This paper develops a representation of statistical dependence on observer-indexed partial information states and determines what it recovers of causal reasoning. Three levels of result are distinguished. The first is observational. For factorized states in the regime of mutually exclusive alternatives, a correlation forces connectivity through graded couplings, separating families screen, and every screener carries the whole covariance; this is the statistical screening structure associated with Reichenbach’s common-cause principle, located in graphical sufficient conditions, factorization equivalences and covariance identities. The second is conditional on supplied structure. Given directed mechanism histories with independent mechanism weights, settling an attribute is a surgery and the interventional calculus is inherited; given functional mechanism entries, counterfactual evaluation coincides with the functional-model one. A representation theorem shows that hard invalidity together with independent auxiliary weights, constrained and renormalized, represents every exclusive-regime state; the construction is distinct from a directed mechanism history and supplies no direction. The third is a boundary. In the regime of agreeing alternatives, Bell-violating statistics admit no global noncontextual, measurement-independent valuation extending the observed table, while the observational results stand on that table. The framework’s record discipline, stated as a premise, supplies its proposed explanation of why no admissible state carries such a mediator; it adds a restriction on admissible states, not a further statistical exclusion. The construction motivates an account of causal dependence in terms of indexed coupling. Causal orientation remains additional structure that the framework supplies by convention and does not derive.
This paper develops a representation of statistical dependence on observer-indexed partial information states and determines what it recovers of causal reasoning. Three levels of result are distinguished. The first is observational. For factorized states in the regime of mutually exclusive alternatives, a correlation forces connectivity through graded couplings, separating families screen, and every screener carries the whole covariance; this is the statistical screening structure associated with Reichenbach’s common-cause principle, located in graphical sufficient conditions, factorization equivalences and covariance identities. The second is conditional on supplied structure. Given directed mechanism histories with independent mechanism weights, settling an attribute is a surgery and the interventional calculus is inherited; given functional mechanism entries, counterfactual evaluation coincides with the functional-model one. A representation theorem shows that hard invalidity together with independent auxiliary weights, constrained and renormalized, represents every exclusive-regime state; the construction is distinct from a directed mechanism history and supplies no direction. The third is a boundary. In the regime of agreeing alternatives, Bell-violating statistics admit no global noncontextual, measurement-independent valuation extending the observed table, while the observational results stand on that table. The framework’s record discipline, stated as a premise, supplies its proposed explanation of why no admissible state carries such a mediator; it adds a restriction on admissible states, not a further statistical exclusion. The construction motivates an account of causal dependence in terms of indexed coupling. Causal orientation remains additional structure that the framework supplies by convention and does not derive.
A Kernel-Role Determinacy Theorem for Bell-Witness Fixation, No-Signaling, and Tensor-Level Compatibility This manuscript develops a fixed-domain AASC analysis of Bell-nonlocal quantum entanglement as a theorem of reusable witness determinacy. It does not introduce hidden variables, modify quantum mechanics, derive Hilbert-space formalism from below, or propose a new signaling mechanism. Instead, it asks a prior structural question: once a Bell-type operational family is used as the same non-degenerate witness across settings, lawful transformations, retained records, comparison, and later classification, what admissible same-domain standing form is forced? The governing claim is that AASC is not an optional interpretive overlay on physics. Once an operational Bell family is asserted as a determinate reusable witness, admissibility, standing, reference, and irreversibility are already active as minimal necessity conditions of same-witness objecthood. Target instantiation therefore carries governance occupancy: an alleged determinate Bell witness with no admissible governance realization is not an empty alternative, but a refusal or retyping of the target. The manuscript defines finite operational Bell objects with explicit setting carriers, outcome families, channel/interface data, standing-token valuations, continuation and report/reuse structure, comparison profiles, and act-time status. It then defines object-indexed query sorts, dependent response families, exactly recoverable operational simulations, lawful Bell groupoids, six governance-effect functors, and target-active extensional governance equivalence. The result is a typed interface in which arbitrary native formalisms can be compared by their target-bearing governance effects rather than by their internal syntax. The central Bell-specific theorem states that every same-target candidate-admissible Bell-governance construction is forced component by component into the certified boundary-compatible standing form on the complete target-active practice. Candidate admissibility does not assume the canonical form at the outset. Instead, target occupancy, lawful transport, standing-flow exclusion, compatibility certification, coordinate-deviation exhaustion, and componentwise closure force exact target-bearing realization and governance equivalence to the canonical representative CP∗C^{*}_{P}CP∗. The target-induced governance quotient therefore has exactly one element. The Bell carrier is treated as a compatible empirical model on a finite measurement cover. Bell-local completion is identified with the existence of a global section, and Bell nonlocality is the obstruction to such a section. The manuscript separates operational marginal invariance, absence of controllable communication, and exclusion of same-domain standing transport. No-signaling is therefore preserved without retyping Bell nonlocality as superluminal communication, metric transport, distant repair, or hidden standing transfer. The finite-dimensional quantum specialization uses the standard bipartite tensor-product and local-POVM carrier. Every separable realization in that carrier is Bell-local; therefore, if the fixed Bell-nonlocal empirical model has such a finite-dimensional quantum realization, every realizing state in that carrier is entangled. Post-quantum Bell-nonlocal no-signaling models remain within the general witness theorem but outside the quantum-entanglement corollary. The accompanying Lean 4 development, release v0.8.0, directly verifies the finite Bell-side witness carrier: denominator-32 vector/Born weights, structural no-signaling, CHSH numerator 808080, all sixteen deterministic local extrema, finite denominator-32 Bell-local-envelope exclusion, and conditional endpoint routing. Its direct witness certificate is vectorBorn_flagship_spine, and its deepest released endpoint is reasonableDeepestFiniteEntanglement_spine. The manuscript-level typed governance interface, empirical lawful groupoid, compatibility equivalence, coordinate-deviation exhaustion, completed role collapse, candidate-to-canonical derivation, and finite-dimensional quantum specialization are not attributed to the released Lean layer. This paper is the Bell-witness member of the paired AASC quantum determinacy arc. The record-side manuscript, Admissible Record Construction in Physically Non-Selective Quantum Regimes, fixes when local physical record occurrences stand as the same evidential record objects. The present manuscript fixes when the Bell operational family sampled by such records stands as the same reusable witness. The paired endpoint is therefore: record-role fixation+Bell-witness compatibility.\text{record-role fixation} + \text{Bell-witness compatibility}.record-role fixation+Bell-witness compatibility. The manuscript is classificatory and eliminative rather than mechanistic. It does not claim that AASC generates the Bell probabilities or supplies a hidden physical influence. Its claim is that reusable Bell-witness determinacy strongly constrains how Bell-nonlocal correlations may be coherently classified on a fixed domain: not as independently complete local states later connected by a mechanism, not as Bell-local hidden-variable value assignments, not as superluminal signaling, and not as same-act repair, but as boundary-level compatibility carried by one standing-preserving Bell witness.
Reichenbach's principle asserts that if two observed variables are found to be correlated, then there should be a causal explanation of these correlations.Furthermore, if the explanation is in terms of a common cause, then the conditional probability distribution over the variables given the complete common cause should factorize.The principle is generalized by the formalism of causal models, in which the causal relationships among variables constrain the form of their joint probability distribution.In the quantum case, however, the observed correlations in Bell experiments cannot be explained in the manner Reichenbach's principle would seem to demand.Motivated by this, we introduce a quantum counterpart to the principle.We demonstrate that under the assumption that quantum dynamics is fundamentally unitary, if a quantum channel with input A and outputs B and C is compatible with A being a complete common cause of B and C, then it must factorize in a particular way.Finally, we show how to generalize our quantum version of Reichenbach's principle to a formalism for quantum causal models and provide examples of how the formalism works.
This is Paper 142 in the Anaxiomatic Mechanics / pq-Spacetime stack. It develops a finite mechanical account of quantum entanglement within pq-spacetime. Entanglement is identified with the persistence of a non-factorable family of admissible future histories. Two measurement regions can therefore appear as separate local systems in emergent spacetime while still remaining projections of one joint finite closure problem. Bell inequality violation follows because the joint outcomes are not generated by two independent local completion families. No-signalling is nevertheless preserved because complete changes to a distant measurement boundary do not alter the local marginal outcome weights. The paper establishes the Entanglement Closure Theorem and distinguishes microscopic non-factorability from observable entanglement after coarse-graining into stable measurement records. It also gives an explicit minimal singlet construction using two opposed history fibers carrying the relevant four-phase weights. The resulting finite ledger is antisymmetric, nonseparable, and exactly balanced at each local wing. Complete changes of basis on the distant side preserve those local marginals. Using the previously derived Hilbert-space and beta-Dirac bridges of pq-spacetime, the paper recovers the familiar spinor overlap law, the quantum singlet correlation, the maximal Bell-CHSH value, monogamy of maximal entanglement, and decoherence through environmental boundary enlargement. The analysis also explains why no preferred measurement ordering is required and why entanglement remains compatible with relativistic causality. The resulting picture is direct. Entangled systems do not exchange superluminal messages, carry classical answer sheets, or require a force acting across space. Their local outcomes arise from one shared finite admissibility structure whose joint correlations are nonlocal while its controllable local statistics remain causal. Entanglement is therefore physically real, nonclassical, and nonlocal in correlation, but not a signalling mechanism.
Reichenbach's principle asserts that if two observed variables are found to be correlated, then there should be a causal explanation of these correlations.Furthermore, if the explanation is in terms of a common cause, then the conditional probability distribution over the variables given the complete common cause should factorize.The principle is generalized by the formalism of causal models, in which the causal relationships among variables constrain the form of their joint probability distribution.In the quantum case, however, the observed correlations in Bell experiments cannot be explained in the manner Reichenbach's principle would seem to demand.Motivated by this, we introduce a quantum counterpart to the principle.We demonstrate that under the assumption that quantum dynamics is fundamentally unitary, if a quantum channel with input A and outputs B and C is compatible with A being a complete common cause of B and C, then it must factorize in a particular way.Finally, we show how to generalize our quantum version of Reichenbach's principle to a formalism for quantum causal models and provide examples of how the formalism works.
Quantum mechanics supplies outcome probabilities through the Born rule, while measurement physics describes how interactions, decoherence, amplification, and environmental encoding produce records. We reformulate quantum admissibility around the distinction between quantum support, Born probability, operational record support, and realized record. The reformulation is motivated by a no-go result for a legacy strong ansatz in which Born probabilities are multiplied by an independently specified scalar admissibility factor: independence from the Born distribution together with arbitrary coarse-graining consistency forces that factor to be uniform, while the corresponding positive-operator construction reduces to an ordinary quantum state update. Rather than replacing this failed weighting by an unstructured support predicate, we connect record support explicitly to existing quantum-to-classical formalisms. Quantum-Darwinist redundancy, classically accessible information, quantum discord, and distance to spectrum-broadcast structure provide a context-dependent operational record profile from which prospectively specified support criteria can be constructed without modifying the Born rule. We also show why Bell correlations cannot supply the missing content of a binary support relation: a non-product joint support set is shared by classically correlated systems, while generic Bell-violating distributions may have full Cartesian support and differ only in their probabilityweights. Bell and no-signaling therefore constrain any future probability-modifying extension but do not establish relational realization as a new physical quantity. The resulting framework has three levels: a conceptual grammar, an operational record-support layer entirely within standard quantum theory, and a distinct strong route requiring independently predicted deviations from the best standard quantum-plus-apparatus model. The principal claim is consequently a boundary result: objective record support can be operationalized without a second probability law, whereas the natural scalar attempt to convert such support into probability reweighting is stronglyconstrained.
A causal model is an abstract representation of a physical system as a directed acyclic graph (DAG), where the statistical dependencies are encoded using a graphical criterion called ' d -separation'. Recent work by Wood and Spekkens shows that causal models cannot, in general, provide a faithful representation of quantum systems. Since d -separation encodes a form of Reichenbach's common cause principle (RCCP), whose validity is questionable in quantum mechanics, we propose a generalized graph separation rule that does not assume the RCCP. We prove that the new rule faithfully captures the statistical dependencies between observables in a quantum network, encoded as a DAG, and reduces to d -separation in a classical limit.