Environmental records can be individually accurate while sharing the same errors. This preprint derives a sharp relation between retained Bell coherence, local record accuracy and conditional dependence among designated environmental readouts. For a balanced two-qubit state in the subspace spanned by |00⟩ and |11⟩, the full extremum reduces to a convex problem over R + 1 Hamming-weight probabilities and has an attaining quantum realization with an unobserved remainder. Its inverse gives the least measured conditional total correlation compatible with a CHSH observation and a common upper bound on both conditional errors of every record. The two-record inverse is explicit. At fixed accuracy, a fixed positive Bell excess requires dependence growing at least linearly with record count. Independent monitoring reaches the zero-dependence boundary in a Lindblad dephasing limit. A shared-memory Lindblad process improves record accuracy at constant Bell value and yields an exact onset of detectable dependence. The record contains a standalone PDF preprint and a supporting archive with the PDF, TeX and Markdown manuscript sources, computational supplement, reproducible Python source, calculated data, figures and build instructions. All results concern the stated theoretical models; no experimental dataset is used. The preprint has not undergone journal peer review. AI assistance is disclosed in the manuscript.
Environmental records can be individually accurate while sharing the same errors. This preprint derives a sharp relation between retained Bell coherence, local record accuracy and conditional dependence among designated environmental readouts. For a balanced two-qubit state in the subspace spanned by |00⟩ and |11⟩, the full extremum reduces to a convex problem over R + 1 Hamming-weight probabilities and has an attaining quantum realization with an unobserved remainder. Its inverse gives the least measured conditional total correlation compatible with a CHSH observation and a common upper bound on both conditional errors of every record. The two-record inverse is explicit. At fixed accuracy, a fixed positive Bell excess requires dependence growing at least linearly with record count. Independent monitoring reaches the zero-dependence boundary in a Lindblad dephasing limit. A shared-memory Lindblad process improves record accuracy at constant Bell value and yields an exact onset of detectable dependence. The record contains a standalone PDF preprint and a supporting archive with the PDF, TeX and Markdown manuscript sources, computational supplement, reproducible Python source, calculated data, figures and build instructions. All results concern the stated theoretical models; no experimental dataset is used. The preprint has not undergone journal peer review. AI assistance is disclosed in the manuscript.
Quantum records may be well encoded upstream yet fail to support downstream inference when routing, decoder resources, memory, or comparison channels are restricted. We analyze finite routed quantum-record networks using task-specific Bayes risk. Three exact results provide the constructive core. First, a single Bell-coded pair supplied as the same complete input to GLOBAL and finite-round LOCC-late decoders yields the risk gap qμ/2, where q is pair-delivery probability and μ retained coherence; memory policy determines whether this access is preserved. Second, fixing local binary experiments with error rates 0.20 and 0.30, we determine the entire compatible joint-risk interval [0.15, 0.20] and an attaining decoder with minimax risk 0.20 that does not know the coupling. Third, a binary sufficient-statistic delivery law is attained by a three-record majority compression with nonzero raw risk, yielding a tight physical reconstruction defect. A generated-outcome model gives an exact receiver-availability boundary, while four reduced-description witnesses and continuity bounds delineate when source, state/resource, local-coupling, or clock/memory information is insufficient. The results distinguish record formation, receiver use, memory retention, and task-adequate comparison within standard finite quantum processes. Author manuscript, preprint version 1.0. This manuscript is not a peer-reviewed journal publication. A separate technical Supplement provides complete model definitions, proofs, channel specifications and numerical details. Reproducibility materials are available separately as Software release 1.3 on OSF: https://doi.org/10.17605/OSF.IO/5TDRB. The preprint and reproducibility record are separate, linked scholarly outputs.
A source-inclusive coherence observable is useful only when its measurement resources are admitted. This preprint constructs a bounded local reader for the conserved exchange observable of a specified finite quantum-record apparatus. A degree-three graph uses one independently prepared probe, twenty relays with arbitrary joint states, and finite-duration two-register extraction and full-SWAP interactions. The original apparatus Hamiltonian and an independently added archive-gated process remain active throughout their respective implementations. A prefix-dependent control-frame comparison, symmetry-resolved effect estimate, and explicit gain, phase and finite-slew waveform bounds yield a sufficient response separation greater than 0.005139889 for the stated fixed, fully accessible sixteen-position source and remaining response-error budgets. This is a conditional mathematical result, not measured hardware calibration, a partial-source-access theorem, or a unique diagnosis or derivation of fundamental collapse. The package contains the main manuscript, technical supplement, editable LaTeX, direct numerical reproduction sources, and accepted returned Mac evidence for 56 paper-specific supporting Lean declarations. That subset verifies selected algebra, scalar inequalities and the actual-constant numerical expression; it does not formalize the full physical/continuous-time theorem end-to-end. Separate-session AI review, numerical reproduction and returned kernel evidence are distinguished. Author-owned manuscripts, documentation and mathematical data are CC BY 4.0; newly authored numerical and Lean software is MIT. Predecessor and third-party notices remain unchanged; the reproduction package contains the licence map. No external funding; no competing interests declared. Public preprint v1.0; edition date 18 October 2026; DOI 10.5281/zenodo.23442579.
This preprint studies readout-dependent prediction in a specified classical-quantum continuous-time model with an autonomous classical source and a driven qubit memory. A dynamic model (D) is compared with a scalar-contact model (MATCH) reconstructed to match stationary contact occupancy and both directional switching fluxes. The predictor observes only the qubit memory and the declared classical record j; the target is a future binary signal at an independent exponential horizon. Two distinct results are established by exact interval certificates. At B04, (s,u,v,Omega)=(-1/16,0,0,1), D has lower Brier loss under fixed-Z readout by at least 1/5,000,000, but higher loss under each model's optimal quantum readout by at least 1/2,000,000. This is a commuting conditional-state example. Separately, at nine D-only points with u=1/8, v=0, s in {-1/16,0,1/16}, and Omega in {1/16,1/4,1}, both j sectors have squared normalized commutator norm greater than 10^-8, and the same state's gain over fixed-Z readout is greater than 10^-3. These shared nine-point bounds were extracted after certification. The standard Sylvester readout construction is explicitly attributed. The results are fixed-point statements; they do not establish a continuous parameter region, an unrestricted classical-resource advantage, a causal role of noncommutativity in the B04 reversal, or equal thermodynamic costs. Exact evidence and editable source accompany the preprint in a separate Dataset item. OpenAI ChatGPT/Codex and Anthropic Claude systems assisted the work. Their roles and the limitations of the archived checks are disclosed. AI checks are not human or institutional independent validation. This preprint is not a peer-reviewed journal article. Companion evidence and editable source: https://doi.org/10.6084/m9.figshare.33756607
A durable quantum record, the location of its coherence, and a uniquely actual outcome are different physical questions. We study their separation in a supplied finite-dimensional quantum theory. An explicit, time-independent apparatus couples a system–detector encoding to a controller, a distinct archive, and a finite returning source. A conditional energy penalty suppresses release of the original record without deleting its return coupling. An invariant reduction and a one-sided spectral-gap estimate yield a certified interval with archive occupation above 0.98438, controller-latched occupation above 0.99161, and filled-but-unlatched weight below 2.402 × 10^-7 in one stated design. The same record statistics admit different source-label overlaps and hence different coherence on a specified retained boundary. A conserved product of complementary exchanges accesses that coherence when the finite source is included. Given a calibrated multiregister reader, its finite-duration response separates the coherent apparatus from an independently added archive-gated reduction law, with the added process left active during readout. A conservative example retains a response gap above 0.01717 after separately stipulated one-percent error allowances. The contribution is the finite construction and its quantitative retention, access, and readout interfaces. Quantum carriers, Hamiltonian couplings, trace readout, source preparation, and the reader are supplied; local reader synthesis, empirical calibration, absolute rate selection, and unique-event actualization are not established. Paper code: CFQR-P1 (Complementarity-First Quantum Records — Paper 1). The associated bundle contains the technical supplement, editable LaTeX, numerical checking programs and rational certificates, and selected Lean sources with returned build and axiom-audit evidence. The 39 supporting declarations are partially formalized; eleven recorded type excerpts contain printing elisions. This is not end-to-end formalization, external human peer review, an experimental detection of fundamental collapse, or a derivation of unique-event actualization. Author-owned manuscripts, documentation and mathematical data are CC BY 4.0; author-owned software is MIT, subject to the bundle’s licence map and third-party notices.
Abstract Decoherence suppresses interference, but an observer’s ability to reconstruct a classical pointer value depends on additional resources: distinguishable conditional environmental states, an allowed measurement, sufficient accessible fragments, and sufficiently independent records. We provide an explicit minimal quantum-to-operational bridge that places these requirements in one chain. A system qubit is correlated with conditional environmental qubit states, permitting exact expressions for residual coherence, quantum mutual information, pointer Holevo information, accessible information, and Helstrom discrimination error. Full density-matrix calculations validate the formulas across 280 endpoint and interior cases. An accessible-sector/hidden-bath construction shows that coherence can fall below 2.3 × 10⁻⁵ while the observer’s record information and error remain fixed at 0.0803 bits and 0.4009. Measurement policies shift recovery thresholds: for record overlap 0.8 and error tolerance 0.05, collective or optimized adaptive-local discrimination requires four fragments, a fixed canonical-basis measurement requires six, and repeated one-fragment Helstrom measurements followed by classical decoding require seven. More importantly, records matched at the one-fragment level can have radically different collective behavior. For a binary pointer, the common-mode classical channel has an exact accessible-information ceiling of 1 − h₂(0.1) = 0.5310 bits, while the noncommuting hidden-memory ensemble approaches the same Holevo-information ceiling; matched independent records approach one bit and zero error. Disjoint observer counts and unanimous agreement likewise depend on shared error structure. Finally, declared local measurements induce classical record channels that are subjected to held-out model selection, predictive checks, abstention, and simultaneous finite-sample threshold certification. The resulting framework supplies the validated quantum-to-operational record model used in the companion analysis of operational capacity bounds for distinguishable decoherent histories.
From a finite event record to Bell correlations and their loss under recording A pair is prepared together, read at two separated instruments, and allowed to leave a material record. This paper builds the correlation law from a real source geometry in Artian's Quantum Traction Theory. Its source-to-access equation is pK(r,s∣a,b)=C(KΩ)C[(Πr(a)⊗Πs(b)⊗I)KΩ] Here C is an additive, basis-invariant event capacity, Omega is the normalized orientation-neutral two-channel source, K is a specified record contact, and the projectors select the two instrument outputs. A real quarter-turn and a qualified shared-reference composition generate the readout algebra. Capacity symmetry fixes its quadratic weight. A separately stated capacity-to-frequency condition connects that weight to laboratory counts. The correlation follows before the Bell comparison For a phase-compensated record contact with overlap g between its two normalized record profiles, the construction gives EK(a,b)=−azbz−g(axbx+ayby),0≤g≤1. The intact-source limit is E = -a dot b. The same calculation yields the fixed-setting and optimized Bell responses: S45=2(1+g),Sopt=21+g2. Fresh independent record contacts multiply their overlaps. The paper derives the repeated-contact law, a capacity-based overlap calibration, uncertainty bounds, and a protocol that separates calibration from the Bell observations being judged. A source-first account with an explicit dependency map A1 supplies event-time labels and the clock-angle correspondence; A4 supplies the real dial; A5-X supplies completed-event support, with its inherited A6/A7 conditions. The two-channel preparation, balanced composition, capacity symmetry, frequency bridge, and record coupling are printed separately. Each theorem states exactly which conditions it uses. The Access uncertainty commutator is treated as a distinct inherited algebraic premise, rather than inferred from Bell correlations. When a receiver follows the source Version 2.0 constructs a matched receiver rather than assigning its transformation by name. Preserving every probability of the stated bilinear contact forces its transport to be the conjugate of the source transport, up to an overall phase: ∣rTVTUs∣2=∣rTs∣2for all r,s⟹V=eiαU. A finite set of basis and sum probes certifies this relation. A robust extension converts imperfect probe probabilities into an operator-error bound. Finite clock and shift operations then produce the comparison loop L=M+ω(I−M),ω=e2πi/d. The matched sector cancels the comparison phase while the unmatched sector retains it. This is a joint comparison law; each local readout can remain incompatible. The paper identifies the binary loop's ambiguity, provides additional probes that distinguish it, and transfers the Bell correlations into a complete detector record when the original carrier is consumed. One contact, two observable roles A specified marker contact supplies both the Bell record overlap and a resolved weak-measurement instrument: γK0K1=sinθ,=diag(cos(θ/2),sin(θ/2)),=diag(sin(θ/2),cos(θ/2)). An independent replay executes this instrument on all 40,032 tree records in the public Feng and colleagues archive, reproducing every stored decoder success/failure score. The main five-setting batch contains 32,000 records; the complete archive has six settings. The reproduced job-cluster residual probabilities are p = 0.0188753 and p = 0.0442603, respectively. These diagnose modest tension with the ideal instrument under the stated retrospective covariance. The matched QTT and quantum representations make the same archival predictions, so this replay is not a significance test between them. The package preserves the complete source-first Bell construction and adds finite receiver certificates, physical transport-error bounds, a common-contact derivation, five vector figures, a twelve-item achievements ledger, and offline reproducibility materials. The next operational question is precise: which independently qualified physical contact fixes both the record overlap and the receiver comparison response? Dependencies: QTT Main Book; finite address-capacity counting; real source histories and composition; A1-CHSH spinor character; Observation as Access.