything failed. Both moves are unstable unless the level of failure has been specified.

The paper proceeds from the narrowest defensible claim. It does not assume that CBR is true. It does not claim that standard quantum mechanics is operationally inadequate. It does not claim that decoherence is false. It does not claim that all interpretations of quantum mechanics must accept the single-outcome target. It does not claim empirical confirmation. It asks instead: if one treats individual outcome realization as a physical target, what burdens must any candidate law of realization carry, and what follows when one particular instantiation of such a law succeeds or fails?

That formulation matters. Standard quantum mechanics supplies state spaces, amplitudes, dynamical evolution, observables, measurement statistics, and Born-rule probabilities. Decoherence theory explains how environmental entanglement suppresses interference in reduced descriptions and stabilizes effectively classical record structures. These achievements are not challenged here. The question is narrower. Probability assigns weights to possible outcomes. Decoherence explains the physical suppression of interference and the emergence of stable records. Neither, by itself and without an additional interpretive or ontological move, states a law-form selecting one realized outcome channel from an admissible candidate class in an individual context. That is the target of the realization-law thesis.

The thesis does not say that such a law has been found. It says that if unique realization is treated as a physical event rather than merely an update of description, then the demand for a law-form is structurally natural. CBR is one attempt to answer that demand. It does so by treating realization as context-indexed constrained selection: for a physical context C, define an admissible class 𝒜(C), compare candidates by a pre-outcome burden ordering ≼_C or realization functional ℛ_C, identify minimizers, quotient by operational equivalence ≃_C, and obtain a selected realization channel or selected operational equivalence class Φ∗_C. In compact form:

Φ∗_C ∈ argmin{ℛ_C(Φ) : Φ ∈ 𝒜(C)}.

This expression is not treated here as proof of CBR. It is treated as the canonical representation of a burden-bearing law-form class. Its significance depends on whether the burdens leading to it are genuinely required, whether the admissible class is physically motivated rather than engineered, whether the functional is fixed before the outcome, whether probability discipline is preserved, whether decoherence is not merely renamed, and whether the resulting theory can fail.

The present paper is therefore not a fallback paper. It is not written to say that CBR survives whatever happens. It is written to make failure exact. If an accessibility-sensitive CBR instantiation fails under its own strong-null conditions, the model dies. If repeated strong nulls eliminate the accessibility-sensitive sector across all admissible implementations, then the relevant framework class may die. If a superior account shows that single-outcome realization requires no law-form because the target itself is dissolved, then the realization-law thesis may fail. But each level requires its own argument. No level should be destroyed by implication without the bridge needed to reach it; no level should be preserved after its own commitments have failed.

The guiding standard is therefore stricter than ordinary defensive theory management. CBR may not revise η after a null result. It may not move η_c after the fact. It may not change ℬ retroactively. It may not reinterpret a predicted deviation as unnecessary once no deviation appears. It may not take an unpredicted anomaly as confirmation unless that anomaly belonged to the declared observable class. Any successor model must concede the failed instantiation, identify the failed assumption, state new law objects before new testing, and generate a new public defeat condition. A surviving framework must not become a shelter for failed models.

At the same time, critics must not compress all theoretical levels into the narrowest empirical test. A failed instantiation is not automatically a failed representation class. A failed representation class is not automatically a refutation of the realization-law thesis. A refutation of one accessibility model is not a proof that probability is selection, decoherence is selection, or branching descriptions solve the single-outcome target on terms they do not accept. The proper conclusion must match the jurisdiction of the result.

The sections that follow build this adjudication structure. Section 2 separates the four objects that must not be confused: the realization-law thesis, the CBR representation class, canonical CBR, and the accessibility-signature instantiation. Section 3 states the realization-law thesis and its limits. Section 4 defines the minimum burdens of a disciplined realization law. Section 5 proves the representation-class result: under finite, compact, regular, or quotient-representable conditions, a realization-law candidate satisfying those burdens admits a CBR-form or CBR-equivalent representation. Later sections then specialize the structure to canonical CBR, define empirical exposure, formulate the jurisdiction-of-failure principle, state the strong-null model-death theorem, and develop the framework-null and non-evasion standards.

The claim of this paper is deliberately bounded. It does not establish CBR as physics. It does not claim that nature obeys the canonical realization functional. It does not prove that the accessibility signature will be observed. It does something prior and necessary: it states how a realization-law theory candidate should be judged, what kind of failure kills which part of the theory, and what burden remains after a local instantiation succeeds or fails.

A mature theory candidate does not ask to be spared from failure. It asks that failure be assigned to the right object. That is the jurisdiction this paper defines.

---

2. Four Objects That Must Not Be Confused

The central difficulty in evaluating CBR is that the program contains layered commitments. Some are broad and structural. Others are narrow and empirical. A fair assessment requires keeping them separate. If these layers are collapsed, the theory becomes either too easy to kill or too easy to rescue. A critic may treat the failure of one experimental instantiation as the death of the entire realization-law question. A defender may treat the survival of the broader question as if it saves the failed instantiation. Both moves are invalid. The objects must first be distinguished.

The four relevant objects are the realization-law thesis, the CBR representation class, canonical CBR, and the accessibility-signature instantiation. Each has its own content, its own burden, and its own mode of failure. The hierarchy is strict: a lower-level failure reaches a higher level only if an additional bridge theorem carries it there.

2.1 The Realization-Law Thesis

The realization-law thesis is the broadest object considered in this paper. It is not yet a commitment to CBR. It is not a commitment to a particular functional ℛ_C, a particular accessibility parameter η, or a particular empirical signature. It is the structural claim that if individual outcome realization is treated as a physical event, then a theory must either specify a law-form for that event or explain why no such law-form is needed.

The thesis begins from a distinction among evolution, registration, and realization. Evolution concerns the ordinary dynamical behavior of the state or reduced state. Registration concerns the formation of record-bearing structures, including stable correlations, pointer-like degrees of freedom, environmental encodings, and accessible traces. Realization, in the sense relevant here, concerns the further question of why one outcome structure is actual in an individual context rather than merely one element in a formal range of possible, weighted, decohered, or branch-described structures.

A theory may deny that this third question is well posed. A branching framework may reject unique outcome selection and treat multiplicity as physically fundamental. An operational framework may decline to ask for a physical law of realization beyond predictive correlations and state update rules. A collapse theory may introduce additional dynamics. A hidden-variable theory may assign underlying variables that determine outcomes. The realization-law thesis does not refute these positions. It identifies the burden that arises if one does not dissolve the single-outcome target.

Accordingly, the thesis is conditional:

If one outcome is treated as physically realized, and if that realization is not exhausted by ordinary evolution, probability assignment, observer update, branching description, or non-selective decoherence, then a disciplined theory must state what law-form or law-equivalent structure governs that realization.

This thesis can fail. It would be weakened if probability assignment alone were shown to entail individual realization, rather than merely weighting possible outcomes. It would be weakened if non-selective decoherence were shown to entail unique realization without additional ontology, selection rule, or interpretive stipulation. It would be weakened if the single-outcome target were successfully dissolved by a superior framework, making the demand for a realization law unnecessary. It would also be weakened if the burdens proposed for realization-law candidates were shown to smuggle in CBR-specific assumptions rather than neutral requirements of law-form discipline.

The thesis is therefore not immune. But its failure conditions are not the same as the failure conditions of a particular CBR experiment. A strong null against one accessibility-sensitive instantiation may show that the tested model is false. It does not, without further argument, show that the realization-law thesis itself is false.

2.2 The CBR Representation Class

The CBR representation class is narrower than the realization-law thesis but broader than canonical CBR. It is the class of candidate law-forms in which realization is represented as constrained selection from a physically admissible class.

The structural sequence is:

C → 𝒜(C) → ≼_C or ℛ_C → M_C / ≃_C → Φ∗_C.

Here C denotes the physical context. It is not merely a label for an observable or basis. It includes the measurement architecture, relevant degrees of freedom, record-bearing structure, timing, accessibility conditions, and operational constraints relevant to the realization question. The class 𝒜(C) denotes the admissible realization-compatible candidates in that context. These may be represented as channels, record structures, or outcome maps, provided they are physically meaningful and not merely arbitrary formal constructions.

The relation ≼_C denotes a pre-outcome burden ordering over admissible candidates. When representable by a functional, it is written as ℛ_C. The minimizer set M_C contains the candidates that best satisfy the burden structure. Operational equivalence ≃_C identifies candidates that differ formally but not in any physically relevant or experimentally accessible way in context C. The selected realization channel Φ∗_C is then the selected candidate or selected equivalence class.

In functional form, the representation is:

Φ∗_C ∈ argmin{ℛ_C(Φ) : Φ ∈ 𝒜(C)}.

The importance of this representation is not that it proves the truth of CBR. Its importance is that it makes the law-form burden explicit. A realization law cannot merely say that “one outcome occurs.” It must say what physical context is being considered, what candidates are eligible, what makes them admissible, how they are compared, what counts as the same outcome under operational equivalence, how probability discipline is preserved, how the proposal differs from non-selective decoherence, and what would defeat it.

The representation class can fail in several ways. The context C may be underspecified. The candidate class 𝒜(C) may be empty, arbitrary, or outcome-smuggled. The burden ordering may be post hoc. The equivalence relation may hide physically meaningful differences. The probability discipline may fail. The decoherence-separation condition may collapse. The model may have no defeat condition. Or a materially distinct realization-law candidate may satisfy the same burdens without admitting a CBR-form or CBR-equivalent representation.

Those are failures of the representation class. They are not identical to failures of canonical CBR or failures of one accessibility instantiation. The representation class is a formal bridge between the broad realization-law thesis and specific CBR models. It is the level at which the realization-law thesis becomes a disciplined law-form architecture without yet becoming a single empirical model.

2.3 Canonical CBR

Canonical CBR is a fixed member of the CBR representation class. It does not merely state that realization is constrained. It fixes a specific law-form architecture.

For a physical context C, canonical CBR defines a restricted admissible class 𝒜(C) of realization-compatible channels. It defines a context-indexed realization-burden functional ℛ_C on that class. It identifies a selected realization channel or selected operational equivalence class Φ∗_C by constrained minimization. In schematic form:

Φ∗_C ∈ argmin{ℛ_C(Φ) : Φ ∈ 𝒜(C)}.

In its canonical specialization, the realization burden may be represented as a structured combination of terms such as:

ℛ_C(Φ) = αΞ_C(Φ) + βΩ_C(Φ) + γΛ_C(Φ),

where α, β, and γ are fixed nonnegative coefficients, and the terms represent distinct context-relative burdens. The exact interpretation of these terms depends on the canonical model, but their role is to prevent selection from becoming arbitrary. They must be fixed before outcome comparison. They must not be tuned after the result. They must not conceal the selected outcome inside the functional.

Canonical CBR adds several burdens beyond the general representation class. It requires restricted admissibility, so that not every formally writable channel belongs to 𝒜(C). It requires representational invariance, so that physically irrelevant relabelings do not change the selected verdict. It requires operational uniqueness, so that minimizers are unique at the level of physically meaningful equivalence, even if formal representatives multiply. It requires probability discipline, so that realization does not casually violate Born-compatible ensemble behavior. It requires non-reduction to decoherence, so that Φ∗_C is not merely Φ_mix renamed. It requires empirical vulnerability, so that the model can fail.

Canonical CBR is therefore narrower than the realization-law thesis and narrower than the general CBR representation class. Its strength comes from this narrowing. By fixing more structure, it becomes more evaluable. But by fixing more structure, it also becomes more exposed. A validated strong null may kill canonical CBR in a way that it does not kill the broader realization-law thesis.

This distinction is not a weakness. It is the mark of disciplined theory construction. A broad thesis becomes scientifically useful only when it is compressed into models with consequences. Canonical CBR is such a compression. It should neither be inflated into the whole realization-law thesis nor weakened into a purely interpretive posture.

2.4 Accessibility-Signature Instantiation

The accessibility-signature instantiation is narrower still. It is the empirical exposure of canonical CBR through a designated accessibility-sensitive protocol family.

The central variable is η, an operational accessibility parameter. It is intended to quantify, within a specified context, the physically relevant accessibility of record-bearing outcome information. The critical regime η_c denotes the region in which accessibility becomes realization-effective according to the instantiated model. The empirical question is whether varying η across a designated protocol family produces a non-baseline response in an observable such as interference visibility, relative to a declared standard-quantum baseline comparator ℬ and a bounded nuisance envelope.

This instantiation matters because it converts a law-form into an empirical liability. A theory that remains only at the level of broad structure may be coherent, but it is difficult to test. The accessibility instantiation narrows the theory to a finite question: given a fixed C, fixed 𝒜(C), fixed ℛ_C, fixed η, fixed η_c, fixed ℬ, fixed nuisance class, fixed observable burden, and fixed tolerance ε_total, does the predicted non-baseline signature appear under detectability-valid conditions?

If it does not, and if the strong-null conditions are satisfied, then the instantiated model is false.

That sentence must remain intact. The broader realization-law thesis cannot be invoked to rescue the failed instantiation. Nor can canonical CBR retroactively modify η, move η_c, alter ℬ, widen the nuisance envelope, or change the observable class after the result is known. The accessibility instantiation is valuable precisely because it can fail.

At the same time, the failure of the accessibility instantiation does not automatically show that no realization law exists. It does not automatically show that the CBR representation class is impossible. It does not automatically show that canonical CBR could not have another admissible implementation unless a framework-null theorem establishes that all admissible implementations entail the excluded consequence.

The accessibility-signature instantiation is therefore the first hard empirical window, not the entire theory. Its specificity is a strength when evaluating the model. It becomes a mistake only if its failure is treated as having broader jurisdiction than its commitments entail, or if its survival is treated as confirming more than its controls establish.

The remainder of this paper depends on preserving this hierarchy. The realization-law thesis defines the broad target. The CBR representation class formalizes the burden-bearing structure. Canonical CBR fixes one exact law object. The accessibility-signature instantiation exposes that object to finite empirical risk. Each level can be challenged. Each level can fail. But no level should be confused with another, and no failure should be allowed to travel upward without the bridge theorem required to carry it.

3. The Realization-Law Thesis

The realization-law thesis is the broadest claim in the paper and must therefore be stated with particular care. If formulated too strongly, it becomes metaphysical overreach. If formulated too weakly, it loses the reason CBR is being developed at all. The correct formulation is conditional, structural, and target-dependent.

The thesis does not say that nature has been shown to obey CBR. It does not say that a new empirical deviation has been observed. It does not say that standard quantum mechanics is predictively defective. It does not say that all interpretations of quantum mechanics must accept a single-outcome selection problem. It says something narrower: if individual outcome realization is treated as a physical event not exhausted by existing non-selective structures, then a law-form burden arises.

3.1 Statement of the Thesis

The realization-law thesis may be stated as follows:

If an individual outcome is treated as physically realized in a measurement context, and if that realization is not identified with ordinary dynamical evolution, probability assignment, observer update, branching description, or non-selective decoherence, then a disciplined physical theory must either specify a law-form for outcome realization or explain why no such law-form is required.

Several features of this statement are essential.

First, the thesis is conditional on the single-outcome target. It does not require all interpretations to accept that target. A many-branch ontology may reject the demand for unique selection. An operational framework may refuse to treat realization as a physical event beyond the predictive formalism. Such approaches are not directly refuted by the thesis. Rather, they occupy a different location in the conceptual landscape: they deny, dissolve, or redirect the target that a realization law attempts to address.

Second, the thesis distinguishes realization from probability. Born-rule probabilities assign weights to outcomes across repeated trials or equivalent contexts. They are indispensable to quantum theory. But a probability assignment is not, merely as such, a law selecting which outcome is realized in an individual case. Probability may constrain any acceptable realization law. It may govern ensemble frequencies. But unless supplemented by an account of sampling, selection, hidden variables, collapse, branching, or some other physical or interpretive structure, it does not by itself state the law-form of individual realization.

Third, the thesis distinguishes realization from decoherence. Decoherence explains why interference between alternatives becomes suppressed in reduced descriptions and why stable record structures emerge through environmental coupling. It is central to any serious treatment of measurement. But non-selective decoherence, represented schematically by Φ_mix, does not by itself identify a unique realized outcome channel Φ∗_C. If one claims that decoherence is sufficient, one must state how the non-selective structure becomes, entails, or replaces single-outcome realization. CBR does not deny decoherence. It denies that decoherence can simply be renamed as realization without an additional law-form or interpretive commitment.

Fourth, the thesis distinguishes realization from observer update. Learning an outcome changes an observer’s state assignment. It does not, by itself, explain the physical occurrence of the outcome if that occurrence is treated as objective. The realization-law thesis concerns the physical target, not merely the epistemic update.

Fifth, the thesis is not yet CBR. CBR is one proposed way of satisfying the law-form burden. The realization-law thesis is the broader claim that such a burden exists if the target is accepted.

The thesis therefore occupies a disciplined middle position. It is stronger than the statement that the measurement problem is interesting. It is weaker than the claim that CBR has been established. It identifies a conditional burden: accept objective single-outcome realization as a physical target, and one must either supply a law-form or explain why the demand is misplaced.

3.2 What the Thesis Does Not Claim

Because the realization-law thesis is broad, its limits must be explicit.

It does not claim that CBR is confirmed. Confirmation would require empirical and theoretical achievements not supplied by the thesis itself. The thesis states a burden; it does not discharge all burdens.

It does not claim that standard quantum mechanics is operationally wrong. The predictive success of the standard formalism is not in dispute. The thesis concerns whether the formalism, without supplementation or interpretation, states a law of individual realization. That is a different question from whether it correctly predicts outcome statistics.

It does not claim that the Born rule is false or incomplete as a probability rule. On the contrary, any serious realization-law candidate must preserve Born-compatible ensemble behavior unless it declares a controlled and testable deviation. CBR’s burden is not to replace probability with realization, but to avoid confusing the two.

It does not claim that decoherence is false. Decoherence is treated as physically indispensable to record formation and interference suppression. The claim is only that non-selective decoherence does not automatically equal single-outcome selection. If a framework claims otherwise, it must specify the bridge.

It does not claim that branching frameworks are refuted. Branching frameworks may reject the unique-realization target and thereby avoid the need for a selection law of the kind considered here. The present paper does not attempt to defeat that move. It asks what follows if the single-outcome target is retained.

It does not claim that all candidate realization laws must use CBR’s final canonical functional. The thesis demands a law-form or law-equivalent explanation. The CBR representation class is argued later to be the natural form of the burden-bearing class under stated representability conditions. But that claim remains conditional and is open to challenge.

It does not claim that a failed accessibility-signature test would be irrelevant. On the contrary, if the test satisfies strong-null conditions, the instantiated model fails. The thesis only denies that such a result automatically reaches the broader realization-law question without a framework-null bridge.

These non-claims are not concessions of weakness. They are part of the thesis’s discipline. A broad law-form paper should not expand its claim beyond its authority. The credibility of the realization-law thesis depends on refusing both inflation and evasion.

3.3 Why the Thesis Is Motivated

The motivation for the realization-law thesis lies in a structural gap among several distinct explanatory roles.

Ordinary quantum evolution describes how state structure changes. In closed systems this is unitary. In open or measurement-like contexts it may be represented through effective maps, instruments, or reduced descriptions. This dynamical layer is necessary, but it is not the same as outcome realization. Evolution tells us how amplitudes, phases, correlations, and entanglement structures develop. It does not, without more, identify one realized outcome channel in an individual context.

Registration describes the formation of records. A measurement interaction can correlate system and apparatus, stabilize pointer-like structures, and distribute information into an environment. Registration is a physical achievement. It makes records possible. But record formation alone is not automatically the same as selecting one record as the realized outcome. A formal description may contain multiple record-correlated structures, and the question remains whether one is actual, all are actual in branches, or the demand for actual selection is misplaced.

Probability assignment describes weighting. Born-rule probabilities constrain observed frequencies and are empirically central. But probability is not identical to selection. A probability distribution over alternatives does not, merely by existing, specify which alternative is realized in a single event. A theory may include stochastic dynamics, hidden variables, sampling postulates, collapse rules, or decision-theoretic accounts, but those are additional structures. The realization-law thesis asks for the law-form or law-equivalent structure that plays this role if unique outcome realization is accepted.

Decoherence describes suppression and stabilization. It explains why interference between alternatives becomes inaccessible in reduced descriptions and why classical-like records emerge. But non-selective decoherence produces mixture-like structure without, by itself, selecting one term as the realized outcome. If one wants single-outcome realization, the bridge from non-selective record stabilization to unique actualization must be stated.

Observer update describes knowledge change. It is indispensable in operational practice. But an observer learning an outcome is not the same as the physical selection of that outcome, unless one adopts an explicitly epistemic or operational stance that declines the physical realization question.

Branching description avoids unique selection by treating multiplicity as real or otherwise fundamental. This is a powerful and serious strategy, but it does not answer the same question CBR asks. It rejects the need for a single selected outcome in the relevant sense.

These distinctions motivate the realization-law thesis. If one outcome becomes actual, and if that actualization is not reduced to any of the foregoing structures, then a theory should specify what selects, what is selected from, what fixes the selection rule, how probability is preserved, how decoherence is not merely renamed, and what would count as defeat.

CBR’s significance, at the broadest level, is that it makes this burden explicit. It does not merely assert that constraints matter. It attempts to turn the realization question into a law-form problem:

physical context → admissible candidates → burden ordering → selected realization class.

This structure may be right or wrong. It may be too narrow, too strong, or insufficiently derived. But it addresses the right kind of burden if the realization-law thesis is accepted.

The realization-law thesis is therefore not a claim of certainty. It is a claim of conditional necessity: given the single-outcome physical target, a disciplined law-form or law-equivalent explanation is required. The remaining question is whether CBR supplies the right form of that explanation and how far any success or failure of one CBR instantiation can reach.

---

4. Minimum Burdens of a Realization Law

A candidate law of outcome realization cannot be evaluated unless it first states the burdens it accepts. Without those burdens, the proposal remains too plastic. It may appear to explain realization while leaving its domain undefined, its candidates unspecified, its selection rule adjustable, its relation to probability ambiguous, its relation to decoherence unresolved, and its failure conditions absent.

This section states the minimum burdens of a disciplined realization law. These burdens do not prove CBR. They define the standard any candidate must meet if it is to be treated as a law-form proposal rather than an interpretive gesture. They are not optional refinements. They are the conditions under which a realization-law proposal becomes evaluable as a candidate law rather than as a retrospective restatement of whatever outcome occurred.

The burdens are deliberately general. A theory may satisfy them in different form. It need not use CBR’s final canonical functional. It need not predict the accessibility signature. It need not adopt all of canonical CBR’s internal machinery. But if it claims to be a physical law of individual outcome realization, it must answer the following questions: What is the context? What is being selected? What makes candidates admissible? How are they compared? What prevents post hoc tuning? What counts as the same result? How is probability preserved? How is decoherence not merely renamed? What would defeat the proposal?

4.1 Domain Burden: Define C

A realization law must specify its physical domain. Let C denote the context in which realization is being considered. C is not a purely verbal description and not merely a basis label. It is the physical and operational structure relevant to the realization question. Depending on the case, C may include the measured system, apparatus, interaction architecture, record-bearing degrees of freedom, environmental couplings, timing relations, accessibility conditions, coarse-graining scale, and readout constraints.

Without C, there is no determinate law application. A candidate cannot be admissible or inadmissible except relative to a context. A burden functional cannot be evaluated except relative to a context. An operational equivalence relation cannot be defined except relative to what the context permits one to distinguish.

The domain burden also prevents retrospective redescription. If C can be rewritten after the outcome is known, then the theory can be made to favor the actual result by redefining the situation. A disciplined law must fix C before outcome comparison.

4.2 Candidate Burden: Define 𝒜(C)

A realization law must specify what it selects among. Let 𝒜(C) denote the admissible candidate class in context C. Its elements may be represented as candidate realization channels Φ, record structures, or outcome maps, provided they are physically meaningful relative to C.

Selection without candidates is empty. A theory cannot claim that a realization channel is selected while leaving the candidate space undefined. Nor may it define the candidate class after observing the result. Such a maneuver would not explain realization; it would hide the result in the setup.

The candidate burden therefore requires 𝒜(C) to be nonempty, physically motivated, and fixed independently of Φ∗_C.

4.3 Admissibility Burden: Exclude Arbitrary Candidates

Not every mathematically writable candidate belongs in 𝒜(C). A formal map may be expressible while failing to correspond to any physically admissible realization structure. The admissibility burden requires a candidate law to state why the candidates it compares are eligible.

Admissibility may involve dynamical compatibility, representational invariance, record-structural relevance, accessibility relevance, probability discipline, operational coherence, and independence from the selected outcome. The exact conditions may vary by model, but the burden cannot be omitted. If every formal candidate is admissible, the theory becomes arbitrary. If only the observed outcome is admissible by construction, the theory becomes circular.

Admissibility is therefore the first anti-arbitrariness filter. It makes realization selection a constrained physical problem rather than a labeling exercise.

4.4 Selection Burden: Define ≼_C or ℛ_C

A realization law must state how candidates are compared. This comparison may be given by a burden ordering ≼_C or, when representable, by a realization-burden functional ℛ_C. The role of the ordering or functional is to determine which admissible candidate best satisfies the law’s constraints.

The selection burden is not satisfied by saying that the realized outcome is the one nature selects. That is a restatement, not a law. The comparison rule must be fixed before the outcome is known. It must be defined over 𝒜(C). It must not contain hidden dependence on Φ∗_C. It must support a verdict, or else specify what happens when no unique verdict is available.

In CBR-form representation, the selected realization channel is written:

Φ∗_C ∈ argmin{ℛ_C(Φ) : Φ ∈ 𝒜(C)}.

But the broader burden does not initially require functional notation. It requires a physically meaningful pre-outcome comparison structure. Functional representation is addressed in Section 5.

4.5 Non-Circularity Burden: Fix the Rule Before the Result

A realization law must not depend on the outcome it is supposed to explain. This requires pre-outcome fixity of the law-defining objects:

C, 𝒜(C), ≼_C or ℛ_C, ≃_C, parameters, tolerances, coefficients, calibration rules, baseline comparators, and failure conditions.

The forbidden structure is retrospective success. A theory cannot observe an outcome and then adjust its admissible class, burden functional, or equivalence relation so that the observed outcome appears selected. Such a procedure does not explain realization. It performs after-the-fact accommodation.

Pre-outcome fixity does not require that every parameter be known without calibration. Calibration may be legitimate if its procedure is defined before the outcome test and separated from the data used for adjudication. What is prohibited is outcome-driven tuning.

4.6 Operational-Equivalence Burden: Define ≃_C

A realization law need not always produce strict syntactic uniqueness. Formal representatives may differ while being physically indistinguishable in context C. The theory must therefore define an operational equivalence relation ≃_C.

If Φ₁ ≃_C Φ₂, then Φ₁ and Φ₂ are equivalent for all realization-relevant operational purposes in context C. A minimizer set containing multiple formal candidates may still yield a unique physical verdict if all minimizers are equivalent under ≃_C. Conversely, if operationally distinct minimizers remain and no pre-specified tie rule exists, the law has failed to select one realization class.

Operational equivalence prevents both false multiplicity and false uniqueness. It allows the law to ignore merely representational differences while preserving physically meaningful distinctions.

4.7 Probability Burden: Preserve Born-Compatible Discipline

A realization law must not casually break quantum probability. Born-rule statistics are among the most secure empirical structures in quantum theory. Any candidate realization law must preserve Born-compatible ensemble behavior unless it explicitly declares a controlled, pre-specified, empirically vulnerable deviation.

This burden prevents a category error. Probability assignment and realization selection are distinct, but they are not independent in the sense that either can ignore the other. A realization law must coexist with probability discipline. It must not derive empirical freedom from the mere fact that it addresses a different question.

A model that violates Born-compatible frequencies without a declared and tested deviation does not become stronger by being radical. It fails the probability burden.

4.8 Decoherence-Separation Burden: Do Not Rename Φ_mix

A realization law must state how it differs from non-selective decoherence. Let Φ_mix denote a non-selective decoherence-compatible channel. Such a channel may describe interference suppression, environmental entanglement, record stabilization, and mixture-like reduced structure. The question is whether it selects one realized outcome channel.

If a proposed realization law yields Φ∗_C ≃_C Φ_mix in every relevant context and supplies no additional realization content, then it reduces to decoherence and fails as an independent realization law. This is not a criticism of decoherence. It is a burden on any theory claiming to add a law of realization.

The burden may be satisfied in different ways. A theory may add collapse dynamics, hidden variables, branch ontology, or a constraint-governed selection law. But it cannot simply rename non-selective decoherence as single-outcome realization without explaining the bridge.

4.9 Parameter-Fixity Burden: Prevent Post Hoc Tuning

Any coefficients, thresholds, tolerances, weights, nuisance bounds, or calibration maps used by the law must be fixed before adjudication. In CBR notation, this includes any coefficients inside ℛ_C, any definition of η, any identification of η_c, any baseline comparator ℬ, and any total tolerance ε_total.

The parameter-fixity burden is central because a flexible enough law can be made to fit almost anything. Without fixity, the theory becomes a fitting device rather than a law. Fixity does not forbid context dependence. It forbids outcome dependence.

4.10 Vulnerability Burden: State Defeat Conditions

A candidate law must be able to fail. Failure may be structural or empirical.

Structural failure occurs if C is undefined, 𝒜(C) is empty or arbitrary, admissibility is post hoc, the comparison rule is circular, the minimizer set is empty, operationally distinct minimizers remain unresolved, probability discipline fails, decoherence-separation collapses, or parameters are tuned after the result.

Empirical failure occurs when a model makes a fixed prediction or fixed observable burden, the validity conditions are satisfied, and the result contradicts the declared consequence beyond the stated tolerance.

The vulnerability burden is not an optional virtue. It is part of what makes the proposal law-like. A theory that cannot fail may be meaningful as metaphysics, but it has not become a disciplined candidate law of outcome realization.

4.11 The Realization-Law Burden Theorem

Theorem 1 — Realization-Law Burden Theorem.

If individual outcome realization is treated as a physical target not exhausted by ordinary evolution, probability assignment, observer update, branching description, or non-selective decoherence, then any disciplined candidate law of realization must specify at least the following: a physical context C; a nonempty admissible candidate class 𝒜(C); a pre-outcome comparison structure ≼_C or realization-burden functional ℛ_C; an operational equivalence relation ≃_C; probability discipline; decoherence-separation discipline; parameter fixity; and explicit defeat conditions.

Proof sketch.

A law of realization must apply somewhere; hence it requires C. It must select something; hence it requires 𝒜(C). It must distinguish selected from non-selected candidates; hence it requires ≼_C or ℛ_C. It must determine when formal differences are physically irrelevant; hence it requires ≃_C. It must respect the empirically established role of quantum probability; hence it requires probability discipline. It must not collapse into a non-selective account of record stabilization; hence it requires decoherence separation. It must avoid retrospective accommodation; hence it requires parameter fixity. It must be evaluable as a candidate law; hence it requires defeat conditions. These requirements follow from the functional role of a realization law and do not depend on the truth of canonical CBR.

What this establishes.

This establishes necessary burdens for any disciplined realization-law candidate. It shows why a proposal cannot remain at the level of interpretive assertion if it claims law-form status. A candidate law must specify its domain, objects, comparison structure, equivalence relation, probability discipline, decoherence relation, parameter discipline, and defeat conditions before it can be evaluated.

What this does not establish.

This establishes burden, not truth. It establishes law-form discipline, not empirical confirmation. It establishes the conditions under which a realization-law proposal becomes evaluable, not that CBR is the final physical law. It does not require all interpretations to accept the single-outcome target. It says only that if the target is accepted, these burdens must be carried.

---

5. Representation-Class Theorem

The previous section identified the minimum burdens of a realization law. This section shows why those burdens naturally generate a CBR-form or CBR-equivalent representation under appropriate representability conditions. The result is not an empirical confirmation of CBR. It is a structural theorem about the form taken by any burden-bearing realization-law candidate within the class considered here.

The key idea is simple. Once a theory specifies a context C, a nonempty admissible candidate class 𝒜(C), a pre-outcome comparison relation over that class, an operational equivalence relation, and defeat conditions, it already has the skeleton of constrained realization selection. If the comparison relation is representable by a functional, the CBR expression follows directly.

5.1 Definition: Realization-Law Candidate

A realization-law candidate in context C is a structure:

L_C = (C, 𝒜(C), ≼_C, ≃_C, P_C, D_C, F_C).

Here C is the physical context. 𝒜(C) is the nonempty admissible candidate class. ≼_C is a pre-outcome burden ordering over 𝒜(C), where Φ₁ ≼_C Φ₂ means that Φ₁ is no more burdened than Φ₂ in context C. The relation ≃_C is operational equivalence. P_C denotes probability discipline, including Born-compatible ensemble behavior or a declared controlled deviation. D_C denotes decoherence-separation discipline, requiring that the selected realization structure not merely rename Φ_mix unless the theory explicitly reduces to decoherence. F_C denotes the set of defeat conditions.

This definition is intentionally general. It does not require that ≼_C initially be expressed by a numerical functional. It does not require that canonical CBR’s specific ℛ_C be adopted. It does not require a particular experimental protocol. It captures the burden-bearing structure of a realization-law candidate before canonical specialization.

5.2 Admissible Selection

Given L_C, define the minimally burdened set M_C by:

M_C = {Φ ∈ 𝒜(C) : for every Ψ ∈ 𝒜(C), Φ ≼_C Ψ}.

If M_C is empty, the candidate law fails to select in context C. If M_C contains multiple elements that are all equivalent under ≃_C, the law selects a unique operational realization class. If M_C contains operationally distinct candidates and no pre-specified tie rule resolves them, the law is incomplete in context C.

The selected realization channel Φ∗_C should therefore be understood as a representative of the selected operational equivalence class, not necessarily as an absolutely unique syntactic object. More precisely, the law selects [Φ∗C]≃, the equivalence class of minimizers under ≃_C, when such a class is unique.

This point is essential. Realization-law uniqueness should not be confused with formal uniqueness under every possible representation. A law may be physically determinate even if multiple mathematical descriptions represent the same operational verdict. Conversely, a law may be formally compact while hiding unresolved operational multiplicity. The equivalence relation ≃_C is what prevents both errors.

5.3 Ordering-to-Functional Representation

The CBR-form expression arises when the burden ordering ≼_C can be represented by a realization-burden functional ℛ_C.

Proposition 1 — Ordering-to-Functional Representation.

Let 𝒜(C) be a nonempty admissible candidate class equipped with a pre-outcome burden ordering ≼_C. If ≼_C is finite, compact with appropriate continuity, regular, or representable on the quotient space 𝒜(C)/≃_C, then there exists an order-preserving realization-burden functional ℛ_C such that, for admissible candidates Φ₁ and Φ₂,

Φ₁ ≼_C Φ₂ whenever ℛ_C(Φ₁) ≤ ℛ_C(Φ₂),

with equality corresponding either to equal burden or to operationally irrelevant distinction under ≃_C where specified.

Proof sketch.

If 𝒜(C) is finite, an order-preserving numerical assignment can be constructed by ranking equivalence classes. If 𝒜(C) has compactness and continuity properties, standard representation reasoning permits a continuous or lower-semicontinuous functional under appropriate regularity conditions. If the ordering is best defined only up to operational equivalence, the functional may be defined on the quotient 𝒜(C)/≃_C and then lifted to representatives. In each case, the functional represents the pre-outcome comparison structure without introducing outcome dependence.

The proposition is deliberately conditional. Not every conceivable ordering must be numerically representable without loss. If a proposed realization law uses a non-representable ordering, it may remain outside the functional subclass. But where the ordering is representable under the stated conditions, the CBR-form expression follows.

5.4 The Representation-Class Theorem

Theorem 2 — Representation-Class Theorem.

Under finite, compact, regular, or quotient-representable conditions, any realization-law candidate L_C = (C, 𝒜(C), ≼_C, ≃_C, P_C, D_C, F_C) satisfying the burden set of Section 4 admits a CBR-form or CBR-equivalent representation:

Φ∗_C ∈ argmin{ℛ_C(Φ) : Φ ∈ 𝒜(C)}.

Here Φ∗_C denotes the selected realization channel or selected operational equivalence class, ℛ_C represents the pre-outcome burden ordering ≼_C, and 𝒜(C) is the physically admissible candidate class in context C.

Proof sketch.

By the domain burden, the candidate law supplies C. By the candidate and admissibility burdens, it supplies a nonempty physically restricted class 𝒜(C). By the selection burden, it supplies a pre-outcome comparison relation ≼_C over 𝒜(C). By Proposition 1, under finite, compact, regular, or quotient-representable conditions, ≼_C is representable by a realization-burden functional ℛ_C. By the operational-equivalence burden, the minimizer set is interpreted modulo ≃_C. By the non-circularity and parameter-fixity burdens, ℛ_C and all associated law-defining objects are fixed before outcome comparison. By the probability and decoherence-separation burdens, the selected candidate remains constrained by P_C and D_C. By the vulnerability burden, failure conditions F_C remain attached to the representation. Therefore the law admits the CBR-form or CBR-equivalent representation Φ∗_C ∈ argmin{ℛ_C(Φ) : Φ ∈ 𝒜(C)}.

5.5 What the Theorem Establishes

The Representation-Class Theorem establishes representation, not truth. It establishes admissible form, not empirical confirmation. It establishes a burden class, not universal closure.

Within the burden-bearing class considered here, the CBR structure arises naturally from the requirements of disciplined law-form specification. The theorem shows that a realization-law candidate must have a context, candidates, admissibility restrictions, a comparison structure, operational equivalence, probability discipline, decoherence separation, parameter fixity, and defeat conditions. Once those are supplied, and once the comparison relation is representable, the result is a constrained minimization or equivalent selection structure. That is the CBR-form representation.

This is important because it relocates the debate. The question is not merely whether one accepts the phrase “Constraint-Based Realization.” The question is whether the burdens identified in Section 4 are legitimate burdens of any realization law. If they are, and if the ordering is representable, then the CBR-form is not decorative. It is the natural representation of the burden class.

5.6 What the Theorem Does Not Establish

The theorem does not prove that nature obeys CBR. It does not prove that the canonical functional ℛ_C used in any particular CBR model is the correct physical functional. It does not prove universal uniqueness across all measurement contexts. It does not prove universal Born-rule closure. It does not prove the accessibility signature. It does not refute interpretations that reject the single-outcome target.

The theorem also does not show that every conceivable realization-law framework must be forced into CBR notation. A rival may deny the single-outcome target, reject representability, adopt a fundamentally different ontology, or satisfy the realization burden through a structure outside the class considered here. Such rivals must be assessed on their own terms.

The theorem establishes something narrower and more useful: if a theory accepts the single-outcome realization target, accepts the minimum law-form burdens, and supplies a representable pre-outcome ordering over an admissible candidate class, then it admits a CBR-form or CBR-equivalent representation. The burden then shifts to the physical adequacy of the chosen context, admissibility class, functional, equivalence relation, probability discipline, decoherence-separation claim, and empirical failure conditions.

5.7 Corollary: Failure Must Track the Represented Object

Corollary 1 — Representation-Level Failure.

If a CBR-form representation fails because C is undefined, 𝒜(C) is empty or arbitrary, ℛ_C is post hoc, ≃_C hides operationally meaningful differences, probability discipline fails, decoherence separation collapses, or defeat conditions are absent, then the failure attaches to the represented law candidate in that context.

This corollary anticipates the jurisdiction-of-failure principle developed later. The object that fails is the object whose burden is violated. If the admissible class is arbitrary, the candidate law fails at the admissibility level. If the empirical prediction fails under strong-null conditions, the instantiation fails at the model level. If every admissible implementation of a framework entails an excluded consequence, the framework fails. These are different verdicts.

The representation theorem therefore does not merely generate formal notation. It prepares the adjudication structure of the paper. Once the law object is specified, failure is no longer rhetorical. It has an address.

---

6. Canonical CBR as a Fixed Member of the Class

The Representation-Class Theorem establishes a structural result: if a candidate law of realization accepts the single-outcome target, satisfies the minimum burdens of law-form discipline, and supplies a representable pre-outcome ordering over an admissible candidate class, then it admits a CBR-form or CBR-equivalent representation. That theorem identifies a burden-bearing law-form class. It does not yet identify a fixed physical model.

Canonical CBR is the point at which the representation class becomes liable. It is not merely a law-form. It is a law-form fixed enough to die. Its purpose is not to make the broader thesis safer, but to make one member of that thesis exact enough to be judged.

That distinction is central. A broad realization-law thesis may motivate the need for a law-form. A representation class may show the structural shape such a law-form naturally takes. But neither has the same empirical exposure as a canonical model whose admissible class, realization functional, equivalence relation, accessibility parameter, baseline comparator, nuisance envelope, observable burden, and verdict rule have been fixed. Canonical CBR is the stage at which risk attaches.

The canonical move is therefore not decorative. It is the transition from architecture to liability. It fixes enough of the theory that failure can acquire an address.

Canonical CBR specifies the relevant objects more sharply than the general representation class: the admissible class 𝒜(C), the realization-burden functional ℛ_C, the operational equivalence relation ≃_C, the accessibility parameter η, the critical accessibility regime η_c, the baseline comparator ℬ, the nuisance envelope, the observable burden, and the strong-null verdict rule. In doing so, canonical CBR moves from law-form generality to model-level exposure.

This does not make canonical CBR established physics. It makes it evaluable. Its strength lies not in avoiding failure, but in accepting enough structure that failure becomes possible.

6.1 From Representation Class to Canonical Law Object

The CBR representation class has the general structure:

C → 𝒜(C) → ≼_C or ℛ_C → M_C / ≃_C → Φ∗_C.

Canonical CBR specializes this structure by treating the comparison relation as representable by a context-indexed realization-burden functional ℛ_C. The selected realization channel or selected operational equivalence class is then written:

Φ∗_C ∈ argmin{ℛ_C(Φ) : Φ ∈ 𝒜(C)}.

This expression carries several commitments.

First, C must be physically specified. It is not a symbolic placeholder for “the experiment.” It must include the physical and operational features relevant to realization: the measurement architecture, record-bearing degrees of freedom, timing structure, accessibility conditions, operational readout limits, and any other features needed to define admissibility and comparison.

Second, 𝒜(C) must be restricted. Canonical CBR does not select from all mathematically writable channels. It selects from candidates that survive the admissibility constraints associated with C. If 𝒜(C) is too broad, the model becomes arbitrary. If it is too narrow in a way that embeds the desired result, the model becomes circular.

Third, ℛ_C must be fixed before outcome comparison. The functional may be context-indexed, but it may not be outcome-indexed. Its terms, coefficients, thresholds, tolerances, and calibration rules must be specified independently of Φ∗_C.

Fourth, ≃_C must identify operationally irrelevant multiplicity. Canonical CBR does not require absolute syntactic uniqueness of formal representatives. It requires uniqueness at the level of physically meaningful verdicts.

Fifth, the model must preserve probability discipline and decoherence separation. It must not violate Born-compatible ensemble behavior without a declared and testable deviation. It must not merely rename a non-selective decoherence-compatible channel Φ_mix as a selected realization channel.

These commitments make canonical CBR narrower than the representation class. They also make it more scientifically legible. A theory cannot be tested while it remains indefinitely permissive about its law-defining objects. Canonical CBR becomes evaluable by fixing them.

6.2 The Canonical Functional

In canonical form, the realization-burden functional may be schematically represented as:

ℛ_C(Φ) = αΞ_C(Φ) + βΩ_C(Φ) + γΛ_C(Φ),

where α, β, and γ are fixed nonnegative coefficients, and Ξ_C, Ω_C, and Λ_C denote context-indexed burden terms. The purpose of this expression is not to assert that this is already the final physical law of nature. Its purpose is to make explicit that canonical CBR treats realization as constrained comparison among admissible candidates.

The term Ξ_C may be read as capturing a definiteness or constraint-satisfaction burden. The term Ω_C may be read as capturing record-structural coherence or admissibility burden. The term Λ_C may be read as capturing accessibility-consistency burden. The precise interpretation of these terms depends on the fully specified canonical model. What matters at this stage is not the rhetorical naming of the terms, but their law-form role. Each term must be physically motivated, context-fixed, and non-circular. Each must contribute to comparison among candidates in 𝒜(C), not to retrospective accommodation of the observed outcome.

The coefficients α, β, and γ are equally important. If they remain adjustable after the result, the functional ceases to be a law candidate and becomes a fitting mechanism. If they are fixed by theory, they must be specified before adjudication. If they are fixed by calibration, the calibration procedure must be independent of the outcome test. Canonical CBR’s credibility depends not only on the existence of ℛ_C, but on the discipline by which ℛ_C is fixed.

The functional should therefore be read as a burden object, not as a decorative equation. It is the mathematical site at which CBR either becomes law-like or fails. If ℛ_C is physically motivated, pre-fixed, non-circular, probability-disciplined, decoherence-distinct, and empirically vulnerable, then canonical CBR has the structure of a serious candidate law. If ℛ_C is arbitrary, post hoc, outcome-smuggled, or reducible to Φ_mix without remainder, canonical CBR fails at the model level.

6.3 Restricted Admissibility

The admissible class 𝒜(C) is not a passive domain. It is part of the law object. The selection rule cannot be assessed independently of the class over which selection occurs.

A canonical CBR model must therefore state admissibility conditions before comparison. These conditions may include dynamical compatibility, representational invariance, record-structural relevance, accessibility relevance, probability discipline, and operational coherence. The function of admissibility is to prevent arbitrary selection. A candidate Φ may be mathematically expressible without being physically admissible in context C. Conversely, a model cannot define admissibility so narrowly that only the eventual outcome is eligible.

Restricted admissibility is one of the main reasons canonical CBR should not be confused with a generic interpretive statement. The proposal is not simply that “constraints select.” The proposal is that, in a specified context C, a restricted class 𝒜(C) of realization-compatible candidates is fixed in advance, and a realization burden ℛ_C selects within that class. The law’s content lies in both parts: the restriction of candidates and the comparison among them.

This also clarifies a possible failure mode. If a critic shows that 𝒜(C) has been defined in an outcome-dependent manner, canonical CBR fails in that context. If a critic shows that 𝒜(C) excludes a materially relevant candidate without principled reason, the model is incomplete or biased. If a critic shows that 𝒜(C) includes candidates with no physical realization content, the selection problem becomes diluted. Admissibility is therefore not auxiliary. It is one of the primary sites where canonical CBR is judged.

6.4 Operational Uniqueness and Probability Discipline

Canonical CBR does not require that the minimization problem always yield one syntactically unique formal representative. It requires that the selected verdict be unique up to operational equivalence.

Let M_C denote the minimizer set:

M_C = {Φ ∈ 𝒜(C) : ℛ_C(Φ) = inf{ℛ_C(Ψ) : Ψ ∈ 𝒜(C)}}.

If all elements of M_C are equivalent under ≃_C, the model selects a unique operational realization class. If M_C contains operationally distinct elements and no pre-specified tie rule resolves them, the model fails to select in that context. This is not a minor technicality. A realization law that leaves operationally distinct minimizers unresolved has not delivered a determinate realization verdict.

Probability discipline imposes a separate burden. CBR is not entitled to break Born-compatible ensemble behavior merely because it addresses realization rather than probability. A canonical model must either preserve Born-compatible statistics or declare a controlled deviation with a corresponding empirical burden. In the absence of such a declared deviation, violations of Born-compatible frequencies count against the model.

This preserves the distinction between probability and realization. CBR does not ask probability to do selection’s work. But neither may CBR ignore probability’s empirical authority. The two roles are distinct but mutually constrained.

6.5 Decoherence Separation

Canonical CBR must also satisfy decoherence separation. Decoherence explains interference suppression, environmental entanglement, record stabilization, and effective classicality in reduced descriptions. Canonical CBR does not reject these achievements. Its claim is that non-selective decoherence, by itself, does not state a single-outcome realization law unless supplemented by additional ontology, dynamics, or interpretive structure.

Let Φ_mix denote a non-selective decoherence-compatible channel. If canonical CBR’s selected channel Φ∗_C is operationally equivalent to Φ_mix in every relevant respect, and if no additional realization content is supplied, then canonical CBR reduces to decoherence and fails as an independent realization law. This is a legitimate failure condition. It should not be avoided.

The burden on canonical CBR is therefore precise. It must show that its selected realization structure does not merely reproduce non-selective decoherence under another name. It must either supply distinct realization content or concede reduction. If it concedes reduction, then it may still be a useful redescription, but it is no longer an independent law of outcome realization.

6.6 The Canonical Specialization Theorem

Theorem 3 — Canonical Specialization Theorem.

Canonical CBR is one exact specialization of the CBR representation class obtained by fixing, for a physically specified context C, a restricted admissible class 𝒜(C), a realization-burden functional ℛ_C, an operational equivalence relation ≃_C, an accessibility parameter η where relevant, a critical accessibility regime η_c where relevant, a baseline comparator ℬ for empirical comparison, a nuisance envelope, an observable burden, and a strong-null verdict rule.

Proof sketch.

By the Representation-Class Theorem, a burden-bearing realization-law candidate with a representable pre-outcome ordering admits a CBR-form representation. Canonical CBR specializes this representation by replacing the generic ordering ≼_C with a specified realization-burden functional ℛ_C; by restricting 𝒜(C) through declared admissibility conditions; by interpreting selection modulo ≃_C; by introducing η and η_c in accessibility-sensitive contexts; by specifying ℬ and nuisance bounds for empirical comparison; and by declaring a strong-null verdict rule. These additional commitments convert the representation class into a fixed canonical model.

What this establishes.

This establishes that canonical CBR is not identical to the broad realization-law thesis. It is a fixed member of the CBR representation class. Its strength lies in accepting additional commitments. Its vulnerability lies in the fact that those commitments can fail.

What this does not establish.

This does not establish that canonical CBR is true. It does not establish that the chosen ℛ_C is the final physical realization functional. It does not establish that η is realization-effective in nature. It does not establish that the accessibility signature will appear. It establishes only the status of canonical CBR as a fixed specialization of the broader representation class.

6.7 Canonical Fixity and Model-Level Risk

The significance of canonical CBR is that it becomes exposed. A broad realization-law thesis may motivate inquiry. A representation class may organize burden-bearing candidates. But a canonical model can be wrong in determinate ways.

If 𝒜(C) is not physically justified, the model fails at admissibility. If ℛ_C is post hoc, the model fails at non-circularity. If ≃_C erases meaningful distinctions, the model fails at operational equivalence. If η cannot be independently calibrated, the empirical exposure layer fails. If ℬ is not a valid baseline comparator, the test cannot adjudicate the model. If a strong null appears under validated conditions, the instantiated model is false.

This is not a defect. It is the point of canonization. A model that cannot die has not yet become exact. Canonical CBR’s merit as a law candidate lies partly in the fact that it allows failure to be assigned. Once the law object is specified, failure is no longer rhetorical. It has an address.

7. The Empirical Exposure Layer

Canonical CBR becomes scientifically exposed when its law-form commitments are tied to an empirical setting in which they can succeed or fail. The empirical exposure layer is the point at which the model stops being only a formal candidate and accepts a public burden. For CBR, this exposure is organized around accessibility-sensitive measurement contexts.

The core idea is that if record accessibility is relevant to realization, then changes in accessibility should not remain forever empirically inert. A model may be subtle, context-specific, and bounded in its expected manifestation. It need not predict broad deviations across ordinary measurement settings. But if accessibility enters the realization law nontrivially, then a designated protocol family should exist in which accessibility-sensitive structure imposes a finite empirical burden.

The empirical exposure layer therefore does not claim that every measurement context should show anomaly. It identifies a restricted domain in which the canonical model becomes vulnerable. This restriction is not a retreat. It is what makes the test meaningful. A theory becomes empirically serious not by claiming universal deviation everywhere, but by specifying where, how, and under what conditions its distinctive commitments must matter.

7.1 Operational Accessibility

Let η denote an operational accessibility parameter associated with record-bearing measurement contexts. The purpose of η is to represent, in a context-specific and calibratable way, the physically relevant accessibility of outcome-defining record information. It is not a psychological variable. It is not a measure of human observation. It is not a free fitting parameter. It is a physical-operational quantity that must be defined before the outcome test.

The parameter η must satisfy several constraints. It must be tied to features of C. It must be calibrated independently of the predicted realization-sensitive effect. It must be stable enough to support comparison across the designated protocol family. It must not be redefined after data are observed. And it must connect to the canonical functional only through pre-specified law terms, such as the accessibility-consistency burden Λ_C where that term is used.

The critical accessibility regime η_c denotes the region in which accessibility is hypothesized to become realization-effective in the instantiated model. The notation should not be read as automatically implying an infinitely sharp physical phase transition. Depending on the canonical assumptions, the predicted signature may take a strong form, such as a derivative break or kink, or a weaker bounded non-baseline deviation in a neighborhood of η_c. What matters for adjudication is that the model pre-specifies the admissible response class before comparison with data.

If η is not independently calibratable, the empirical exposure layer weakens. If η_c is identified only after the result, the model fails. If the predicted response is altered after the result, the model is no longer the same instantiation. Accessibility becomes scientifically meaningful only when it is fixed before adjudication.

7.2 Baseline Comparator and Observable Burden

Empirical exposure requires a baseline comparator. Let ℬ denote the declared baseline class against which the CBR response is tested. In the intended use, ℬ represents the standard-quantum, platform-specific expectation after ordinary decoherence, detector effects, apparatus behavior, and noise sources have been modeled within the accepted baseline.

The baseline must be valid for the test to have jurisdiction. If ℬ is underdeveloped, the result cannot cleanly adjudicate the CBR instantiation. If ℬ omits known platform effects, an apparent deviation may be spurious. If ℬ is adjusted after the result to absorb or reject an effect opportunistically, the test loses discipline. The baseline comparator is therefore not merely background modeling. It is part of the empirical law object.

The observable burden must also be fixed. If the relevant observable is interference visibility, then the model must state what visibility function or response class is expected under ℬ and what response class is expected under the CBR instantiation. If the observable is something else, the same discipline applies. A theory cannot wait to see which quantity deviates and then declare that quantity its evidence. The observable class must be specified before adjudication.

The total tolerance ε_total represents the declared uncertainty or tolerance envelope, including statistical, systematic, calibration, and nuisance contributions where applicable. A claimed deviation must exceed the relevant tolerance in the declared way. A claimed null must be evaluated against the same tolerance. Neither side may change ε_total after seeing the result.

The empirical exposure layer therefore requires four fixed objects at minimum: η, ℬ, the observable burden, and ε_total. Without them, there is no disciplined test of the instantiation.

7.3 Nuisance Separation

No empirical test of this kind is meaningful without nuisance separation. A nuisance effect is any platform-specific or experimental contribution that can mimic, obscure, or distort the predicted CBR response without being part of the realization law itself. Such effects may include detector inefficiency, phase drift, imperfect alignment, environmental fluctuations, source instability, finite-sampling noise, calibration error, or other ordinary physical imperfections.

The nuisance envelope must be declared before adjudication. It must not be widened after the fact to rescue a failed prediction or narrowed after the fact to manufacture a deviation. A CBR signature is meaningful only if it separates from the nuisance class by the declared criterion. A null is meaningful only if the test was sensitive enough to detect the predicted effect beyond the nuisance envelope.

This requirement protects both the theory and its critics. Without nuisance separation, a critic may dismiss every apparent deviation as apparatus error, while a defender may claim every anomaly as CBR. Neither posture is acceptable. The model must state what counts as a realization-sensitive effect and what belongs to ordinary nuisance structure.

The nuisance envelope is therefore part of the jurisdictional machinery. It determines what a result can decide. If the observed behavior falls within the baseline plus nuisance envelope, and if the test has adequate sensitivity, the strong-null consequence may be triggered. If the observed behavior exceeds the envelope in the declared form, the result may support the instantiation. If the nuisance envelope is not controlled, neither verdict is available.

7.4 The Accessibility-Signature Claim

The accessibility-signature claim can now be stated in disciplined form.

In a designated accessibility-sensitive protocol family, if η is independently calibrated, η_c is fixed in advance, ℬ is validated, the nuisance envelope is bounded, the observable burden is declared, and the canonical model predicts a non-baseline response in the critical regime, then the model incurs an empirical burden: the declared response must appear beyond ε_total under detectability-valid conditions, or the instantiated model fails.

This claim is intentionally restricted. It does not state that CBR predicts visible deviations in all ordinary experiments. It does not state that every measurement context must show an accessibility anomaly. It does not state that any deviation near an accessibility-controlled setup confirms CBR. It states only that, in the designated empirical exposure layer, the fixed model must meet the burden it has declared.

The accessibility signature may be strong or weak depending on the assumptions built into the instantiation. A strong-form signature might involve a kink, derivative break, or other nonanalytic response near η_c. A weak-form signature might involve a bounded non-baseline deviation in a specified critical neighborhood. The distinction must be fixed before testing. A model cannot predict a strong-form signature, observe none, and then retroactively declare that a weaker undefined response was always sufficient. Such a move would be a model revision, not a successful prediction.

7.5 Detectability-Valid Conditions

A null result has force only if the test could have detected the predicted effect. Detectability-valid conditions require that the experiment’s sensitivity, calibration, baseline control, nuisance bounding, and sampling structure are sufficient to distinguish the declared CBR response from ℬ within ε_total.

This condition prevents premature falsification. If the apparatus cannot resolve the predicted effect, a null result is not a strong null. If η was not properly calibrated, the test may not have crossed the relevant accessibility regime. If ℬ was invalid, the comparison is inconclusive. If nuisance effects dominate the predicted signal, the test does not adjudicate the model.

But detectability discipline also prevents evasion. Once detectability-valid conditions are satisfied, a null result cannot be dismissed merely because it is inconvenient. If the model’s declared response should have appeared and did not, the model fails.

This is the beginning of model-level accountability. The empirical exposure layer does not merely offer a possible test. It defines the conditions under which the test has authority.

7.6 Proposition: Empirical Exposure Validity

Proposition 2 — Empirical Exposure Validity.

An accessibility-signature test has adjudicative force only if η, η_c, ℬ, the observable burden, the nuisance envelope, ε_total, and the validity gates are fixed before comparison with outcome data.

Proof sketch.

A test can adjudicate a model only if the model’s empirical commitments are specified before the result is known. If η is redefined after the result, the accessibility variable loses independence. If η_c is moved after the result, the critical regime becomes retrospective. If ℬ is adjusted after the result, baseline comparison loses force. If the observable burden is expanded after the result, the model can claim unpredicted anomalies. If the nuisance envelope or ε_total is altered after the result, the threshold for success or failure becomes unstable. Therefore these objects must be fixed before adjudication for the result to have model-level authority.

What this establishes.

This establishes the conditions under which an accessibility-signature test can decide the fate of a fixed instantiation. It gives the test jurisdiction only when the relevant law objects and empirical thresholds have been fixed.

What this does not establish.

This does not establish that the accessibility signature will appear. It does not establish that η is realization-effective. It does not establish that the canonical model is true. It establishes only the preconditions for a result to count as an adjudication rather than as an exploratory observation.

7.7 Empirical Exposure and the Jurisdiction Principle

The empirical exposure layer illustrates the paper’s central principle: a result falsifies only the theoretical object whose fixed commitments entail the failed prediction, and confirms only what its controls establish.

If a validated accessibility experiment observes the declared non-baseline response, the result may support the accessibility-sensitive instantiation, subject to replication and exclusion of nuisance alternatives. It does not prove all of CBR. It does not prove the realization-law thesis. It does not prove that no rival framework can account for the data.

If the experiment produces a strong null, the instantiated model fails. The result does not automatically defeat the representation class or the realization-law thesis. To do that, a further bridge theorem would be required.

The empirical exposure layer is therefore neither a shield nor a universal tribunal. It is a precise adjudication site. Its virtue is not that it decides everything. Its virtue is that it decides something exactly. The exposure layer is not the proof of CBR; it is the point at which CBR stops being merely coherent and becomes answerable.

8. The Jurisdiction of Failure

Failure is not a single undifferentiated verdict. A failed prediction may indicate a defective apparatus, an invalid baseline, a failed instantiation, a failed model class, a failed framework, or a failed thesis. These are not the same. Scientific evaluation requires identifying which theoretical object made the commitment that failed.

This section states the general principle governing that assignment. The principle is not special pleading for CBR. It is a rule of fair theory adjudication. A result should be neither weakened by defenders nor exaggerated by critics. It should be assigned to the strongest theoretical object whose fixed commitments entail the failed consequence under the declared validity conditions.

The jurisdiction of failure is therefore a matter of entailment. What did the object commit itself to? Under what conditions? Were those conditions satisfied? Did the predicted consequence fail? If so, the object whose commitments generated that consequence bears the failure. Objects that did not entail the consequence are not automatically falsified. Objects whose commitments did entail it cannot escape by appeal to broader surviving ideas.

The governing hierarchy is:

local failure → model failure → sector failure → framework failure → thesis failure.

Each upward movement requires a stronger entailment. Failure can travel upward only through a bridge theorem.

8.1 Levels of Failure

A local failure occurs when some part of the test environment fails to realize the declared conditions. This may involve apparatus instability, calibration breakdown, insufficient sampling, failure to access the intended η-domain, or invalid execution of the protocol. A local failure may prevent adjudication altogether.

A baseline failure occurs when ℬ does not adequately represent the standard comparator. If the baseline omits relevant ordinary physics or platform-specific effects, then apparent agreement or disagreement with ℬ may be misleading.

A model failure occurs when a fixed CBR instantiation makes a declared empirical commitment, the validity conditions are satisfied, and the result contradicts that commitment. This is the primary case considered in the strong-null model-death theorem.

A sector failure occurs when a defined sector of a framework fails across its admissible implementations. For CBR, an accessibility-sector failure would require more than one failed test. It would require showing that the accessibility-sensitive sector, as a sector, entails the excluded consequence or cannot produce its declared burden under valid conditions.

A framework failure occurs when every admissible implementation of a framework entails an excluded consequence or violates a necessary structural burden. This is stronger than model failure and requires a framework-null bridge theorem.

A thesis failure occurs at the deepest level. It would require showing that the realization-law thesis itself is unnecessary, incoherent, or already discharged by some other structure such as probability assignment, non-selective decoherence, branching ontology, operational update, or another superior framework.

These levels are ordered but not automatically connected. A model may fail while the sector remains open. A sector may fail while the broader framework remains open. A framework may fail while the broader realization-law thesis remains open. Each step upward must be earned.

8.2 The Jurisdiction-of-Failure Principle

The central rule can now be stated:

A failed prediction has falsificatory jurisdiction only over the theoretical object whose fixed commitments entail the failed prediction.

This rule has two sides.

First, it blocks over-falsification. A strong null against one instantiation does not automatically refute the broad realization-law thesis. Unless the thesis itself entails the excluded prediction, the result has no direct jurisdiction over it. The broader thesis may be pressured, but it is not logically falsified.

Second, it blocks under-falsification. If a fixed instantiation entails a non-baseline response under declared conditions, and those conditions are satisfied, then the instantiation fails when the response does not appear. The model cannot escape by appealing to the fact that the broader representation class remains possible.

The jurisdiction principle is double-edged: it prevents critics from turning model death into framework death without proof, and it prevents defenders from turning framework survival into model survival after failure.

That symmetry is the core of the paper. The jurisdiction principle protects theories from unfair extension of failure while preventing them from evading legitimate failure.

8.3 The Jurisdiction-of-Failure Theorem

Theorem 4 — Jurisdiction-of-Failure Theorem.

Let T be a theoretical object with fixed commitments K(T), and let E be an empirical or structural consequence entailed by K(T) under declared validity conditions V. If V is satisfied and E fails, then the failure has direct jurisdiction over T. The failure has jurisdiction over a broader theoretical object T⁺ only if a bridge theorem shows that T⁺ entails E, or entails a class of consequences that includes E, under the same or appropriately generalized validity conditions.

Proof sketch.

A falsifying result bears on the commitments from which the failed consequence follows. If E follows from K(T), and V is satisfied, then failure of E contradicts T as fixed. A broader object T⁺ is not contradicted unless T⁺ also entails E, or unless T is not merely one member of T⁺ but an unavoidable consequence of T⁺. That unavoidable relation must be established by a bridge theorem. Without such a bridge, the failure of T establishes failure of T, not automatic failure of T⁺.

What this establishes.

This establishes that falsification must be assigned by entailment. It prevents a local null result from being inflated into universal refutation without an argument connecting the local commitment to the broader framework. It also prevents a failed model from surviving by retreating to a broader thesis that did not make the failed prediction.

What this does not establish.

This does not make broad frameworks immune to failure. It does not say that repeated failures are irrelevant. It does not say that CBR can revise itself indefinitely. It says only that the scope of failure must be earned by the scope of the entailment.

8.4 Corollary: No Upward Travel Without a Bridge

Corollary 2 — No Upward Travel Without a Bridge.

A strong null against an accessibility-sensitive CBR instantiation does not automatically falsify canonical CBR, the CBR representation class, or the realization-law thesis unless it is shown that the higher-level object entails the excluded consequence.

This corollary is not a defense of the failed instantiation. The instantiation remains false if its strong-null conditions are satisfied. The corollary concerns only the scope of the verdict.

For example, if a specific implementation fixes η, η_c, ℬ, a nuisance envelope, and an observable burden, then a strong null may defeat that implementation. To defeat the entire accessibility-sensitive sector, one must show that all admissible accessibility-sensitive implementations require the excluded response. To defeat the CBR representation class, one must show that no burden-bearing CBR-form law can avoid the failed consequence while preserving its defining commitments. To defeat the realization-law thesis, one must show that the law-form burden itself is unnecessary or invalid.

The bridge does the work. Without it, failure remains local.

8.5 Corollary: No Downward Rescue from a Broader Thesis

Corollary 3 — No Downward Rescue.

A broader surviving thesis cannot rescue a narrower failed instantiation whose fixed commitments have been contradicted under declared validity conditions.

This corollary prevents evasion. If an accessibility-sensitive CBR instantiation predicts a non-baseline response and a validated strong null occurs, the model is false. The fact that the realization-law thesis remains open does not save it. The fact that another CBR-form model might be constructed does not save it. The fact that the representation class remains meaningful does not save it.

A successor model may be proposed only as a successor. It cannot reinterpret the failed model as successful. It must concede the failure, identify the failed assumption, state new law objects before new testing, and accept a new defeat condition.

8.6 Jurisdiction and Scientific Accountability

The jurisdiction principle is stricter than both overconfident falsification and defensive survival. It requires critics to identify the theoretical object actually contradicted. It requires defenders to accept the death of that object when contradiction occurs.

In the context of CBR, this means that a strong null has real force. It can kill the instantiated model. It may also pressure canonical CBR. Repeated strong nulls across admissible implementations may motivate a framework-null argument. But each step requires additional structure. The paper’s purpose is to make those steps explicit.

Failure is therefore not rhetorical. It is addressable. The question is always: which object made the failed commitment?

9. Strong-Null Model Death

The jurisdiction principle becomes most concrete in the case of a strong null. A strong null is not merely the absence of an observed effect. It is the absence of a declared effect under conditions sufficient to detect it. In the CBR context, a strong null occurs when the accessibility-sensitive instantiation has fixed its law objects and empirical burden, the test satisfies the declared validity conditions, and the observed behavior remains within the baseline class across the relevant accessibility-critical regime.

A weak null may be inconclusive. A failed apparatus may be inconclusive. An invalid baseline may be inconclusive. An uncontrolled nuisance envelope may be inconclusive. But a strong null is different. It means the model had the opportunity to show its declared effect and did not.

A strong null does not weaken the instantiation. It kills it.

That consequence is not rhetorical. It is the meaning of empirical exposure. A model that fixes its law objects, declares a response, passes validity gates, and then fails to produce the response is false as that model. The broader realization-law thesis cannot rescue it. The representation class cannot rescue it. Canonical language cannot rescue it. A failed instantiation may produce a successor model, but it may not survive as itself.

9.1 Definition of a Fixed Accessibility-Sensitive Instantiation

An accessibility-sensitive CBR instantiation is fixed when the following objects have been specified before adjudication:

the physical context C;
the admissible candidate class 𝒜(C);
the realization-burden functional ℛ_C;
the operational equivalence relation ≃_C;
the accessibility parameter η;
the critical accessibility regime η_c;
the designated protocol family;
the baseline comparator ℬ;
the nuisance envelope;
the observable burden;
the total tolerance ε_total;
the validity gates;
and the verdict rule.

These objects define the model under test. If any of them are changed after the result, the model has been revised. Such revision may be legitimate only under the non-evasion rules developed later, but it cannot save the original instantiation.

A model is therefore not fixed merely because it has a general verbal prediction. It is fixed when the objects required for adjudication are specified in a way that permits the result to be classified as success, failure, or inconclusive.

9.2 Strong Null

A strong null occurs when three conditions are satisfied.

First, the model’s empirical burden is fixed. It has declared the expected non-baseline response class, the relevant η-domain or critical regime, the observable burden, and the tolerance structure.

Second, the test is detectability-valid. The calibration of η is adequate, η_c or the relevant critical region is reached, ℬ is valid as the baseline comparator, nuisance effects are bounded, and the experimental sensitivity is sufficient to detect the predicted response beyond ε_total.

Third, the observed behavior remains baseline-class across the declared critical regime. That is, no strong-form or admissible weak-form accessibility signature appears beyond the declared tolerance.

When these conditions hold, the null is not merely absence. It is contradiction of the model’s declared empirical burden.

9.3 The Strong-Null Model-Death Theorem

Theorem 5 — Strong-Null Model-Death Theorem.

If an accessibility-sensitive CBR instantiation fixes C, 𝒜(C), ℛ_C, ≃_C, η, η_c, ℬ, nuisance bounds, observable class, tolerance ε_total, validity gates, and verdict rule, and if the experiment satisfies detectability-valid conditions while producing only baseline-class behavior across the declared critical regime, then the instantiated canonical model is false.

Proof sketch.

The fixed instantiation entails that, under the declared validity conditions, the accessibility-sensitive response must appear in the specified observable class beyond the declared tolerance. Detectability-valid conditions ensure that the experiment is capable of resolving that response if present. If the observed behavior remains within the baseline class across the declared critical regime, the entailed response fails. By the jurisdiction principle, the failure attaches directly to the theoretical object whose commitments entailed the response: the instantiated canonical model. Therefore that instantiation is false.

What this establishes.

This establishes model-level falsification. It gives the accessibility test real force. A strong null does not merely inconvenience the model. It defeats it.

What this does not establish.

This does not automatically establish framework-level failure. It does not by itself refute the CBR representation class. It does not refute the realization-law thesis. It does not prove that probability assignment is outcome selection or that non-selective decoherence is a single-outcome law. Those stronger conclusions require additional bridge arguments.

9.4 What Falls Under a Strong Null

Under the theorem, the fixed accessibility-sensitive instantiation falls. More specifically, the declared mapping from η to the predicted response falls. The specified empirical burden fails. The claim that this model, with this C, this 𝒜(C), this ℛ_C, this η, this η_c, this ℬ, this nuisance envelope, and this observable burden correctly captures the realization-sensitive effect is defeated.

The model may not preserve itself by claiming that η meant something else. It may not move η_c. It may not change the nuisance envelope. It may not redefine the observable class. It may not convert a missing predicted signature into a success. It may not claim that the failed data confirm a subtler version unless that subtler version was fixed in advance.

A failed model may have successors. It may have lessons. It may identify a faulty assumption. But it is not still the same successful model.

9.5 What Does Not Automatically Fall

A strong null does not automatically defeat every higher-level object.

It does not automatically defeat the realization-law thesis, because that thesis does not entail the specific accessibility signature. The thesis states a law-form burden if the single-outcome target is accepted. It does not require this particular η-response.

It does not automatically defeat the CBR representation class, because that class states a structural form for burden-bearing realization laws. A failed instantiation may show that one member of the class is wrong, not that the class is empty or incoherent.

It does not automatically defeat canonical CBR in all possible forms unless the failed instantiation is shown to be unavoidable for canonical CBR as such. That requires a bridge theorem.

It does not automatically prove that decoherence supplies unique realization. It shows only that the tested CBR response failed.

This distinction protects the logic of falsification. It ensures that the model dies where it should, without pretending that its death decides more than it entails.

9.6 Model Death and Program Maturity

The ability of a model to die is not a weakness. It is a condition of seriousness. The empirical exposure layer gives CBR an address for failure. The strong-null theorem states what happens if the address is reached.

This is why the broader law paper cannot be framed as a strategy for survival. Its function is adjudicative. It says that a failed model fails. It also says that a failed model is not the same thing as a failed thesis unless the relevant bridge has been proved.

CBR’s maturity lies in accepting both sides of that result. The instantiation must die if its strong-null conditions are met. The broader law-form question remains open unless the failure has jurisdiction over it.

10. The Framework-Null Standard

The previous section stated the model-level consequence of a strong null. This section asks what would be required for a strong null to reach a broader framework. The answer is a framework-null standard.

A framework null is stronger than an instantiation null. It does not show merely that one fixed model failed. It shows that every admissible implementation of a relevant framework entails the excluded consequence, or an equivalent consequence, under appropriate validity conditions. Only then does a local or class-specific empirical failure rise to framework-level failure.

This standard is demanding by design. It prevents premature over-falsification. But it also gives critics a clear route. To defeat a framework, one must show that the failed prediction was not merely a feature of one implementation, but an unavoidable consequence of the framework’s defining commitments.

A bridge theorem must prove necessity, not resemblance. It must show that the failed consequence is not an artifact of one implementation, but a necessary implication of the framework’s defining commitments.

10.1 Instantiation Null, Sector Null, Framework Null

Three forms of null result should be distinguished.

An instantiation null defeats one fixed model. This is the case described by the Strong-Null Model-Death Theorem.

A sector null defeats a defined sector of a framework. For example, repeated strong nulls across admissible accessibility-sensitive implementations may defeat the accessibility-sensitive sector of canonical CBR if it is shown that the sector requires the excluded response class.

A framework null defeats the broader framework. This requires showing that every admissible implementation of the framework entails the excluded consequence or a consequence equivalent to it.

The distinction matters because a framework may contain multiple admissible implementations. It may contain different contexts C, different admissible classes 𝒜(C), different admissible functional specifications ℛ_C, different operational equivalence relations ≃_C, or different empirical exposure routes. A null against one of these does not automatically defeat all.

At the same time, a framework cannot use this plurality to evade failure. If all admissible implementations entail the failed consequence, then the framework falls with them.

10.2 Definition of a Framework Null

A framework null occurs when the following conditions are satisfied.

First, the relevant framework class is defined. Its admissible implementations must be specified clearly enough that the claim “every admissible implementation” has determinate content.

Second, the excluded consequence class is defined. The null must identify what empirical or structural consequence has been ruled out.

Third, a bridge theorem connects the framework to the consequence. The theorem must show that every admissible implementation of the framework entails the excluded consequence or an equivalent consequence.

Fourth, the empirical or structural exclusion must be valid. If the exclusion is empirical, the relevant tests must satisfy detectability, baseline, nuisance, and calibration requirements. If the exclusion is structural, the proof must be internal to the framework’s defining commitments.

Only when these conditions are met does a null result rise from model-level failure to framework-level failure.

10.3 The Framework-Null Elevation Theorem

Theorem 6 — Framework-Null Elevation Theorem.

A strong null against one accessibility-sensitive CBR instantiation becomes a framework null only if a separate bridge theorem proves that every admissible implementation of the relevant CBR framework class entails the excluded deviation class or an equivalent excluded consequence under the appropriate validity conditions.

Proof sketch.

A strong null directly falsifies the fixed instantiation whose commitments entail the excluded response. A broader framework is falsified only if the framework itself entails that response through all admissible implementations. That entailment is not supplied by the failure of one implementation. It must be established independently by a bridge theorem. If the bridge theorem succeeds, the null has framework-level jurisdiction. If it does not, the null remains at the level of the instantiation or defined sector.

What this establishes.

This establishes the standard for elevating model failure into framework failure. It gives critics a precise route: show that the failed consequence is unavoidable for the framework, not merely present in one model.

What this does not establish.

This does not make frameworks immune to failure. It does not allow CBR to preserve failed instantiations. It does not permit indefinite revision. It says only that framework-level failure requires framework-level entailment.

10.4 Requirements for a Bridge Theorem

A bridge theorem must do real work. It cannot merely assert that the failed model was representative. It must show that the failed consequence follows necessarily from the framework’s defining commitments.

For CBR, such a theorem would need to establish several things. It would need to define the relevant framework class. It would need to specify which implementations are admissible. It would need to show that the accessibility-sensitive response is not an optional feature of one model but a necessary consequence of the framework’s law-form. It would need to show that variations in C, 𝒜(C), ℛ_C, ≃_C, η, η_c, and empirical protocol do not remove the consequence without leaving the framework. It would need to show that any implementation avoiding the excluded consequence either violates a burden, reduces to decoherence, loses probability discipline, becomes non-falsifiable, or exits the framework class.

This is a high standard. It should be high. Framework-level falsification is a stronger claim than model-level falsification and requires stronger support.

A bridge theorem does not say that two models are similar. It says that the failed implication is unavoidable. Similarity may create pressure. Necessity creates jurisdiction.

10.5 Repeated Strong Nulls

Repeated strong nulls matter. They may not automatically constitute a framework null, but they can increase pressure on the framework. If multiple independently valid tests across different admissible implementations all produce baseline-class behavior, the burden shifts. The defender must explain whether the failures attach to distinct instantiations, to a common accessibility assumption, to the canonical functional, or to the broader framework.

Repeated nulls may support a sector-level conclusion even before a full framework null is available. For example, if every plausible accessibility-sensitive implementation fails under strong-null conditions, the accessibility-signature sector may be severely weakened. But even then, the conclusion should be stated precisely. A weakened sector is not automatically a defeated realization-law thesis.

The jurisdiction principle therefore does not make repeated failure irrelevant. It makes repeated failure interpretable.

10.6 Framework Nulls and Non-Evasion

The framework-null standard also prevents illegitimate survival. A defender cannot avoid framework-level pressure by continually declaring failed implementations non-representative after the fact. If an implementation was presented as admissible before testing, and if it fails under strong-null conditions, that failure counts. If many such failures accumulate, the framework owes an explanation.

A legitimate response must identify the failed assumption and state a revised model before new testing. It must not reinterpret failed data as success. It must not change the framework boundaries solely to exclude failed cases. It must not preserve the framework by making it too vague to entail anything.

The standard is therefore balanced. Critics may not treat one model death as framework death without a bridge theorem. Defenders may not use the absence of a bridge theorem as permission for indefinite retreat.

10.7 The Meaning of Framework-Level Failure

If a framework null is established, the result is severe. It means not merely that one implementation failed, but that the framework’s admissible implementations all entail an excluded consequence. At that point, the framework class is false under its own commitments.

For CBR, such a result would not necessarily prove that no realization law exists. It would defeat the relevant CBR framework class. The realization-law thesis could still remain as a broader target unless the framework null also showed that every possible disciplined realization-law form is impossible or unnecessary. That is an even higher burden.

This hierarchy should be preserved even at the strongest levels of failure. Model death, sector death, framework death, and thesis death are different verdicts. Each requires its own bridge.

The framework-null standard therefore completes the upward side of the jurisdiction argument. A strong null kills the fixed instantiation. A bridge theorem may elevate that failure to a framework null. Without the bridge, failure remains local. With the bridge, the framework itself has an address for defeat.

Framework death requires framework-level entailment; anything less is pressure, not verdict.

11. Symmetry of Success and Failure

The jurisdiction principle is symmetrical. CBR may not claim modest failure and maximal success. A theory cannot use one standard of jurisdiction for its defeats and another for its victories.

This symmetry is not a matter of rhetorical fairness alone. It is a structural requirement of disciplined theory evaluation. The same logic that prevents a local strong null from automatically destroying the realization-law thesis also prevents a local positive result from automatically confirming the entire CBR program. A result falsifies only the theoretical object whose fixed commitments entail the failed prediction, and it confirms only what its controls establish.

The previous sections developed the failure side of the principle. A validated strong null against a fixed accessibility-sensitive instantiation kills that instantiation. It does not automatically kill canonical CBR as a whole, the CBR representation class, or the broader realization-law thesis unless a bridge theorem carries the verdict upward. That protection is legitimate only because it is matched by a parallel restraint on success. If an accessibility-sensitive experiment produced the declared non-baseline signature under valid conditions, the result would support the tested instantiation. It would not, by itself, prove all of CBR, establish the finality of the canonical functional, defeat every rival framework, or confirm the realization-law thesis in universal form.

The symmetry principle is therefore a constraint on both defender and critic. Critics may not convert local model death into framework death without proof. Defenders may not convert local model support into framework confirmation without proof. In both directions, the scope of the verdict is fixed by the commitments actually tested.

11.1 The Symmetry Doctrine

The symmetry doctrine may be stated as follows:

A theory may not demand narrow jurisdiction for failure and broad jurisdiction for success.

For CBR, this doctrine is essential. If the program insists that a failed accessibility-signature instantiation does not automatically destroy the realization-law thesis, then it must also concede that a successful accessibility-signature instantiation would not automatically establish the realization-law thesis. The same hierarchy applies in both directions:

accessibility-signature instantiation → canonical CBR → CBR representation class → realization-law thesis.

A result at the lowest level may pressure or support higher levels, but it does not decide them without additional argument. Positive travel upward requires a confirmation bridge just as negative travel upward requires a failure bridge. The bridge may be empirical, mathematical, structural, comparative, or explanatory, but it must exist. Without it, the verdict remains local.

This is not a weakening of CBR. It is the condition under which CBR becomes evaluable without becoming opportunistic. A theory that treats success expansively and failure narrowly has not accepted genuine adjudication. It has accepted only favorable asymmetry.

11.2 Positive Results and Their Jurisdiction

A positive result has jurisdiction over the theoretical commitments actually exposed by the test. In the accessibility-signature case, those commitments include the fixed relation among η, η_c, ℬ, the declared observable burden, the nuisance envelope, ε_total, and the predicted non-baseline response class. If the response appears as declared, and if all validity conditions are satisfied, then the result supports the instantiated model.

The degree of support depends on the strength of the controls. Was η independently calibrated? Was η_c fixed before the result? Was ℬ a valid baseline comparator? Were nuisance effects bounded before adjudication? Was the observable class declared rather than selected after inspection? Did the observed response exceed ε_total in the predicted form? Were ordinary platform effects excluded or bounded? Was the result replicated, or at least robust under reasonable variations of the declared protocol?

Only to the extent that these questions are answered affirmatively does the positive result acquire strong jurisdiction. A suggestive anomaly is not yet confirmation. A post hoc pattern is not yet a prediction. A deviation without nuisance separation is not yet a realization signature. A positive result becomes support only when it lands inside the previously declared burden structure.

Even then, its scope remains limited. It would not prove that the canonical functional ℛ_C is the final law of realization. It would not prove that all admissible CBR contexts behave similarly. It would not prove that rival theories cannot account for the result. It would not prove that the realization-law thesis is universally correct. It would show that one fixed CBR instantiation passed one serious empirical burden.

That conclusion is significant. It is also bounded. The discipline that makes a successful result meaningful is the same discipline that limits its reach.

11.3 Negative Results and Their Jurisdiction

The negative case is governed by the same rule. A null result has force only when the model’s commitments and the test’s validity conditions jointly make the missing response consequential.

If η was not calibrated, the test may not have evaluated the declared accessibility variable. If η_c was not reached, the critical regime may not have been tested. If ℬ was invalid, the baseline comparison may be defective. If nuisance effects were uncontrolled, the result may be indeterminate. If the observable burden was not fixed, the model was not genuinely exposed. In such cases, a null result may be weak, suggestive, or procedurally useful, but it is not a strong null.

If all validity gates are satisfied, however, the consequence changes. A validated strong null against the declared accessibility response falsifies the fixed instantiation. It does not merely weaken the model. It kills the model as that model.

The symmetry doctrine therefore does not dilute falsification. It sharpens it. Weak nulls should not be overstated. Strong nulls should not be softened. A failed instantiation may produce lessons, but it does not survive its own declared failure condition.

11.4 Proposition: Success-Failure Symmetry

Proposition 3 — Success-Failure Symmetry.

For any theoretical object T with fixed commitments K(T), and any empirical consequence E evaluated under declared validity conditions V, a successful observation of E confirms T only to the extent that E is entailed by K(T), discriminative under V, and not absorbed by admissible rival explanations or nuisance structure; a failure of E falsifies T only to the extent that K(T) entails E and V is satisfied.

Proof sketch.

Both confirmation and falsification depend on the same relation among commitments, consequences, and controls. If K(T) entails E under V, then failure of E under V contradicts T. If E is observed under V, the result supports T only if E was a declared consequence of T and if the controls make the result discriminative. In neither direction can the verdict exceed the commitments and controls that generate it.

What this establishes.

This establishes that the jurisdiction principle is not a one-sided protection against falsification. It governs favorable and unfavorable results alike. CBR may not claim more from success than it permits critics to claim from failure.

What this does not establish.

This does not imply that all results are weak. A strong positive result may substantially support an instantiation. A strong null may defeat it. The proposition states only that the scope of either verdict must match the tested commitments.

11.5 Corollary: No Asymmetric Jurisdiction

Corollary 4 — No Asymmetric Jurisdiction.

A theory that restricts the reach of negative results must restrict the reach of favorable results by the same jurisdictional standard.

This corollary is immediate from the success-failure symmetry principle. If failure requires entailment, success requires controlled discrimination. If model failure does not automatically imply framework failure, model success does not automatically imply framework confirmation. If a bridge theorem is needed to move a null result upward, an analogous bridge is needed to move a favorable result upward.

For CBR, this means that a successful accessibility test would be important but bounded. It could support the tested instantiation. It could motivate greater confidence in the accessibility-sensitive sector. It could justify further tests. It could strengthen the case that η-like variables deserve law-level attention. But it would not, by itself, establish the whole program.

The same standard protects CBR from over-falsification and restrains CBR from over-confirmation. That is the symmetry required of a serious law-candidate program.

11.6 Why Symmetry Matters for CBR

CBR operates across layered theoretical objects. That makes symmetry especially important. A positive accessibility result would be tempting to treat as confirmation of the entire program. A negative accessibility result would be tempting to treat as refutation of the entire program. Both moves would be premature without bridge arguments.

The correct discipline is narrower and stronger. A positive result supports the fixed instantiation and may motivate broader framework-level inquiry. A negative strong null defeats the fixed instantiation and may pressure the relevant sector. Repeated results, positive or negative, may justify movement toward broader conclusions. But movement is not automatic. It must be earned.

This gives CBR a stable evaluative posture. The program is not inflated by success and not prematurely erased by failure. It is judged where its commitments have been fixed. That is the only standard under which a candidate law of outcome realization can be both ambitious and accountable.

11.7 Symmetry and Program Maturity

The symmetry of success and failure is a mark of program maturity. A theory that treats success broadly and failure narrowly has not accepted real risk. A critic who treats failure broadly and success narrowly has not accepted fair evaluation. The jurisdiction principle rejects both asymmetries.

For CBR, the result is exact. If the accessibility signature appears in the declared form under valid conditions, the instantiation gains support. If the signature fails to appear under strong-null conditions, the instantiation dies. Neither verdict decides more than its premises allow.

The symmetry doctrine therefore strengthens the paper’s central claim. CBR is not mature because it can interpret every result in its favor. It is mature only if it accepts the same jurisdictional limits in victory that it demands in defeat.

12. Non-Evasion Rule

The jurisdiction principle protects CBR from over-falsification, but it also imposes a severe constraint on CBR itself. A failed instantiation cannot be preserved by semantic migration. If its terms change after the verdict, the original model has not survived; a successor has been proposed.

Semantic migration occurs when the vocabulary of the failed model is preserved while the commitments that made it testable are replaced. The words remain; the law object changes. That is not survival. It is replacement under inherited language.

This section states the non-evasion rule. The rule is necessary because a layered framework can become slippery if lower-level failures are continually absorbed into higher-level abstractions. The realization-law thesis may remain open after an accessibility-sensitive instantiation fails. The CBR representation class may remain formally meaningful. A revised canonical model may later be proposed. But none of those facts saves the failed instantiation. Framework survival is not model survival. Revision is not rescue.

The non-evasion rule is the downward counterpart of the framework-null standard. The framework-null standard prevents critics from pushing model failure upward without a bridge theorem. The non-evasion rule prevents defenders from pushing framework survival downward onto a model whose fixed commitments have failed. Together, they make the jurisdiction principle double-edged.

12.1 The Need for a Non-Evasion Rule

A realization-law program must allow revision. Scientific development often proceeds by failed instantiations, corrected assumptions, improved variables, and sharper experimental designs. But revision becomes evasion when it refuses to concede what failed.

The danger is acute in a theory with many law-defining objects. If η can be redefined after a null result, the accessibility test loses independence. If η_c can be moved after no signature appears, the critical regime was never truly fixed. If ℬ can be altered after comparison, the baseline becomes opportunistic. If the nuisance envelope can be widened after the fact, any missing signal can be hidden. If the observable class can be expanded after inspection, any anomaly can be claimed as support. If the functional ℛ_C can be modified after the verdict, the model no longer had a law-like burden.

These moves are not legitimate refinement. They are semantic migration. The model attempts to keep the prestige of its old exposure while escaping the consequence of its old commitments.

A disciplined CBR instantiation must therefore accept a strict rule: after a strong null, the failed model cannot preserve itself by redefining the objects that made it testable. A successor may be developed. The original model is dead.

12.2 Forbidden Rescue Moves

The non-evasion rule forbids several classes of post-verdict rescue.

A model may not redefine η after the result. The accessibility parameter must be fixed before adjudication. If its definition changes after the data are known, the original accessibility claim has failed or been abandoned.

A model may not move η_c after the result. The critical regime is part of the empirical burden. Moving it after a null result relocates the target.

A model may not alter ℬ opportunistically. The baseline comparator must be declared before testing. If ℬ is changed after the result to manufacture or erase a discrepancy, the comparison loses jurisdiction.

A model may not widen or narrow the nuisance envelope after the result. The nuisance envelope determines what counts as signal, baseline behavior, or inconclusive behavior. It cannot be adjusted to match the outcome.

A model may not expand the observable class after inspection of the data. An unpredicted anomaly may motivate a future hypothesis. It is not confirmation of a model that did not predict it.

A model may not reinterpret a missing predicted response as success. If the model required a declared response under valid conditions and the response did not appear, the model failed.

A model may not treat failed data as confirmation of a revised model unless that revised model was specified before those data were used for adjudication.

The common structure in all these cases is the same: the model tries to survive by changing the meaning of the commitment that failed. The non-evasion rule prohibits that move.

12.3 Permitted Revision

The non-evasion rule does not forbid revision. It distinguishes revision from rescue.

A revision is admissible if it concedes the failed instantiation, identifies the failed assumption or law object, supplies a physically motivated replacement, fixes the revised law objects before new testing, and states a new public failure condition. The revised model may remain within the broader CBR program if it preserves the relevant law-form burdens. But it is a successor model, not the original model rescued by reinterpretation.

For example, a failed accessibility-signature instantiation might motivate reconsideration of how η was operationalized. That can be legitimate if the original η definition is acknowledged as failed or inadequate, if the revised definition is physically motivated independently of the failed result, and if the revised η is fixed before a new test. It is not legitimate if the revised η is selected because it makes the old data appear favorable.

Similarly, a failed nuisance model may justify improved nuisance modeling. But the original verdict must be stated accurately. If the test was invalid because the nuisance envelope was inadequate, the result may be inconclusive rather than a strong null. If the test was valid and the model failed, the nuisance envelope cannot be retroactively widened to erase that failure.

Post-null revision is allowed only as succession, never as rescue.

12.4 The Non-Evasion Revision Theorem

Theorem 7 — Non-Evasion Revision Theorem.

After a strong-null failure, a revised realization-law model is admissible only if it satisfies five conditions: it concedes the failed instantiation; identifies the failed assumption or law object; states the revised C, 𝒜(C), ℛ_C, ≃_C, η, η_c, ℬ, observable burden, or other relevant objects before new testing; does not reuse the failed data as confirmation of the revision; and creates a new public failure condition.

Proof sketch.

A strong null falsifies the fixed instantiation whose commitments entailed the missing response. If the model is revised after that failure, either the revision changes the law object or it does not. If it does not, the original failure remains. If it does, the revised model is no longer the failed instantiation. To avoid post hoc rescue, the revision must acknowledge the failure, identify what changed, fix the new objects before adjudication, avoid treating failed data as confirmatory, and expose itself to a new defeat condition. Otherwise the revision is indistinguishable from retrospective accommodation.

What this establishes.

This establishes the conditions under which CBR may continue after a failed instantiation without evading the failure. It preserves the possibility of legitimate successor models while denying survival to the failed model itself.

What this does not establish.

This does not guarantee that any revision will be successful. It does not immunize the broader framework. It does not permit indefinite retreat. It states only the minimum discipline required for revision to remain scientific rather than evasive.

12.5 Continuity Without Rescue

A successor model may remain continuous with CBR in several ways. It may preserve the realization-law thesis. It may preserve the representation class C → 𝒜(C) → ℛ_C → Φ∗_C. It may preserve the distinction between evolution, registration, and realization. It may preserve probability discipline and decoherence separation. It may preserve the demand for empirical exposure.

But continuity does not erase discontinuity. If η changes, the change must be acknowledged. If ℛ_C changes, the change must be acknowledged. If the observable burden changes, the change must be acknowledged. If the admissible class changes, the new class must be justified. The successor may belong to the same research program, but it is not the same instantiation.

This distinction is essential. A program can learn from failure without denying it. Indeed, that is the only legitimate way for a serious law-candidate program to evolve. Revision is not rescue. A revised model may inherit a research program, but it does not inherit the empirical standing of the model that failed.

12.6 Non-Evasion and the Jurisdiction Principle

The non-evasion rule completes the downward side of the jurisdiction argument. Earlier sections showed that failure cannot travel upward without a bridge theorem. This section shows that survival cannot travel downward without preserving the failed object’s commitments. If a broader thesis survives, that survival does not automatically save the model beneath it.

The rule is double-edged. It protects the broader law-form question from premature erasure, but it forces the fixed model to accept death where its commitments fail. CBR may survive as a research program only by refusing to pretend that failed instantiations survived as predictions.

The result is stricter, not weaker, falsifiability. A failed model fails. A broader thesis may remain open. A revision may be proposed. But the revision must earn its own address for failure.

13. Revision Admissibility Test

The non-evasion rule states what a revision must not do. This section states what a revision must do. A post-failure revision is admissible only if it passes a structured test that distinguishes legitimate theoretical development from retrospective rescue.

The need for such a test is especially acute in a program like CBR, where the hierarchy contains multiple levels. After a failed instantiation, it may be genuinely unclear whether the problem lies in η, η_c, ℬ, the nuisance envelope, the observable burden, the canonical functional, the admissible class, or the broader framework. A revision may therefore be scientifically appropriate. But to remain admissible, it must state what changed, why it changed, what remains continuous, and how the revised model can fail.

The revision admissibility test consists of five gates: continuity, discontinuity, motivation, fixity, and exposure. If any gate fails, the revision is not an admissible successor model. It is either a new theory, an exploratory conjecture, or a post hoc accommodation. Failure at any gate means the revision has no inherited standing from the failed model.

13.1 The Continuity Gate

A revision must first state what remains continuous with the prior framework. Without continuity, the revision is not a revision of CBR but a different theory.

The continuity gate asks which elements of the earlier structure are preserved. Does the revised model retain the realization-law thesis? Does it preserve the CBR representation class? Does it still define C, 𝒜(C), ℛ_C or ≼_C, ≃_C, probability discipline, decoherence separation, parameter fixity, and defeat conditions? Does it preserve the distinction among evolution, registration, and realization? Does it continue to treat probability assignment as distinct from outcome selection? Does it maintain the requirement that a failed instantiation cannot be saved by redescription?

A revision that preserves none of these commitments may still be valuable, but it is no longer a CBR revision. It is a replacement. A replacement may be scientifically superior, but it should not be presented as survival of the failed model.

13.2 The Discontinuity Gate

A revision must also state what has changed. This is just as important as stating what remains.

The discontinuity gate asks which law object failed or was found inadequate. Was the failure in C, 𝒜(C), ℛ_C, ≃_C, η, η_c, ℬ, the nuisance envelope, the observable burden, ε_total, or the verdict rule? Was the defect structural, empirical, or operational? Did the model fail because its assumptions were wrong, because its empirical exposure was invalid, or because its predicted response did not appear under valid conditions?

A revision that does not identify the changed object is not disciplined. It leaves the failed model ambiguous and makes future adjudication unstable. If the functional changed, say so. If the accessibility parameter changed, say so. If the baseline was invalid, say so. If the original model was falsified, say so.

Discontinuity is not an embarrassment. It is the condition of honest revision.

13.3 The Motivation Gate

A revision must be physically motivated rather than outcome-motivated. This is the most difficult gate and the most important.

A physically motivated revision is supported by independent theoretical, mathematical, operational, or experimental reasons. It explains why the prior object was inadequate in a way that does not depend solely on making the failed result appear favorable. An outcome-motivated revision is selected because it rescues the model from the result.

The difference is not always simple, but the burden is clear. If η is revised, the new definition must be justified by physical accessibility structure, not by its ability to move η_c away from the null region. If ℛ_C is revised, the new term or coefficient must be justified by the law’s burdens, not by curve-fitting. If ℬ is revised, the new baseline must reflect omitted ordinary physics, not a desire to recategorize an inconvenient effect.

A revision may be prompted by failure. It may not be justified only by failure. A motivation that exists only because it saves the failed model is not yet a physical reason.

13.4 The Fixity Gate

A revision must fix its law objects before new adjudication. This gate applies the same standard to the successor model that the original model had to satisfy.

The revised model must state its C, 𝒜(C), ℛ_C or ≼_C, ≃_C, η, η_c, ℬ, nuisance envelope, observable burden, ε_total, validity gates, and verdict rule where those objects are relevant. If the revised model does not include an accessibility test, it must state whatever empirical or structural burden replaces it.

The fixity gate prevents endless flexibility. A revision that remains indefinite cannot be evaluated. It may serve as a research direction, but it is not yet a law-candidate instantiation.

13.5 The Exposure Gate

A revision must create a new public failure condition. Without exposure, revision becomes retreat.

The exposure gate asks what would defeat the revised model. If the model predicts a new accessibility response, what is the response class? If it shifts to a different empirical domain, what is the observable burden? If it becomes purely structural, what structural result would count against it? If it modifies 𝒜(C) or ℛ_C, what would show that the modification is arbitrary, circular, probability-violating, or reducible to decoherence?

A revised model that cannot fail is not an admissible successor to a failed empirical instantiation. It may be a conceptual proposal, but it has not regained law-candidate standing.

13.6 Proposition: Revision Admissibility

Proposition 4 — Revision Admissibility.

A post-failure CBR revision is admissible as a successor model only if it passes the continuity, discontinuity, motivation, fixity, and exposure gates. Failure at any gate means that the revision has no inherited evidentiary standing from the failed model.

Proof sketch.

A revision must preserve enough structure to remain within the relevant program; hence the continuity gate. It must identify what changed; hence the discontinuity gate. It must be justified by reasons independent of mere outcome rescue; hence the motivation gate. It must be evaluable before new data are considered; hence the fixity gate. It must be capable of failure; hence the exposure gate. Without these gates, revision collapses into post hoc accommodation. If any gate fails, the proposed revision may still be exploratory, but it cannot inherit the standing of the model whose commitments failed.

What this establishes.

This establishes a disciplined path for theory development after failure. CBR may evolve, but only by making its revised commitments explicit and vulnerable. The gates prevent both premature program death and illegitimate model rescue.

What this does not establish.

This does not guarantee that a successor model remains within CBR. It does not guarantee that a revision is true. It does not erase the failure of the prior instantiation. It establishes only when revision remains admissible rather than evasive.

13.7 Revision as Scientific Continuation

The possibility of revision is not a defect in a law-candidate program. It is part of scientific development. What matters is whether revision is disciplined.

A failed CBR instantiation may teach that the accessibility parameter was improperly operationalized, that the critical regime was misidentified, that the nuisance envelope was incomplete, that the canonical functional was too restrictive, or that the accessibility-signature sector was misguided. Each of these lessons could lead to a successor model. But none permits the failed model to be counted as successful.

The revision admissibility test therefore serves two purposes. It protects CBR from premature program death after one failed instantiation, and it protects scientific evaluation from indefinite model rescue. It allows learning without evasion.

A successor model may inherit a research lineage, but it does not inherit the evidentiary standing of the model that failed.

14. Relation to Rival Theories

The realization-law thesis and the CBR representation class must be situated against rival approaches without overstating what this paper establishes. The present paper does not claim to refute all interpretations of quantum mechanics. It does not claim that every rival must accept the CBR target. It does not claim that CBR has defeated collapse theories, hidden-variable theories, branching ontologies, operational approaches, or decoherence-based accounts. Its claim is narrower: if one accepts single-outcome realization as a physical target requiring law-form treatment, then the burdens developed above apply.

CBR is not claiming jurisdiction over rivals that reject its target. It claims jurisdiction only over theories that accept individual outcome realization as a physical target requiring law-form treatment. Rivals are not defeated merely by refusing CBR’s vocabulary. They are accountable only to the burdens attached to the target they accept.

The governing rule is target-relative accountability:

Rivals are accountable to the target they accept, not to the vocabulary they reject.

Different rival frameworks relate to the target in different ways. Some attempt to answer it. Some reject it. Some dissolve it. Some relocate it into ontology, dynamics, or epistemic practice. The purpose of this section is not to rank those frameworks, but to clarify how the jurisdiction principle applies to them.

14.1 Decoherence-Based Accounts

Decoherence-based accounts explain an indispensable part of the measurement process. They show how environmental entanglement suppresses interference in reduced descriptions, how pointer-like structures become stable, and how effectively classical records emerge. CBR does not deny this. On the contrary, any serious realization-law model must be compatible with the physical role of decoherence.

The question is narrower: does non-selective decoherence itself constitute a single-outcome realization law?

If the answer is yes, the bridge must be stated. One must show how Φ_mix, a non-selective decoherence-compatible channel, entails or replaces the selected realization channel Φ∗_C. If the answer is no, then decoherence remains a theory of suppression, registration, and effective classicality, but not by itself a law of unique realization.

CBR’s decoherence-separation burden should therefore not be read as hostility toward decoherence. It is a demand for role clarity. Decoherence may be necessary for realistic measurement accounts without being sufficient for individual outcome selection.

A successful decoherence-based defeat of the realization-law thesis would have to show more than that decoherence explains record formation. It would have to show that non-selective decoherence, without added selection rule, ontology, or interpretive stipulation, fully accounts for unique realization if that target is accepted.

14.2 Branching Frameworks

Branching frameworks, including Everett-type approaches, relate to the realization-law thesis differently. They may reject the single-outcome target rather than attempt to solve it. On such views, the demand for a unique selected outcome may be misplaced because the physical ontology includes multiple branches or branch-relative outcomes.

This paper does not claim that branching frameworks are refuted. A framework that denies unique realization is not failing to provide a CBR-style selection law; it is rejecting the premise that such a law is needed. The disagreement is therefore at the level of the target, not merely at the level of model construction.

The jurisdiction principle is important here. A failed CBR instantiation would not prove branching correct. A successful CBR instantiation would not automatically refute branching unless the result were shown to be incompatible with the branching framework under its own commitments. Likewise, the existence of branching interpretations does not by itself defeat the realization-law thesis; it offers a different strategy for dissolving or redirecting the single-outcome question.

A serious comparison must therefore ask which target is being evaluated. If unique realization is retained, CBR-like burdens arise. If unique realization is rejected, the burden shifts to explaining why branch multiplicity is the correct account of measurement outcomes and probability.

14.3 Collapse Models

Collapse models accept that standard unitary evolution requires supplementation and introduce modified dynamics to account for outcome definiteness. In that sense, they are closer to CBR than purely operational or branching approaches: they treat outcome selection or definiteness as requiring additional physical structure.

The difference lies in the form of the added structure. Collapse models typically modify dynamics through stochastic or objective collapse mechanisms. CBR, by contrast, formulates realization as constrained selection over an admissible class in context C, governed by ℛ_C or an equivalent ordering. Collapse models make realization dynamical in a particular way. CBR makes realization law-like through admissibility and burden minimization.

This paper does not claim that CBR defeats collapse models. A collapse model may satisfy some realization-law burdens through a different architecture. The proper question is whether the collapse model specifies its domain, candidate structure, probability discipline, decoherence relation, parameter fixity, and failure conditions. If it does, it is a rival law-form candidate rather than an object already excluded.

The jurisdiction principle applies symmetrically. A failed CBR instantiation does not refute collapse models. A collapse-model success does not automatically refute CBR unless it excludes the relevant CBR commitments. A meaningful comparison requires identifying the commitments each model actually exposes.

14.4 Hidden-Variable Theories

Hidden-variable theories address outcome selection by supplementing the quantum state with additional variables that determine, or help determine, the realized outcome. They therefore offer a different answer to the realization-law burden.

From the standpoint of this paper, hidden-variable theories are not automatically rivals at the same representational level as CBR. They may supply selection through underlying ontology rather than through context-indexed burden minimization. The key question is whether they satisfy their own version of the law-form burdens: domain specification, variable dynamics or distribution, probability discipline, relation to decoherence, parameter discipline, and empirical vulnerability.

CBR does not need to deny the coherence of hidden-variable strategies. It asks whether a law of realization can be stated through admissibility and burden structure without adopting the same underlying ontology. If a hidden-variable theory succeeds, it may answer the single-outcome target differently. If CBR succeeds, it may supply a distinct realization-law architecture. Neither outcome is settled by the present paper.

14.5 Operational and Copenhagen-Type Approaches

Operational and Copenhagen-type approaches often decline to state a physical law of individual realization. They may treat the formalism as a tool for predicting observations, with state update representing a change in description, information, or experimental context. Such approaches can be highly effective as practical frameworks.

The realization-law thesis does not deny their practical success. It asks a different question: if one outcome is treated as physically actual rather than merely registered in an observer-relative or operational account, what law-form governs that actualization?

An operational approach may answer by rejecting the question. That is a coherent strategy, but it is not the same as satisfying the realization-law burden. It dissolves or brackets the target rather than providing a selection law for it.

The jurisdiction principle again prevents overclaiming. CBR does not refute operationalism by formulating the realization-law thesis. Operationalism does not refute CBR merely by declining the target. The disagreement lies in whether the target should be treated as a physical question.

14.6 Rival Theories and Jurisdiction

The relation to rival theories reinforces the paper’s central principle. A result confirms or falsifies only what its commitments and controls reach.

A positive CBR accessibility result would not automatically defeat decoherence-based, branching, collapse, hidden-variable, or operational approaches. It would support the tested CBR instantiation unless rivals can also account for the result. A strong CBR null would not automatically confirm any rival. It would defeat the tested CBR model and perhaps pressure related CBR sectors.

Likewise, a rival success does not automatically defeat CBR unless it excludes CBR’s commitments. A rival may solve a different problem, reject the target, or explain the same data through a different mechanism. The adjudication must occur at the level of explicit commitments.

Rivals are not defeated by being different. They are defeated only if they accept the same burden and fail it, or if their own target-dissolution strategy fails. This is the proper jurisdictional standard for comparison.

The present paper is therefore not triumphal. It does not declare CBR victorious over all alternatives. It specifies how CBR and its rivals should be judged when their commitments succeed or fail.

15. What Would Defeat the Broader Realization-Law Thesis?

A broad thesis is credible only if it states what would defeat it. Without a defeat registry, breadth becomes immunity. A defeat registry is what separates a broad thesis from an unfalsifiable refuge.

The realization-law thesis is broader than canonical CBR, but it is not beyond adjudication. It states that if single-outcome realization is treated as a physical event not exhausted by ordinary evolution, probability assignment, observer update, branching description, or non-selective decoherence, then a law-form burden arises. To defeat the thesis, one must therefore attack either the target, the claimed insufficiency of existing structures, or the necessity and neutrality of the proposed burden.

The defeat conditions fall into three broad classes: target defeats, burden defeats, and framework defeats. Target defeats dissolve the question. Burden defeats narrow the law-form claim. Framework defeats kill a CBR class. Rival replacement may defeat CBR while vindicating the broader thesis.

Keeping these classes separate is essential. Defeating canonical CBR is not identical to defeating the realization-law thesis. Defeating the realization-law thesis is deeper.

15.1 Target Defeats

A target defeat attacks the premise that single-outcome realization requires law-form treatment.

One route is probability sufficiency. The thesis would be weakened if probability assignment alone were shown to entail individual realization. This would require more than showing that Born-rule probabilities correctly predict outcome frequencies. It would require showing that the probability rule itself supplies the physical or law-equivalent fact of which outcome is realized in a single case. If probability assignment is sufficient, then the distinction between weighting and selection collapses, and the realization-law burden becomes unnecessary.

A second route is decoherence sufficiency. The thesis would be weakened if non-selective decoherence were shown to entail unique outcome realization without additional ontology, dynamics, or interpretive stipulation. Decoherence already explains suppression, stability, and record formation. The question is whether it also supplies single-outcome selection. A successful decoherence-sufficiency argument would need to show that Φ_mix is not merely a non-selective mixture-like structure but is sufficient for Φ∗_C.

A third route is target dissolution. Branching frameworks may attempt this by denying that there is a unique outcome requiring selection. Operational approaches may attempt it by declining to treat individual realization as a physical event beyond predictive practice. Other frameworks may dissolve the target differently. If the target is successfully dissolved, then the law-form burden does not arise. A theory need not supply a law of unique realization if unique realization is not part of its ontology or explanatory target.

Target defeats are the deepest defeats because they do not merely replace CBR. They remove the problem CBR is built to address.

15.2 Burden Defeats

A burden defeat accepts, at least provisionally, that realization may be a legitimate target but denies that this paper has correctly stated the burdens of a realization law.

The realization-law thesis would be weakened if the burden list were shown to smuggle in CBR-specific assumptions rather than state neutral conditions of law-form discipline. This is an important challenge. The thesis claims that any disciplined realization-law candidate must specify C, 𝒜(C), ≼_C or ℛ_C, ≃_C, probability discipline, decoherence separation, parameter fixity, and defeat conditions. A critic may argue that some of these requirements are not neutral. Perhaps the candidate-class structure already biases the inquiry toward CBR. Perhaps burden minimization is too restrictive. Perhaps operational equivalence is defined in a way that excludes legitimate alternatives.

A burden defeat may also arise from a materially distinct rival. If a realization-law candidate accepts the single-outcome target, preserves probability discipline, avoids reduction to non-selective decoherence, prevents post hoc tuning, states defeat conditions, and yet does not admit a CBR-form or CBR-equivalent representation, then the representation-class claim is weakened. The rival need not defeat the realization-law thesis. It may instead show that CBR is not the natural or exhaustive form of burden-bearing realization law.

A third burden defeat concerns representability. The Representation-Class Theorem depends on finite, compact, regular, or quotient-representable conditions. If the burden ordering ≼_C cannot be represented by a functional ℛ_C without losing physically relevant structure, then the functional CBR form may fail for that candidate. A non-functional ordering may still define constrained selection, but the specific representation Φ∗_C ∈ argmin{ℛ_C(Φ) : Φ ∈ 𝒜(C)} would no longer be generally available.

Burden defeats do not necessarily kill the realization-law thesis. They may instead narrow it, pluralize it, or force CBR to become one candidate among several. That would still be a serious result.

15.3 Framework Defeats

A framework defeat attacks CBR as a framework or class of implementations.

The clearest route is a framework null. As Section 10 argued, a framework null requires more than one failed instantiation. It requires a bridge theorem showing that every admissible implementation of the relevant framework entails the excluded consequence or violates a necessary structural burden. If such a framework null is established, then the relevant CBR framework class fails under its own commitments.

Another route is structural failure. If canonical CBR’s admissibility conditions are shown to be circular, if ℛ_C is shown to be arbitrary or outcome-smuggled, if ≃_C erases meaningful physical distinctions, if probability discipline cannot be maintained, or if decoherence separation collapses, then the relevant CBR framework may fail structurally even apart from a specific empirical null.

A third route is superior law-form replacement. A rival theory may accept the single-outcome target and provide a law-form more compelling than CBR: more physically derived, less assumption-dependent, more empirically grounded, and more tightly connected to existing quantum theory. Such a theory would not defeat the realization-law thesis. It might vindicate the thesis while replacing CBR.

Framework defeats are severe, but their jurisdiction must be stated precisely. A defeat of one CBR framework class is not automatically a defeat of all possible realization-law structures. A replacement of CBR may be a victory for the broader law-form burden rather than a defeat of it.

15.4 Defeat by Non-Neutrality of the Law-Form Burden

Because this paper argues that CBR-form representation naturally follows from general burdens, one of the most serious possible criticisms is that the burdens are not general. If the burden list is merely CBR translated into supposedly neutral language, the argument becomes circular.

This challenge must be taken seriously. The burden list is intended to be minimal: domain, candidate class, admissibility, selection ordering, operational equivalence, probability discipline, decoherence separation, parameter fixity, and defeat conditions. These are presented as requirements of any disciplined realization-law candidate, not as preferences internal to CBR. But a critic may dispute this.

If the critic shows that a serious realization law can avoid one or more of these burdens without becoming vague, circular, probability-undisciplined, decoherence-reductive, or unfalsifiable, then the burden set must be revised. If the critic shows that the burdens force CBR by definition rather than by argument, the Representation-Class Theorem loses force as a general result.

This would not necessarily destroy CBR. But it would reduce the scope of the present paper’s claim. CBR would remain a candidate law-form, not the natural representation of the burden-bearing class.

15.5 Defeat by a Materially Distinct Burden-Satisfying Rival

A materially distinct rival is one of the most productive ways the program could be challenged. Such a rival would accept the seriousness of the realization-law target while rejecting CBR’s representation as the necessary form.

To defeat or narrow the CBR representation-class claim, the rival would need to satisfy the same general burdens: define a physical context, specify the object of selection or realization, preserve probability discipline, distinguish itself from non-selective decoherence, avoid post hoc tuning, provide operational meaning, and state failure conditions. It would then need to show that it does not reduce to the CBR-form representation or any operationally equivalent structure.

If successful, this would not be a trivial objection. It would show that CBR is not uniquely forced by the realization-law burden. It would also improve the field by expanding the set of disciplined candidate laws. A serious rival of this kind would be evidence that the realization-law problem is real enough to support multiple law-form candidates.

The paper should therefore welcome this route as legitimate. The aim is not to prevent rivals. The aim is to require that rivals carry the burdens attached to the target.

15.6 Defeat by Failure of Representability

The Representation-Class Theorem is conditional. It depends on the representability of the burden ordering ≼_C by a functional ℛ_C under finite, compact, regular, or quotient-representable conditions. If these conditions fail, the theorem must be weakened.

A burden ordering may be physically meaningful without being representable by a scalar functional. It may be partial, context-dependent in a non-scalar way, or structured by constraints that cannot be compressed into ℛ_C without loss. In such a case, the candidate may still be a realization-law theory, but not one captured by the functional CBR form.

This would not necessarily defeat constrained selection. It would defeat, or at least narrow, the claim that the functional expression Φ∗_C ∈ argmin{ℛ_C(Φ) : Φ ∈ 𝒜(C)} captures the relevant class.

The proper response is not to hide the condition. The theorem was stated conditionally because representability is a real assumption. If it fails, the scope of the result contracts.

15.7 Defeat by Framework Null

The broader CBR framework class may be defeated by a framework null. This requires a bridge theorem showing that every admissible implementation of the relevant CBR framework entails the excluded consequence or an equivalent consequence. If that bridge is proved and the consequence is empirically or structurally excluded, the framework fails.

For example, if every admissible accessibility-sensitive CBR implementation necessarily entailed a non-baseline response near η_c, and repeated detectability-valid tests excluded that response across the relevant domain, then the accessibility-sensitive sector would face framework-level defeat. If the accessibility-sensitive sector were shown to be necessary to canonical CBR as such, the defeat could travel higher. If canonical CBR were shown to exhaust the CBR representation class, the defeat could travel higher still.

Each movement requires a bridge. Without it, failure remains at the level supported by the entailment.

15.8 Defeat by Superior Law-Form Replacement

A superior theory may defeat CBR without defeating the realization-law thesis. This distinction is important.

If another theory accepts individual outcome realization as a physical target and supplies a better law-form, then the broader thesis may be vindicated while CBR is replaced. Such a theory might derive its selection structure more directly from known physics, specify its variables more cleanly, preserve probability discipline more naturally, distinguish itself from decoherence more sharply, or expose itself to empirical failure more decisively.

That outcome would be a defeat for CBR as the best candidate law-form. It would not be a defeat for the claim that realization requires law-form treatment. Indeed, it may be the opposite: the broader thesis would have generated a successful rival.

This possibility is important because it prevents the paper from identifying CBR with the entire law-form project. CBR may be the present candidate. It is not entitled to be the final answer by definition.

15.9 The Defeat Registry

The defeat registry can now be stated compactly.

The realization-law thesis is weakened or defeated if the single-outcome target is dissolved, if probability assignment alone is shown to entail individual realization, if non-selective decoherence is shown to entail unique realization without supplementation, if the proposed burden list is shown to be non-neutral or unnecessary, if a materially distinct burden-satisfying rival avoids CBR-form representation, if the representability conditions fail, if a framework null defeats the relevant CBR class, or if a superior law-form replaces CBR while preserving the broader target.

These defeat conditions matter because they show that the thesis is not immune. It is broader than any one empirical instantiation, but it remains vulnerable to target-level, burden-level, framework-level, mathematical, and comparative challenge.

The result is the same standard that has governed the paper throughout. A failed instantiation kills the model. A framework null kills the framework. A successful target dissolution kills the need for a realization law. A superior rival may replace CBR. But no result should be made to do more than its premises entail, and no theory should be permitted to keep more than its failed commitments allow.

16. What This Paper Adds to the CBR Program

The prior papers construct CBR. This paper governs its adjudication.

That distinction is the contribution. The CBR sequence develops a candidate law program in stages: it identifies the realization problem, states the burden of a physical outcome-realization law, reconstructs CBR from that burden, fixes a canonical law form, develops probability discipline, specifies empirical exposure, defines execution standards, blocks post hoc rescue, and narrows the space of internal alternatives. Those works construct, constrain, and expose the theory.

This paper adds the rule system by which that construction is to be judged.

Its central contribution is not another prediction, another functional, or another empirical domain. Its contribution is jurisdiction: the assignment of success, failure, revision, rivalry, and defeat to the correct theoretical object. It states what a strong null kills, what it does not kill, what a positive result supports, what it does not support, when a model may be revised, when revision becomes evasion, and what would be required to move from model failure to framework failure.

The contribution of this paper is therefore not a new physical postulate, but a theory of evaluation for realization-law candidates. It specifies the conditions under which a model-level result may be promoted to a framework-level verdict, the conditions under which revision remains admissible, and the conditions under which the broader realization-law thesis itself could be weakened or defeated.

This paper does not make CBR safer. It makes the verdicts against CBR cleaner.

That is why the paper is not a fallback document. It is an adjudication document. It does not say that CBR survives every failure. It says that each failure must be assigned to the object that earned it. A fixed instantiation can die. A sector can fail. A framework can be defeated by a framework null. The broader realization-law thesis can be defeated if the target is dissolved or if the burden is shown unnecessary. But none of these verdicts should be conflated.

The result is a stricter CBR program, not a more insulated one.

16.1 Construction, Exposure, and Adjudication

The CBR program now has three distinguishable layers.

The first is the construction layer. This layer states the law-form burden, reconstructs CBR as a context-indexed constrained-selection structure, defines the admissible class 𝒜(C), introduces the realization-burden functional ℛ_C or ordering ≼_C, preserves operational equivalence ≃_C, and develops probability discipline. Its function is to make CBR a coherent candidate law architecture rather than a verbal interpretation.

The second is the exposure layer. This layer fixes canonical CBR, identifies accessibility η and the critical accessibility regime η_c, defines a baseline comparator ℬ, specifies nuisance bounds, states an observable burden, and exposes the model to strong-null failure. Its function is to make the theory answerable.

The third is the adjudication layer. This is the role of the present paper. It determines what follows when the exposed model succeeds, fails, is revised, or is compared with rivals. Its function is to make judgment exact.

These layers are related, but they are not interchangeable. Construction without exposure risks remaining formal. Exposure without adjudication risks ambiguity. Adjudication without construction would have no object to judge. The present paper completes the sequence by supplying the rules under which CBR may win, lose, revise, compare, and survive without cheating in any direction.

16.2 The Missing Jurisdictional Constitution

The prior CBR works already contain risk. They define admissibility burdens, probability burdens, decoherence-separation burdens, empirical exposure, and strong-null conditions. But a program can define a test and still fail to specify the scope of the verdict. It can say what would count as a null result and still leave unclear whether the null kills an instantiation, a sector, a framework, or the broader realization-law thesis.

This paper supplies that missing jurisdictional constitution.

It distinguishes four theoretical objects: the realization-law thesis, the CBR representation class, canonical CBR, and the accessibility-signature instantiation. It then assigns success and failure by entailment. A result has jurisdiction only over the object whose fixed commitments generate the result. If a model predicts a non-baseline accessibility response under validated conditions and the response does not appear, the model dies. If one wants that death to travel upward, a bridge theorem is required. If one wants a favorable result to travel upward, an analogous confirmation bridge is required.

The paper therefore blocks two symmetrical errors. It blocks critics from turning model death into framework death without proof. It blocks defenders from turning framework survival into model survival after failure. It also blocks defenders from turning local success into universal confirmation. The same jurisdictional standard governs all directions.

This is the core addition: not another CBR claim, but the rules under which CBR claims acquire or lose force.

16.3 How the Paper Repositions Failure

This paper gives failure an address.

In the absence of jurisdictional discipline, a negative result can be mishandled in two opposite ways. It can be overstated: one failed experiment is treated as the death of the entire realization-law question. Or it can be understated: the failed model is protected by retreating to the broader thesis that motivated it. Both moves are invalid.

The strong-null model-death theorem states the lower-level consequence without dilution. If the accessibility-sensitive instantiation fixes C, 𝒜(C), ℛ_C, ≃_C, η, η_c, ℬ, nuisance bounds, observable class, ε_total, validity gates, and verdict rule, and if detectability-valid conditions obtain while only baseline-class behavior appears across the declared critical regime, then the instantiated canonical model is false.

That is model death. It is not inconvenience, pressure, ambiguity, or partial survival. It is the consequence of the model’s own commitments.

But the framework-null standard states the upper-level boundary. Model death becomes framework death only if a bridge theorem shows that every admissible implementation of the relevant framework entails the excluded consequence or an equivalent excluded consequence. Similarity is not enough. Representativeness is not enough. Repeated pressure is not yet verdict. Framework death requires framework-level entailment.

This is the paper’s most important clarification. It makes failure severe where it is earned and bounded where it is not.

16.4 How the Paper Repositions Success

The same discipline applies to success.

A positive accessibility result under validated conditions would be significant. It could support the fixed instantiation. It could strengthen interest in accessibility-sensitive realization structures. It could justify replication and broader tests. But it would not automatically establish the entire CBR program. It would not prove the realization-law thesis. It would not prove that ℛ_C is final. It would not defeat every rival theory. It would confirm only what the controls establish.

This is not caution for its own sake. It is the symmetry required by the jurisdiction principle. A theory cannot use one standard of jurisdiction for defeats and another for victories. If CBR demands that a strong null be confined to the object whose commitments generated it, CBR must also confine a favorable result to the object whose controls support it.

This paper therefore makes CBR less vulnerable to promotional inflation. That is a strength. A law-candidate program gains credibility when it disciplines its own favorable interpretations as strictly as it disciplines hostile readings.

16.5 How the Paper Clarifies Revision

The present paper also supplies the rule of legitimate continuation after failure.

Scientific programs can learn from failed models. A failed instantiation may reveal that η was poorly operationalized, that η_c was misidentified, that ℬ was inadequate, that the nuisance envelope was incomplete, that ℛ_C was too restrictive, or that the accessibility-signature sector was misguided. Any of those lessons may justify a successor model.

But revision is not rescue. A failed model may generate a research lineage, but it does not retain evidentiary standing.

The non-evasion rule blocks semantic migration: the preservation of vocabulary while replacing the commitments that made the model testable. A model may not redefine η after failure, move η_c after failure, change ℬ after failure, widen the nuisance envelope after failure, expand the observable class after inspecting data, or reinterpret a missing prediction as success. If the commitments change, the model has changed.

The revision admissibility test supplies the constructive alternative. A successor model must pass the continuity, discontinuity, motivation, fixity, and exposure gates. It must state what remains, what changed, why the change is physically motivated, how the revised objects are fixed before new testing, and what would defeat the revision. If any gate fails, the revision has no inherited evidentiary standing from the failed model.

This allows CBR to evolve without becoming evasive.

16.6 How the Paper Clarifies Rival Comparison

The present paper also clarifies the comparison between CBR and rival approaches.

The governing principle is target-relative accountability. Rivals are accountable to the target they accept, not to the vocabulary they reject.

A branching framework that rejects unique realization is not failing to provide a CBR-style selection law. It rejects the target. An operational framework that declines the physical realization question brackets the target. A collapse model may accept the target but answer it through modified dynamics. A hidden-variable theory may accept the target but answer it through underlying variables. A decoherence-based account may claim that record formation suffices, but then it must state the bridge from non-selective decoherence to unique realization if it accepts the single-outcome target.

This prevents overclaiming. CBR does not defeat rivals merely by defining its own burden. Rivals are defeated only if they accept the same burden and fail it, or if their target-dissolution strategy fails. Conversely, a CBR failure does not automatically confirm any rival. Rival adjudication must occur at the level of explicit commitments.

This gives the CBR program a more professional comparative posture. It does not need to claim universal jurisdiction over all interpretations. It needs to state its target clearly and accept that different theories may accept, reject, dissolve, or reframe that target.

16.7 How the Paper Makes the Program More Referee-Resistant

The paper strengthens the CBR program by removing several common vulnerabilities.

It prevents the theory from appearing unfalsifiable, because it states that a strong null kills the fixed instantiation.

It prevents the theory from appearing brittle, because it distinguishes model death from thesis death and requires a framework-null bridge for broader defeat.

It prevents the theory from appearing opportunistic, because it limits favorable results by the same jurisdictional standard that limits negative results.

It prevents post hoc rescue, because semantic migration is forbidden and revision must pass admissibility gates.

It prevents overreach against rivals, because accountability is target-relative.

It prevents breadth from becoming immunity, because the paper supplies a defeat registry.

These are not cosmetic additions. They are conditions of serious law-candidate status. A candidate law must not only state its proposed rule. It must state how the rule can be judged, how failure travels, how success travels, how revision is admitted, and what would defeat the broader thesis.

16.8 What This Paper Does Not Add

This paper does not add empirical confirmation. It does not make canonical CBR true. It does not prove that η is realization-effective. It does not prove that the accessibility signature exists. It does not prove universal Born-rule closure. It does not prove that all rival interpretations fail.

Its contribution is narrower and more fundamental. It states the rules of adjudication.

That narrowness is deliberate. A program that proposes a candidate law of outcome realization must be able to answer not only “what is the law?” but also “what would count against it?”, “what would count for it?”, “what exactly would fail?”, “what could be revised?”, “what would make a revision illegitimate?”, and “what would defeat the broader thesis?”

This paper answers those questions. It turns the CBR program from a sequence of law-candidate works into a program with rules of judgment.

16.9 The Final Role of the Paper

The prior works construct CBR. This paper governs its adjudication.

That is the final role. The paper does not make CBR easier to defend. It makes CBR harder to defend illegitimately. It does not make critics less dangerous. It makes criticism more exact. It does not protect failed models. It protects the integrity of the verdict.

The central contribution is therefore not another prediction, but a jurisdictional constitution for the program.

A law-candidate program reaches a higher level of seriousness when it no longer asks merely whether it can be stated, but whether it can be judged. This paper supplies that judgment structure.

17. Conclusion — Failure Clarifies the Law Question

A candidate law becomes serious when it can lose cleanly.

CBR’s maturity is not that it survives every possible result. Its maturity is that it can say which result kills which object.

That is the conclusion of this paper. The CBR program contains layered theoretical objects: the realization-law thesis, the CBR representation class, canonical CBR, and the accessibility-signature instantiation. These objects are related, but they are not identical. They do not make the same commitments. They do not have the same defeat conditions. They should not receive the same verdict automatically.

The governing principle is jurisdictional:

A result falsifies only the theoretical object whose fixed commitments entail the failed prediction, and confirms only what its controls establish.

This principle structures the entire paper. It prevents a strong null against one accessibility-sensitive instantiation from being inflated into automatic refutation of the realization-law thesis. It also prevents the realization-law thesis from being used to rescue the failed instantiation. It prevents favorable results from being inflated into universal confirmation. It prevents failed predictions from being redescribed as subtler successes. It requires every result to be assigned to the object that earned it.

The paper’s claim is not that CBR wins if its experiment succeeds and survives if its experiment fails. The claim is stricter: success and failure must be assigned to the correct theoretical object. A strong null kills the fixed instantiation. A framework null kills the framework. A target dissolution kills the need for a realization law. A positive result supports only what its controls establish.

This is not weaker falsifiability. It is cleaner falsifiability.

A validated strong null against a fixed accessibility-sensitive CBR instantiation has real force. If C, 𝒜(C), ℛ_C, ≃_C, η, η_c, ℬ, nuisance bounds, observable burden, ε_total, validity gates, and verdict rule are fixed, and if only baseline-class behavior appears under detectability-valid conditions across the declared critical regime, then the instantiated model is false. The model cannot survive by redefining η, moving η_c, altering ℬ, changing the nuisance envelope, expanding the observable class, or converting a missing response into hidden confirmation. A failed instantiation may motivate a successor model. It may not survive as itself.

At the same time, a failed instantiation is not automatically a failed framework. A strong null travels upward only through a bridge theorem. To establish a framework null, one must show that every admissible implementation of the relevant framework entails the excluded consequence or an equivalent excluded consequence. Framework death requires framework-level entailment. Anything less is pressure, not verdict.

The same principle governs success. A favorable accessibility result would support the tested instantiation only to the extent that the response was predicted, the controls were valid, the nuisance structure was bounded, and admissible rivals were constrained. It would not by itself prove the entire CBR program, establish universal closure, or defeat all rival frameworks. CBR may not demand narrow jurisdiction for failure and broad jurisdiction for success.

The paper also clarifies revision. A failed model may produce a research lineage, but it does not retain evidentiary standing. Semantic migration is forbidden: the vocabulary of a failed model cannot be preserved while its testable commitments are replaced. Revision is allowed only as succession, never as rescue. A successor model must pass the continuity, discontinuity, motivation, fixity, and exposure gates. It must state what remains, what changed, why the change is physically motivated, how the revised objects are fixed before adjudication, and what would defeat the revision.

This discipline is necessary because the realization-law thesis is broader than any single model. The thesis does not claim that CBR is established physics. It does not claim empirical confirmation. It does not claim that all interpretations must accept unique outcome selection. It states a conditional burden: if individual outcome realization is treated as a physical event not exhausted by ordinary evolution, probability assignment, observer update, branching description, or non-selective decoherence, then a law-form burden arises.

CBR is one attempt to satisfy that burden. It represents realization as context-indexed constrained selection: define C, define 𝒜(C), compare candidates by ℛ_C or ≼_C, quotient by ≃_C, and identify Φ∗_C. Canonical CBR then fixes a more specific law object. The accessibility-signature instantiation exposes that object to empirical risk. The strong-null condition gives that object a possible point of death.

That is the core virtue of the program when properly disciplined. It does not merely propose an answer. It attempts to make the answer vulnerable.

The broader significance is methodological. The measurement problem should not be treated as a single undifferentiated question. Evolution, registration, probability, decoherence, observer update, branching, and realization play different roles. CBR’s target is the realization role: if one outcome becomes actual, what law-form governs that transition? A rival may reject the target, dissolve it, or answer it differently. But if the target is accepted, the burden remains: what selects, what is selected from, what fixes the selection rule, how probability is preserved, how decoherence is not merely renamed, and what would count as defeat?

This paper does not answer all those questions empirically. It does not need to. Its task is prior: to specify the rules under which any answer, including CBR, should be judged.

The final result is an adjudicative architecture:

A strong null can kill an instantiation.
A sector null can weaken or kill a defined sector.
A framework null can kill a framework.
A successful target dissolution can kill the need for a realization law.
A superior rival may replace CBR while vindicating the broader law-form burden.
A positive result can support only what its controls establish.
A revision may continue the research program only if it does not pretend the failed model survived.

Failure clarifies the law question because it forces the program to identify the object under judgment. The question is not whether CBR can avoid failure. The question is whether it can make failure exact. If it can, then CBR has crossed an important threshold: it has become not merely a proposed answer to quantum outcome realization, but a law-candidate program with rules of judgment.

That is the discipline this paper imposes: no result receives more authority than its premises earn, and no theory retains more standing than its failed commitments allow.

Theorem Spine

The theorem spine proceeds by narrowing jurisdiction. The first two theorems establish the burden and representation class for any disciplined realization-law candidate. The third fixes canonical CBR as a particular member of that class. The fourth assigns failure by entailment. The fifth states when a fixed empirical instantiation dies. The sixth states what is required for that death to travel upward. The seventh states how revision may continue without rescuing the failed model. The sequence is therefore not defensive; it is adjudicative.

Theorem 1 — Realization-Law Burden Theorem

If individual outcome realization is treated as a physical target not exhausted by ordinary evolution, probability assignment, observer update, branching description, or non-selective decoherence, then any disciplined candidate law of realization must specify:

C, the physical context in which the realization question is posed;
𝒜(C), the admissible candidate class in that context;
≼_C or ℛ_C, the pre-outcome comparison structure over admissible candidates;
≃_C, the operational equivalence relation;
P_C, the probability discipline required to preserve Born-compatible ensemble structure or declare a controlled deviation;
D_C, the decoherence-separation discipline required to prevent the proposal from merely renaming non-selective decoherence;
F_C, the defeat conditions under which the candidate law fails.

Function.
This theorem establishes the broad law-form burden before canonical CBR is assumed. It states that if the single-outcome realization target is retained as physical, then a theory must do more than state that an outcome occurs. It must specify the context, candidates, comparison rule, equivalence standard, probability relation, decoherence relation, and failure conditions.

Limit.
It does not prove CBR true. It does not require all interpretations to accept the single-outcome target. It establishes only the burden that arises if that target is retained.

Theorem 2 — Representation-Class Theorem

Under finite, compact, regular, or quotient-representable conditions, any realization-law candidate satisfying the burden set of Theorem 1 admits a CBR-form or CBR-equivalent representation:

Φ∗_C ∈ argmin{ℛ_C(Φ) : Φ ∈ 𝒜(C)}.

Here C is the physical context, 𝒜(C) is the admissible candidate class, ℛ_C represents the pre-outcome burden ordering ≼_C where such representation is available, and Φ∗_C denotes the selected realization channel or selected operational equivalence class.

Function.
This theorem bridges the broad realization-law thesis to CBR as a natural representation class. Once a theory specifies context, admissible candidates, comparison, equivalence, probability discipline, decoherence separation, and defeat conditions, then under representability assumptions it takes the form of constrained selection.

Limit.
It establishes representation, not truth. It does not prove that the canonical CBR functional is correct. It does not prove empirical confirmation, universal closure, or final physical adequacy.

Theorem 3 — Canonical Specialization Theorem

Canonical CBR is one fixed specialization of the CBR representation class. It is obtained by fixing, for the relevant context or protocol family:

𝒜(C), the restricted admissible candidate class;
ℛ_C, the realization-burden functional;
≃_C, operational equivalence;
η, the operational accessibility parameter where applicable;
η_c, the critical accessibility regime where applicable;
ℬ, the baseline comparator;
the nuisance envelope;
the observable burden;
ε_total or the relevant tolerance structure;
and the strong-null verdict rule.

Function.
This theorem prevents confusion between CBR as a broad representation form and CBR as a particular testable model. The representation class is broad. Canonical CBR is narrower. The accessibility-signature instantiation is narrower still. Canonical CBR is the point at which the representation class becomes liable: fixed enough to be judged, and under the right conditions, fixed enough to die.

Limit.
It does not establish that canonical CBR is true. It does not establish that η is realization-effective. It establishes only that canonical CBR is a fixed member of the broader representation class.

Theorem 4 — Jurisdiction-of-Failure Theorem

Let T be a theoretical object with fixed commitments K(T), and let E be an empirical or structural consequence entailed by K(T) under declared validity conditions V. If V is satisfied and E fails, then the failure has direct falsificatory jurisdiction over T.

The failure has jurisdiction over a broader theoretical object T⁺ only if a bridge theorem shows that T⁺ entails E, or entails a consequence class that includes E, under the same or appropriately generalized validity conditions.

Therefore:

A failed apparatus test challenges the protocol.
A weak null pressures the model but does not kill it.
A validated strong null falsifies the fixed instantiation.
A sector null falsifies a defined sector only if the sector entails the excluded consequence.
A framework null falsifies the broader framework only if every admissible implementation entails the excluded consequence or an equivalent consequence.
A thesis null defeats the realization-law thesis only if the single-outcome law-form burden is dissolved, shown unnecessary, or shown non-neutral.

Function.
This is the paper’s main original contribution. It gives failure an address. It prevents critics from turning model death into framework death without proof, and it prevents defenders from turning framework survival into model survival after failure.

Limit.
It does not immunize broader frameworks. It says only that broader failure requires broader entailment.

Theorem 5 — Strong-Null Model-Death Theorem

If an accessibility-sensitive CBR instantiation fixes C, 𝒜(C), ℛ_C, ≃_C, η, η_c, ℬ, nuisance bounds, observable class, tolerance ε_total, validity gates, and verdict rule, and if the experiment satisfies detectability-valid conditions while producing only baseline-class behavior across the declared critical regime, then the instantiated canonical model is false.

Function.
This theorem keeps the paper honest. It states that the accessibility test can kill the model. A strong null does not merely weaken the instantiation. It kills it. The broader realization-law thesis cannot rescue the failed instantiation.

Limit.
It does not automatically falsify the CBR representation class or the realization-law thesis. Those stronger conclusions require a framework-null bridge theorem or a target-level defeat.

Theorem 6 — Framework-Null Elevation Theorem

A strong null against one accessibility-sensitive CBR instantiation becomes a framework null only if a separate bridge theorem proves that every admissible implementation of the relevant CBR framework class entails the excluded deviation class or an equivalent excluded consequence under the appropriate validity conditions.

A bridge theorem must prove necessity, not resemblance. It must show that the failed consequence is not merely an artifact of one implementation, but a necessary implication of the framework’s defining commitments.

Function.
This theorem is the key to the broader-law question. It explains why one failed instantiation does not automatically kill the broader framework, while also stating exactly what would be required for framework-level defeat.

Limit.
It does not permit indefinite retreat. Repeated strong nulls may create severe framework pressure. But pressure becomes verdict only when a bridge theorem establishes framework-level entailment.

Theorem 7 — Non-Evasion Revision Theorem

After a strong-null failure, a revised realization-law model is admissible only if it satisfies the following conditions:

It concedes the failed instantiation.
It identifies the failed assumption or failed law object.
It states the revised C, 𝒜(C), ℛ_C, ≃_C, η, η_c, ℬ, observable burden, or other relevant objects before new testing.
It does not reuse the failed data as confirmation of the revision.
It creates a new public failure condition.

Equivalently, the revision must pass the continuity, discontinuity, motivation, fixity, and exposure gates. Failure at any gate means the revision has no inherited evidentiary standing from the failed model.

Function.
This theorem prevents the paper from becoming a claim that CBR can never lose. It distinguishes legitimate succession from post hoc rescue. A failed instantiation may generate a successor model, but it may not survive as itself.

Limit.
It does not guarantee that a revised model is true. It does not protect failed models. It states the minimum discipline required for revision to remain admissible rather than evasive.

Appendix A — Object-Level Registry

This appendix defines the theoretical objects whose distinction governs the paper. The registry is included to prevent the central category error against which the manuscript argues: treating the realization-law thesis, the CBR representation class, canonical CBR, and the accessibility-signature instantiation as if they were one object.

A.1 Realization-Law Thesis

The realization-law thesis states that if individual outcome realization is treated as a physical event not exhausted by ordinary evolution, probability assignment, observer update, branching description, or non-selective decoherence, then a law-form or law-equivalent burden arises.

This thesis is conditional. It does not assert that CBR is true. It does not require every interpretation to accept unique realization. It states what follows if the single-outcome realization target is accepted.

A.2 CBR Representation Class

The CBR representation class is the law-form structure in which realization is represented as constrained selection from a context-indexed admissible class:

C → 𝒜(C) → ≼_C or ℛ_C → Φ∗_C / ≃_C.

This class is broader than canonical CBR. It captures the burden-bearing form of a realization-law candidate under representability conditions.

A.3 Canonical CBR

Canonical CBR is a fixed member of the representation class. It specifies 𝒜(C), ℛ_C, ≃_C, probability discipline, decoherence separation, and, where relevant, η, η_c, ℬ, nuisance bounds, observable burden, and a strong-null verdict rule.

Canonical CBR is the point at which the representation class becomes liable. It is fixed enough to be judged.

A.4 Accessibility-Signature Instantiation

The accessibility-signature instantiation is a specific empirical exposure of canonical CBR in an accessibility-sensitive protocol family. It fixes η, η_c, ℬ, the nuisance envelope, the observable burden, ε_total, validity gates, and verdict rule.

This is the object directly killed by a validated strong null.

A.5 Jurisdictional Rule

No result automatically travels across these objects. Movement upward requires a bridge theorem. Movement downward requires identity of commitments. A broader thesis cannot rescue a failed instantiation; a failed instantiation cannot automatically defeat the broader thesis.

Appendix B — Verdict Ladder

This appendix states the hierarchy of possible verdicts. Its purpose is to prevent local results from being misassigned as broader conclusions.

B.1 Local Failure

A local failure occurs when the experimental or procedural conditions required for adjudication are not satisfied. This may include apparatus instability, failed calibration, insufficient sampling, invalid protocol execution, or failure to access the intended η-domain.

A local failure prevents adjudication. It does not kill the model.

B.2 Baseline Failure

A baseline failure occurs when ℬ does not adequately represent the relevant standard comparator. If ordinary platform effects, detector behavior, decoherence structure, or noise sources are omitted or mischaracterized, then apparent agreement or disagreement with ℬ may be misleading.

A baseline failure may render both apparent deviations and apparent nulls inconclusive.

B.3 Weak Null

A weak null occurs when the predicted response is not observed, but one or more validity conditions fail. η may be insufficiently calibrated, η_c may not be reached, nuisance effects may dominate, sensitivity may be inadequate, or the observable burden may be insufficiently fixed.

A weak null creates pressure or motivates improved testing. It does not kill the model.

B.4 Strong Null

A strong null occurs when the model’s empirical burden is fixed, detectability-valid conditions are satisfied, and the observed behavior remains baseline-class across the declared critical regime.

A strong null kills the fixed instantiation. It does not automatically kill the sector, framework, representation class, or realization-law thesis.

B.5 Sector Failure

A sector failure occurs when a defined sector of a framework fails across its admissible implementations. For CBR, an accessibility-sector failure would require showing that the accessibility-sensitive sector cannot satisfy its declared burden under valid conditions.

Sector failure is stronger than model failure but weaker than framework failure.

B.6 Framework Null

A framework null occurs when every admissible implementation of a relevant framework entails an excluded consequence or violates a necessary structural burden. A framework null requires a bridge theorem proving necessity.

A framework null kills the relevant framework class. It does not automatically kill the broader realization-law thesis unless that framework is shown to exhaust the thesis.

B.7 Thesis Defeat

A thesis defeat occurs when the realization-law thesis itself is undermined. This may happen if the single-outcome target is dissolved, if probability assignment alone entails individual realization, if non-selective decoherence entails unique realization without supplementation, or if the proposed law-form burden is shown unnecessary or non-neutral.

A thesis defeat is the deepest verdict. It attacks the need for a realization law, not merely one CBR implementation.

Appendix C — Bridge-Theorem Standard

This appendix defines the standard required for a result to travel upward from model failure to broader failure.

C.1 Purpose of a Bridge Theorem

A bridge theorem proves that a failed consequence is not merely an artifact of one implementation, but a necessary implication of a broader theoretical object.

Without such a theorem, model failure remains model failure.

C.2 Required Elements

A bridge theorem must specify the broader object to which failure is supposed to travel. It must define the admissible implementations of that object. It must identify the excluded consequence class. It must show that every admissible implementation entails that consequence or an equivalent consequence. It must show that avoiding the consequence requires leaving the framework, violating a burden, becoming circular, losing probability discipline, reducing to decoherence, or abandoning empirical exposure.

A bridge theorem must prove necessity, not resemblance.

C.3 Insufficient Grounds for Upward Travel

The following are insufficient to establish framework-level failure:

one failed implementation;
similarity among implementations;
a representative example without proof of necessity;
repeated failures without a defined sector or framework entailment;
failure of an optional empirical exposure route;
failure of a model whose assumptions are not required by the broader framework.

These may create pressure. They do not by themselves create verdict.

C.4 Framework-Level Entailment

Framework death requires framework-level entailment. If every admissible implementation entails the excluded consequence, and that consequence is validly excluded, the framework fails. If not, the result remains at the level its entailment supports.

Appendix D — Non-Evasion Audit

This appendix states the audit rules for determining whether a post-failure response is legitimate revision or evasive rescue.

D.1 Semantic Migration

Semantic migration occurs when the vocabulary of a failed model is preserved while the commitments that made it testable are replaced.

Semantic migration is not survival. It is replacement under inherited language.

D.2 Forbidden Post-Verdict Moves

A failed instantiation may not be preserved through any of the following moves:

η may not be redefined after the result.
η_c may not be moved after the result.
ℬ may not be altered opportunistically after comparison.
The nuisance envelope may not be widened or narrowed after the result to change the verdict.
The observable class may not be expanded after data inspection.
A missing predicted response may not be reinterpreted as success.
Failed data may not be treated as confirmation of a revised model unless the revised model was fixed before those data were used for adjudication.
The framework boundary may not be changed solely to exclude failed instantiations.

These moves preserve language while replacing commitments. They are inadmissible as rescue.

D.3 Revision Gates

A successor model is admissible only if it passes five gates.

The continuity gate requires the revision to state what remains continuous with the prior program.

The discontinuity gate requires the revision to state what changed.

The motivation gate requires the change to be physically motivated rather than merely outcome-motivated.

The fixity gate requires the revised law objects to be fixed before new adjudication.

The exposure gate requires the revised model to state a new public failure condition.

Failure at any gate means the revision has no inherited evidentiary standing from the failed model.

D.4 Status of Successor Models

A successor model may inherit a research lineage. It may preserve the realization-law thesis, the CBR representation class, probability discipline, decoherence separation, and the distinction among evolution, registration, and realization.

It does not inherit the empirical standing of the model that failed.

Appendix E — Defeat Registry

This appendix states what would weaken or defeat the broader realization-law thesis, the CBR representation class, or a specific CBR framework.

E.1 Target Defeats

Target defeats dissolve the need for a realization law. They include successful arguments that probability assignment alone entails individual realization, that non-selective decoherence entails unique realization without supplementation, or that the single-outcome target is unnecessary because branching, operational, or other frameworks dissolve it.

A target defeat attacks the problem CBR is built to address.

E.2 Burden Defeats

Burden defeats show that the proposed law-form burdens are not neutral, necessary, or adequate. They include arguments that the burden list smuggles in CBR-specific structure, that a serious realization law can avoid the burden set without becoming vague or unfalsifiable, or that a materially distinct burden-satisfying rival avoids CBR-form representation.

A burden defeat narrows or pluralizes the law-form claim.

E.3 Representability Defeats

Representability defeats challenge the transition from burden ordering ≼_C to functional representation ℛ_C. If the relevant ordering cannot be represented by a functional without losing physically meaningful structure, the functional CBR form must be weakened.

This does not necessarily defeat constrained selection, but it narrows the specific representation theorem.

E.4 Framework Defeats

Framework defeats kill a CBR class. They may arise through a framework null, structural failure of admissibility, circularity in ℛ_C, collapse of probability discipline, loss of decoherence separation, or failure of every admissible implementation in a defined sector.

A framework defeat is severe, but it does not automatically defeat every possible realization-law structure.

E.5 Rival Replacement

A superior rival may defeat CBR while vindicating the broader realization-law thesis. If another theory accepts the single-outcome target and supplies a more physically derived, more disciplined, more empirically grounded law-form, then CBR may be replaced as the best candidate.

Such replacement would defeat CBR as a candidate without defeating the law-form burden.

E.6 Defeat Registry Principle

Breadth without a defeat registry is immunity. Breadth with a defeat registry is disciplined scope.

The realization-law thesis remains credible only because it states how it could be weakened or defeated.

Appendix F — Claims Not Made

This appendix records the principal claims the paper does not make. It is included to prevent overreading.

F.1 No Claim of Established Physics

The paper does not claim that CBR is established physics.

It presents CBR as a candidate law-form program and develops the jurisdictional rules by which such a program should be judged.

F.2 No Claim of Empirical Confirmation

The paper does not claim that the accessibility signature has been observed or that CBR has received empirical confirmation.

It states what would follow if a fixed accessibility-sensitive instantiation succeeded or failed under valid conditions.

F.3 No Claim of Universal Closure

The paper does not claim universal closure over all possible theories, interpretations, ontologies, or future realization-law frameworks.

Its closure claims are conditional on target, burden, representability, admissibility, and framework definitions.

F.4 No Protection of Failed Instantiations

The paper does not protect failed models. A validated strong null kills the fixed accessibility-sensitive instantiation.

The broader realization-law thesis cannot be used to rescue that failed model.

The paper should not be read as saying that CBR survives every failed experiment. It says the opposite: a fixed instantiation dies under its own strong-null conditions. What the paper denies is only the automatic promotion of that death to broader framework death without a bridge theorem.

F.5 No Refutation of All Rival Interpretations

The paper does not refute branching frameworks, operational approaches, collapse models, hidden-variable theories, or decoherence-based accounts.

It states that rivals are accountable to the targets they accept and the burdens those targets impose.

F.6 No License for Post Hoc Revision

The paper does not permit CBR to revise law objects after failure and claim continuity of evidentiary standing.

Revision is permitted only as succession, never as rescue.

F.7 No Asymmetric Confirmation Standard

The paper does not allow CBR to claim broad confirmation from local success while demanding narrow falsification from local failure.

Success and failure are governed by the same jurisdictional rule.

Appendix G — Theorem and Principle Registry

This appendix records the major theorem-like results and principles developed in the paper.

G.1 Realization-Law Burden Theorem

If individual outcome realization is treated as a physical target not exhausted by ordinary evolution, probability assignment, observer update, branching description, or non-selective decoherence, then any disciplined candidate law of realization must specify C, 𝒜(C), ≼_C or ℛ_C, ≃_C, probability discipline, decoherence-separation discipline, parameter fixity, and explicit defeat conditions.

G.2 Representation-Class Theorem

Under finite, compact, regular, or quotient-representable conditions, any realization-law candidate satisfying the burden set admits a CBR-form or CBR-equivalent representation:

Φ∗_C ∈ argmin{ℛ_C(Φ) : Φ ∈ 𝒜(C)}.

G.3 Canonical Specialization Theorem

Canonical CBR is one exact specialization of the CBR representation class obtained by fixing 𝒜(C), ℛ_C, ≃_C, η, η_c, ℬ, nuisance envelope, observable burden, and strong-null verdict rule.

G.4 Empirical Exposure Validity

An accessibility-signature test has adjudicative force only if η, η_c, ℬ, the observable burden, the nuisance envelope, ε_total, and the validity gates are fixed before comparison with outcome data.

G.5 Jurisdiction-of-Failure Theorem

A failed prediction has falsificatory jurisdiction only over the theoretical object whose fixed commitments entail the failed prediction. Failure reaches a broader object only through a bridge theorem.

G.6 Strong-Null Model-Death Theorem

If the accessibility-sensitive CBR instantiation fixes C, 𝒜(C), ℛ_C, ≃_C, η, η_c, ℬ, nuisance bounds, observable class, tolerance ε_total, validity gates, and verdict rule, and if the experiment satisfies detectability-valid conditions while producing only baseline-class behavior across the declared critical regime, then the instantiated canonical model is false.

G.7 Framework-Null Elevation Theorem

A strong null against one accessibility-sensitive CBR instantiation becomes a framework null only if a separate bridge theorem proves that every admissible implementation of the relevant CBR framework class entails the excluded deviation class or an equivalent excluded consequence under appropriate validity conditions.

G.8 Success-Failure Symmetry

For any theoretical object T with fixed commitments K(T), and any empirical consequence E evaluated under declared validity conditions V, a successful observation of E confirms T only to the extent that E is entailed by K(T), discriminative under V, and not absorbed by admissible rivals or nuisance structure; a failure of E falsifies T only to the extent that K(T) entails E and V is satisfied.

G.9 No Asymmetric Jurisdiction

A theory that restricts the reach of negative results must restrict the reach of favorable results by the same jurisdictional standard.

G.10 Non-Evasion Revision Theorem

After a strong-null failure, a revised realization-law model is admissible only if it concedes the failed instantiation, identifies the failed assumption or law object, states the revised law objects before new testing, does not reuse the failed data as confirmation, and creates a new public failure condition.

G.11 Revision Admissibility

A post-failure CBR revision is admissible as a successor model only if it passes the continuity, discontinuity, motivation, fixity, and exposure gates. Failure at any gate means that the revision has no inherited evidentiary standing from the failed model.

G.12 Target-Relative Accountability

Rivals are accountable to the target they accept, not to the vocabulary they reject.

G.13 Defeat Registry Principle

A broad thesis is credible only if it states what would defeat it. Without a defeat registry, breadth becomes immunity.

G.14 Governing Jurisdictional Principle

A result falsifies only the theoretical object whose fixed commitments entail the failed prediction, and confirms only what its controls establish.

Appendix H — Verdict Examples

This appendix provides illustrative applications of the jurisdictional framework. The examples are not additional predictions. They are audit cases showing how verdicts should be assigned.

H.1 Example One: η Is Not Calibrated

Suppose an accessibility-sensitive experiment is performed, but η is not independently calibrated. The observed data show no non-baseline response.

Verdict: weak null or inconclusive result.

Reason: the test has not established that the declared accessibility variable was actually controlled or that the relevant η-domain was reached. The result may motivate improved testing, but it does not kill the fixed instantiation.

H.2 Example Two: η Is Calibrated, ℬ Is Valid, Nuisance Is Bounded, and No Signature Appears

Suppose η is independently calibrated, η_c or the declared critical regime is reached, ℬ is valid, nuisance effects are bounded, the observable burden is fixed, ε_total is declared, and the experiment has sufficient sensitivity. The observed behavior remains baseline-class across the critical regime.

Verdict: strong null; instantiation death.

Reason: the fixed model’s declared response should have appeared under the validated conditions. It did not. The instantiated canonical model is false.

Scope: the verdict kills the fixed instantiation. It does not automatically kill the CBR representation class or the realization-law thesis.

H.3 Example Three: Repeated Strong Nulls Across Accessibility-Sensitive Implementations

Suppose several independently valid accessibility-sensitive CBR tests produce strong nulls across different platforms or admissible implementations.

Verdict: severe sector pressure; possible sector failure if a sector-level entailment is established.

Reason: repeated strong nulls increase pressure on the accessibility-sensitive sector. But repeated failures do not automatically constitute a framework null unless it is shown that the sector, as defined, necessarily entails the excluded response class.

Scope: pressure may become verdict only when a bridge theorem connects the repeated failures to the defined sector or framework.

H.4 Example Four: Bridge Theorem Proves All Admissible Implementations Entail the Excluded Signature

Suppose a bridge theorem proves that every admissible implementation of the relevant CBR framework entails a non-baseline accessibility response near η_c, and detectability-valid experiments exclude that response across the required domain.

Verdict: framework null.

Reason: the failed consequence is no longer merely a feature of one model. It is a necessary implication of the framework’s defining commitments.

Scope: the relevant CBR framework fails. The broader realization-law thesis fails only if that framework is also shown to exhaust all disciplined realization-law possibilities or if the single-outcome target is otherwise dissolved.

H.5 Example Five: Positive Accessibility Signature Appears Under Valid Conditions

Suppose η is calibrated, η_c is fixed, ℬ is valid, nuisance effects are bounded, the observable burden is declared, and the predicted non-baseline response appears beyond ε_total in the specified form.

Verdict: support for the fixed accessibility-sensitive instantiation.

Reason: the result lands inside the declared burden structure under valid conditions.

Scope: the result supports the instantiation. It does not automatically prove canonical CBR as a whole, the CBR representation class, or the realization-law thesis. It also does not automatically defeat rival frameworks unless those rivals are shown unable to account for the result under their own commitments.

H.6 Example Six: Branching Framework Rejects the Single-Outcome Target

Suppose a branching framework denies that unique outcome realization is the correct physical target and instead treats branch multiplicity as fundamental.

Verdict: target-level disagreement, not ordinary model rivalry.

Reason: the framework is not failing to satisfy CBR’s selection burden. It rejects the need for that burden. The proper evaluation concerns whether the target dissolution succeeds, not whether the branching framework uses CBR vocabulary.

Scope: CBR does not refute branching merely by stating the realization-law thesis. Branching does not refute CBR merely by rejecting the target. The dispute is target-relative.

H.7 Example Seven: Post-Null Revision Redefines η and Claims the Old Data as Support

Suppose a fixed instantiation fails under strong-null conditions. Afterward, η is redefined so that the old data appear compatible with a revised response, and the revision is claimed as confirmation.

Verdict: inadmissible rescue by semantic migration.

Reason: the vocabulary of the failed model is preserved while the commitments that made it testable are replaced. The revised model was not fixed before the failed data were used for adjudication.

Scope: a successor model may be proposed, but it has no inherited evidentiary standing from the failed instantiation and must face a new public failure condition.