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 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.
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.
A calibrated quantum-record test can require both a global target state and a commoncomplete reader input, neither of which is certified by accessible marginal data. We construct theseinputs for the specified source-tagged model at an independently known source length m= 65. Thepublished joint-input work/source reset is followed by 37 finite swaps with fresh reader qubits and a69-slot target sequence: coherent work-label creation, globally conditioned tag injection, and 64neighboring source transfers. The control-only sequence prepares the exact far-target cat or itssigned partner with the required common phase. A retained random sign produces the comparisonmixture without postselection. Full-state comparisons include consumed supplies and arbitraryinitial correlations with exactly inert retained memory. The original clock, holding terms, sourcehopping, both port directions and either actual law, h= 0 or h= J/25, remain active throughout.The constructed initialization fits the existing 1/4000 allowance; target delivery has sufficienterror below 0.004816692 <1/200. With separate complete-interval generator and endpoint-effectallowances, each target response differs from its nominal value by less than 0.007816692 <1/125.The same reader initialization supplies the published reference-preparation interface. The resultis a conditional single-delivery construction: it consumes 37 fresh pure reader qubits, requirespreparation access through site 65 and additional globally conditioned controls, and inherits anextremely costly reset. Application to repeated acquisition still requires almost-sure conditionalsupply and error bounds; practical feasibility and uniform passing power are not established.
A small quantum arrangement — a reader qubit Q₁ coupled to a remainder qubit Q₂ through one fixed gate, with declared operations on Q₁ only — has access to some distinctions of the remainder and not to others. This manuscript follows that arrangement through fourteen research units — thirteen with a model, exact proofs and an executable checker (with certified interval enclosures wherever a propagation is read), and one, the maintenance criterion, a definition with checked decision logic — and organizes what they establish around four distinctions. First, protecting an access restriction is different from preserving the distinctions a reader can use: a universal leakage bound and an exact one-gate value are proved; a reset-based maintenance pulse prolongs limited leakage at the price of previously accessible information, while a reversible pulse prolongs it and preserves the full declared input class. Second, meeting protection criteria does not identify a mechanism: a prepared finite clock-controller meets four declared criteria at four sizes, and so does a static field with the clock decoupled, and so does the clock's free mean field at the largest size. Third, restoring a supporting condition does not necessarily recover the capability: coupling alignment is shown to be a supporting condition of the capability, and a restoring process that improves alignment in six matched realizations meets the full restoration standard in one, misses it narrowly in one and fails in four, while useful access is preserved in none. Fourth, retaining a relation, delivering it to a reader and using it internally are different achievements, and a supplied design's advantage can reverse when its context changes without the comparison identifying the mechanism: a sector record restores access at three of four endpoints under an added permission; an internal coupling improves the primary endpoint without reaching the reference; a two-by-two of axis term and gating cell reverses both contrasts. Each result is stated with what it does not establish. No conclusion about self-maintenance, ownership or experience is drawn. The deposit is a technical manuscript, not peer-reviewed, that consolidates fourteen closed research notes and adds no theorem; the supporting proofs are in the notes. The package contains the manuscript (PDF and Markdown), the fourteen notes with two errata, every checker and its run record, the failure-path harness with its recorded outputs and a release adapter, the two earlier baseline notes, a claim-to-proof map, a correction ledger, a source lock and a manifest with the SHA-256 of every file. Every number printed in the manuscript was read by script from a packaged run record. Running checks/run_all.sh reproduces every checker's recorded summary line with the declared dependencies only (Python 3.11 or later; sympy 1.14, mpmath 1.3, numpy); the harness coverage, including the checkers it does not cover, is stated in §10 and Appendix A. Drafting and computation were AI-assisted under the author's direction. Archive SHA-256: 119d835b2d2e19463f3eb6478ea34ddbdf4deea220a5d6d6fe528dcf7061bedb.
This paper develops phase-sensitive source–readout constructions within Shadow Theory’s research programme. It asks how a relative-phase distinction, invisible in separate mode intensities, can be converted into stable detector records under bounded coupling, finite source lifetime and preparation uncertainty. A complete quantum instrument connects a two-mode source to a coherent reader and terminal detector flags. Every trial uses one original source preparation, with conclusive, null and loss outputs explicitly retained. The construction includes arbitrary inert reference systems and distinguishes coherent quantum outputs from classically registered records. The main results establish: • A sharp attainable limit on error-free conclusive detection under bounded coherent coupling and independent irreversible source loss. • A separate optimum for a bounded jump-hazard model, together with a finite collision realization, showing why the two apparatus models require different resource accounting. • An analytic minimax tradeoff between conditional error and guaranteed conclusive probability under joint amplitude, phase and visibility uncertainty, including uncertain upstream attenuation. • An exact separation between a calibrated entrance filter and uncertain common conversion dynamics, followed by sharp robustness bounds for imperfect matching based on controlled-path overlaps. The analysis keeps source preparation, reader dynamics, retained outputs and permitted measurement access explicit. Retaining a loss output or reference does not automatically make it accessible to the decoder, and agreement of detector counts does not establish equivalence of complete quantum outputs. The accompanying technical companion develops absorbing detector models, complete retained-output comparisons, finite charge-reference measurements, preparation-resource requirements, and calibration and adaptive monitoring methods. Supporting code and verification materials accompany the manuscripts. These are mathematical apparatus constructions within Shadow Theory’s source–readout programme, using standard quantum probabilities and stated preparation and control assumptions. The results do not derive the Born rule or establish a biological or consciousness mechanism.