AbstractRetained measurement records constrain recoverability, but their formation also depends on the available physical controls. We give exact, constructively attained answers to both questions in two specified models. For a balanced nondemolition qubit process with actual binary observer memories unavailable to the decoder, we determine the maximum recovery compatible with average readout accuracy and pair agreement. The finite-record solution includes its feasible region and a common memory-writing and recovery process, without assuming exchangeability of observed records. Under a complete conditional-pairwise-independence promise at fixed informative accuracy, the optimal coherence has a sharp inverse-square-root asymptotic; fully conditionally independent records instead give exponential decay. Thus identical single-record and pair-record calibrations need not justify the product-law recovery bound. We then fix a logical code in four spin-3/2 systems and sequential diagonal contacts with exact controlled-swap endpoints. Hard budgets for net contact action and added spectral control charge yield an exact peak-excursion frontier within a declared quadratic-plus-cubic control class. A single positive-amplitude preparation jointly attains the record, recovery and occupation requirements, connecting the two results through an exact finite-dimensional optimization. A closed three-record example distinguishes fixed complete records from fixed averaged data. Separately calibrated imperfect contacts admit one-sided finite-error extensions. Together, the results characterize both informational compatibility and control-dependent formation through common attaining apparatuses.Preprint status and related materialsPREPRINT - AUTHOR-SUBMITTED MANUSCRIPT; NOT PEER REVIEWED OR ACCEPTED FOR PUBLICATION. This theoretical and computational work addresses the compatibility of retained binary quantum records with optimized accessible-system recovery, and the control-dependent resources required to form those records in a specified spin encoding. The article provides exact finite-record bounds, attainable recovery and resource frontiers, and calibrated finite-error qualifications. The manuscript has been submitted to Foundations of Physics for journal consideration; this Figshare record is not a journal publication. The technical supplement is included as a second PDF in this same record. Related software, verification code, exact certificates, and selected computational evidence are available separately at https://doi.org/10.6084/m9.figshare.34886079 under the MIT licence. When a journal version of record becomes available, a link to its DOI will be added here.AuthorKent Nimmo; Independent Researcher, Vancouver, British Columbia, Canada; ORCID 0009-0003-8503-8891.
AbstractRetained measurement records constrain recoverability, but their formation also depends on the available physical controls. We give exact, constructively attained answers to both questions in two specified models. For a balanced nondemolition qubit process with actual binary observer memories unavailable to the decoder, we determine the maximum recovery compatible with average readout accuracy and pair agreement. The finite-record solution includes its feasible region and a common memory-writing and recovery process, without assuming exchangeability of observed records. Under a complete conditional-pairwise-independence promise at fixed informative accuracy, the optimal coherence has a sharp inverse-square-root asymptotic; fully conditionally independent records instead give exponential decay. Thus identical single-record and pair-record calibrations need not justify the product-law recovery bound. We then fix a logical code in four spin-3/2 systems and sequential diagonal contacts with exact controlled-swap endpoints. Hard budgets for net contact action and added spectral control charge yield an exact peak-excursion frontier within a declared quadratic-plus-cubic control class. A single positive-amplitude preparation jointly attains the record, recovery and occupation requirements, connecting the two results through an exact finite-dimensional optimization. A closed three-record example distinguishes fixed complete records from fixed averaged data. Separately calibrated imperfect contacts admit one-sided finite-error extensions. Together, the results characterize both informational compatibility and control-dependent formation through common attaining apparatuses.Preprint status and related materialsPREPRINT - AUTHOR-SUBMITTED MANUSCRIPT; NOT PEER REVIEWED OR ACCEPTED FOR PUBLICATION. This theoretical and computational work addresses the compatibility of retained binary quantum records with optimized accessible-system recovery, and the control-dependent resources required to form those records in a specified spin encoding. The article provides exact finite-record bounds, attainable recovery and resource frontiers, and calibrated finite-error qualifications. The manuscript has been submitted to Foundations of Physics for journal consideration; this Figshare record is not a journal publication. The technical supplement is included as a second PDF in this same record. Related software, verification code, exact certificates, and selected computational evidence are available separately at https://doi.org/10.6084/m9.figshare.34886079 under the MIT licence. When a journal version of record becomes available, a link to its DOI will be added here.AuthorKent Nimmo; Independent Researcher, Vancouver, British Columbia, Canada; ORCID 0009-0003-8503-8891.
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.
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 quantum record can have locally accessible populations while its distinguishing phase remains correlated with a distant source. We study this access boundary in a specified finite recording apparatus with a returning, vacuum/one-excitation source. Source-position weights give finite-time cutoff bounds without removing any physical hopping or return coupling. For an initially far-tagged record and its incoherent mixture, every reader in a declared position-preserving local-control class obeys a phase-visibility envelope and a necessary access-time inequality. A separate finite local probe shows why that state-discrimination limit is not an unrestricted limit on distinguishing two dynamical laws: fresh local coherence can reveal a stipulated added dephaser without recovering the old record phase. We construct a bounded, degree-three reader accessing only source positions 1–32. With the initial tag fixed at position 65, exact finite-source arrival certificates and an analytical tail comparison yield recovery uniformly over every finite total source length at least 65. Accessible control faults are charged against the arrived signed-phase norm, while source-moving drift is charged against the full norm. At the fixed deadline 25.02/J, the matched phase-dependent difference between coherent and archive-gated dynamics exceeds 0.005, including the stated simultaneous control faults and four additional absolute response allowances of 0.008 each. Complementary results cover a vacuum-ready source and a stronger endpoint-prepared finite example. The conclusions are conditional on the supplied model, preparations, common realized controls and calibration bounds. They are not a switchable-fundamental-law experiment, a nuisance-independent classifier, an optimal-speed theorem or an end-to-end formal verification. The supporting Lean companion contains 59 declarations in eight modules with accepted returned Mac compilation, type and axiom evidence; physical analytical interfaces remain explicit hypotheses or outside that subset. The deposit files include the main manuscript, technical supplement and full research/reproduction package.
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 operational equivalence and recovery in a twenty-dimensional residual system with a fixed four-sector representation of dimensions 8, 8, 2 and 2. It distinguishes what a declared observation algebra can detect, what a channel preserves, and what a retained classical record makes recoverable. Record-resolved criteria separate useful reversible-error records from unrelated labels and measured-sector records, even when the discarded channel is the same. For a specified coarse-record model, the work identifies exactly recoverable observable algebras and proves an optimal entanglement-fidelity expression on a fixed four-state orbit code. Preparation-aware recovery is then classified over all one-use isometric subspaces in the stated family. An explicit ten-dimensional marker code attains exact recovery under a specified stochastic record where the whole-sector support restriction permits only eight dimensions. Its encoding, nonbaseline marker measurement, and conditional inverse operations remain supplied resources. Scoped Lean evidence verifies the explicit arbitrary-complex-matrix recovery construction and related finite identities; it does not formalize the general complete-positivity/reference framework or optimal-dimension theorem. The recorded-error model is not derived from the companion exchange-timing model, and no protection of its long pulse sequence is claimed.
Continuous quantum error correction depends on which parts of a measurement record remain available to the controller at recovery. We study this temporal access using continuous strategic codes, formulated as open continuous process tensors contracted with causal instruments and conditional recovery. For monitored stabilizer codes, a common-optimal-correction criterion identifies when records can be merged without loss and yields a factorization for separated CSS inference. Terminal decision labels and causal persistent memory carry different costs: five persistent classical states reach the complete-record optimum in a finite-strength counting model, whereas its two-window diffusive counterpart has nine terminal decision labels and requires unbounded memory for exact causal recovery. Uniform lower and constructive upper bounds establish an optimal fidelity deficit of order m−2 for m persistent states in the diffusive model. Counting and diffusive stability bounds translate open-process approximation into guarantees for deployed-controller performance and retained access advantages, quantified by explicit quantizers and model-mismatch curves. The same process--instrument framework connects storage with persistent environments and irreversible noise to spacetime interrogation and record-selected paths for a logical T gate. These results specify which record distinctions recovery needs, the memory cost of approximating them, and the logical protection retained under model error.