This preprint examines conditional operational limits on controllable return to an earlier event within the same physical history. A protocol retaining receiver and payload records permits an opposite-payload intervention, yielding an acceptance-weighted incompatibility bound under explicitly stated event-identification and calibration-transfer assumptions. For finite classical product loops, the analysis distinguishes normalization under every allowed controller from normalization of one selected loop. Results include an exact simultaneous repair frontier for the clean derangement family at arbitrary alphabet size, rational optimum certificates for arbitrary three-symbol kernels, and linear-program certificates for the intervention-uniform normalization repair radius. Higher-alphabet examples demonstrate that a selected loop can be normalized while both components remain input dependent. For a specified quantum Bell circuit, finite-strength record instruments yield analytical acceptance and reported-error formulas, distinguishing increased acceptance from faithful record-dependent control. A three-category compatibility test retains rejected trials and is extended to empirical calibrations through simultaneous finite-sample uncertainty bounds under declared sampling assumptions. A self-contained canonical metric–scalar application motivated by SMSR provides a conditional temporal-function certificate and identifies the additional estimate needed to connect geometric perturbations with changes in record distributions. The work does not establish a universal prohibition of time travel, demonstrate a physical return channel, or physically validate SMSR. Invariant historical event attachment and gravitational backreaction remain additional physical requirements. The deposit includes English and Hungarian manuscripts with technical supplements, source files, exact certificates, and executable reproducibility checks.
This preprint examines conditional operational limits on controllable return to an earlier event within the same physical history. A protocol retaining receiver and payload records permits an opposite-payload intervention, yielding an acceptance-weighted incompatibility bound under explicitly stated event-identification and calibration-transfer assumptions. For finite classical product loops, the analysis distinguishes normalization under every allowed controller from normalization of one selected loop. Results include an exact simultaneous repair frontier for the clean derangement family at arbitrary alphabet size, rational optimum certificates for arbitrary three-symbol kernels, and linear-program certificates for the intervention-uniform normalization repair radius. Higher-alphabet examples demonstrate that a selected loop can be normalized while both components remain input dependent. For a specified quantum Bell circuit, finite-strength record instruments yield analytical acceptance and reported-error formulas, distinguishing increased acceptance from faithful record-dependent control. A three-category compatibility test retains rejected trials and is extended to empirical calibrations through simultaneous finite-sample uncertainty bounds under declared sampling assumptions. A self-contained canonical metric–scalar application motivated by SMSR provides a conditional temporal-function certificate and identifies the additional estimate needed to connect geometric perturbations with changes in record distributions. The work does not establish a universal prohibition of time travel, demonstrate a physical return channel, or physically validate SMSR. Invariant historical event attachment and gravitational backreaction remain additional physical requirements. The deposit includes English and Hungarian manuscripts with technical supplements, source files, exact certificates, and executable reproducibility checks.
Abstract Decoherent-histories methods identify time-extended alternatives whose diagonal weights may support probabilistic interpretation, while environmental-record approaches ask which alternatives a specified observer can recover. We formulate their intersection as a finite branch-record packing problem generated from one cross-branch construction. A codebook is admissible only if its declared coarse-graining obeys a bounded probability-sum-rule error and its accessible states can be decoded under a specified observer policy with finite error. Uniform reweighting defines a geometric packing number; a communication interpretation additionally requires a preparation instrument. Retrospective resolution is stricter: the base history family is exhaustive, selected histories must cover sufficient physical diagonal weight and be individually recoverable, and the same declared quantum-to-classical measurement channel used for decoding must preserve approximate consistency after histories are refined by its registered outcomes. This measurement-refined condition quantitatively controls the difference between the actual outcome distribution and the normalized diagonal classical-quantum prediction. For uniform branch-record packing and its communication realizations, general converses follow from accessible dimension, fixed outcome count, Holevo-Fano information, and hypothesis testing. Exact models quantify record compression, access, memory, measurement policy, temporal dependence, and shared latent errors. In a jointly realized four-bit benchmark, scalar consistency and recovery admit six histories, whereas direct measurement-refined consistency under the declared local Helstrom instrument admits four at the same tolerances. Finite-sample procedures distinguish held-out recovery achievability, structure-conditional consistency certification, structural converses, independently constructed parameter intervals, and abstention.
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.
We construct a source-matched reference calibration for distinguishing the coherent law h = 0 from the specified added generator h = J/25 in a finite quantum-record model. A complete-carrier transfer bound connects an accessible reference contrast to a delayed target contrast while retaining the original drift and actual law. On reference coverage and measured admission, restricting both hypotheses by the same observed reference band yields a directed target-set separation of at least 0.0071230619 whenever both compatible classes are nonempty. Rival worlds may have different admitted nuisance parameters. The constants are uniform over independently known finite lengths m >= 65, with tag 65, access prefix 1:32 and target deadline 25.02/J. Finite reference preparation and work/source reset satisfy the declared response budgets. Reset acts on the actual joint input and consumed supply, with the retained reference R exactly inert. It does not assign a universal reduced channel to correlated supplies. Under almost-sure conditional resource and supply bounds, the comparison extends to history-dependent acquisition. A prespecified rule, including abstention below the calibration threshold, has each-law unconditional wrong-declaration probability at most 2 exp(-6) + exp(-85/16) < 0.01. This is neither a posterior probability nor an error bound conditional on admission. The statistical step uses standard bounded-martingale concentration. Global target states and specified auxiliary supplies remain resources. Reset requires additional globally conditioned controls and has very large finite costs. The result is a conditional theorem for the two declared laws; it does not establish practical implementation or a unique diagnosis of fundamental collapse. A supporting Lean 4 companion contains 85 theorem declarations and 30 supporting definitions across Calibration, Operations and Risk. It provides checked scalar, sufficient-bound, resource-arithmetic and finite-history risk consequences under explicit premises. The companion has an executed Linux preflight and accepted returned macOS compilation, named-type and transitive-axiom evidence. The quantum constructions and conditional moment, filtration, tower and tail derivations remain written proofs or external premises; this is not an end-to-end formalization of the physical theorem chain. The original checked companion targeted author v0.4 and is carried forward unchanged, with its scope and execution chronology preserved.
This theoretical and computational preprint integrates standard QND measurement and posterior-martingale results with finite-confidence decisions and physically retained observer records. Under a declared quantum instrument and its standard outcome probabilities, the posterior is a bounded martingale on an increasing observation filtration. A precise sufficient identification condition yields asymptotic terminal weights; a binary Gaussian benchmark gives exact mean stopping times, finite-threshold latch probabilities, and a controlled population-transfer bias bound. Version 2.3 is the first public release. It distinguishes accumulated observations from lossy current memory; assumed Born/instrument probabilities from derived consistency results; expected entropy from pathwise ambiguity; continuous confidence endpoints from discrete overshoot and unresolved runs; and Kramers first escape from endpoint readout error. It also clarifies the conditional D18/D19 persistence-selector interface and the separate D1092 finite-resource ledger, with direct attribution to established QND convergence and filtering literature. The companion archive includes the editable manuscript, PDF, equation sources, a fixed validation protocol, executable independent checks, numerical results, a revision ledger, and unchanged historical inputs. Historical simulation summaries are explicitly distinguished from new executions; some older executable sources were unavailable. The new audit includes exact finite-kernel and stopped-posterior checks, Gaussian likelihood-mixture calculations, five neutral and four population-transfer boundary-value cases, and retention/accounting controls. All examples are analytic or synthetic. No laboratory measurements, independent Born-rule derivation, measurement-problem solution, universal physical selector, or new empirical anchor are claimed.
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.
This preprint develops a rigorous framework for certifying open-loop backward signaling from an earlier committed record while distinguishing it from ordinary explanations such as postselection, hidden memory, conditioning, fine-tuning, and measurement dependence. For explicitly defined alternative classes, the paper derives exact finite-alphabet bounds on the observable record distributions, characterizes the corresponding feasible region through three operational cuts, and proves constructive converses showing that every point inside the region admits an ordinary-route realization. It also introduces a scaled gauge of class-relative violation, transport-based robustness bounds, and projection-closed e-processes that provide anytime-valid sequential evidence under optional stopping. Worked examples and exact rational checks illustrate how the framework can be applied in finite-data experiments. The resulting certification is deliberately class-relative: rejection of an audited ordinary-route class does not by itself identify a unique physical mechanism or establish retrocausality in an unrestricted open world. Instead, the framework specifies what must be committed, randomized, retained, audited, and statistically demonstrated before backward signaling becomes a defensible interpretation rather than an artifact of selection or hidden dependence.