This paper develops local quantum-reader decision problems within Shadow Theory’s source–readout programme. It asks when feedback improves access to a target distinction in a fixed quantum source, and how reliably that distinction can be read under detector noise and calibration uncertainty. The source supplies independent copies conditional on one hidden label, held fixed throughout the experiment, from four equatorial qubit preparations. The task is to identify their common positive or negative sign, rather than reconstruct the full preparation label. Although all four preparations have identical separate-mode intensities, phase-sensitive local measurements provide access to the target. The analysis compares adaptive readers, whose measurement settings depend on earlier records, with randomized nonadaptive readers, whose complete schedules are selected before outcomes are observed. Each measurement consumes one fresh copy. Every protocol must return a sign at a fixed deadline, retaining all settings, outcomes, nulls and specified timing records. Neither class uses collective measurements or coherent quantum memory between specimens. The main results establish equal optimal worst-case error for both reader classes through three copies across the shared efficiency and visibility model. At four copies, explicit rational feedback policies outperform every randomized nonadaptive schedule over the full continuous equatorial measurement menu, in both the ideal model and a specified noisy model. The comparison is supported by continuous-menu lower certificates rather than measurement-grid searches alone. For a one-percent worst-case error target, the minimum copy count is narrowed to either 13 or 14 for each reader class in the nominal model, and either 16 or 17 under the specified asymmetric gain and phase uncertainty. These adjacent thresholds remain unresolved. Further results give an exact robust repeated-angle frontier, extend the comparison to randomized choices of a fixed repeated angle, and identify convex-source conditions under which one reader is globally sufficient. The accompanying technical supplement and reproducibility materials provide measurement-allocation benchmarks, expanded finite-menu comparisons, compact feedback policies, exact optimization certificates, and timing and calibration interfaces. The results quantify target access under explicitly stated preparation, measurement and record-access conditions. They use standard quantum probabilities within Shadow Theory’s research programme and distinguish copy savings from total apparatus, control or calibration savings.
This paper develops local quantum-reader decision problems within Shadow Theory’s source–readout programme. It asks when feedback improves access to a target distinction in a fixed quantum source, and how reliably that distinction can be read under detector noise and calibration uncertainty. The source supplies independent copies conditional on one hidden label, held fixed throughout the experiment, from four equatorial qubit preparations. The task is to identify their common positive or negative sign, rather than reconstruct the full preparation label. Although all four preparations have identical separate-mode intensities, phase-sensitive local measurements provide access to the target. The analysis compares adaptive readers, whose measurement settings depend on earlier records, with randomized nonadaptive readers, whose complete schedules are selected before outcomes are observed. Each measurement consumes one fresh copy. Every protocol must return a sign at a fixed deadline, retaining all settings, outcomes, nulls and specified timing records. Neither class uses collective measurements or coherent quantum memory between specimens. The main results establish equal optimal worst-case error for both reader classes through three copies across the shared efficiency and visibility model. At four copies, explicit rational feedback policies outperform every randomized nonadaptive schedule over the full continuous equatorial measurement menu, in both the ideal model and a specified noisy model. The comparison is supported by continuous-menu lower certificates rather than measurement-grid searches alone. For a one-percent worst-case error target, the minimum copy count is narrowed to either 13 or 14 for each reader class in the nominal model, and either 16 or 17 under the specified asymmetric gain and phase uncertainty. These adjacent thresholds remain unresolved. Further results give an exact robust repeated-angle frontier, extend the comparison to randomized choices of a fixed repeated angle, and identify convex-source conditions under which one reader is globally sufficient. The accompanying technical supplement and reproducibility materials provide measurement-allocation benchmarks, expanded finite-menu comparisons, compact feedback policies, exact optimization certificates, and timing and calibration interfaces. The results quantify target access under explicitly stated preparation, measurement and record-access conditions. They use standard quantum probabilities within Shadow Theory’s research programme and distinguish copy savings from total apparatus, control or calibration savings.
This paper develops task-relative reader certification within Shadow Theory’s source–readout programme. It asks how many source copies are needed to validate a fixed quantum reader, and when access to its retained measurement records reduces that cost compared with observing only its final correct-or-incorrect decisions. The reader is fixed before validation and must return a sign after each complete experiment. A trusted evaluator knows the preparation label for scoring, while the reader does not. The analysis distinguishes terminal-error observations, records with trusted ancillary information, and readable measurement trajectories governed by a shared physical response model. For terminal-error validation, the paper establishes exact finite-budget tests and sequential likelihood tests, together with nearly matching information-theoretic lower bounds on expected source consumption. An unrestricted-record result shows why additional archived data alone need not improve certification: an advantage requires specified information or response constraints. A separate trusted-seed construction gives an exact information-projection test. The central quantitative comparison concerns a fixed fourteen-copy reader in a trusted shared-visibility family. To certify a maximum label error of one percent, a trajectory-based validator achieves a false-certificate probability of at most one in 1,048,576 and a nominal acceptance probability of at least 95 percent, using no more than 720,160 source copies. Under the same preparation and physical-response promises, every validator restricted to terminal errors and meeting the same acceptance requirement needs more than 1,992,371 source copies in expectation. At the exact nominal device, an uncapped trajectory-based test accepts almost surely with expected consumption below 254,746 copies. A separate robustness analysis extends likelihood-test validity to a quantified class of conditional response deviations. Finite-cap guarantees and expected stopping costs remain explicitly distinguished. The results demonstrate a certified resource advantage from access to retained classical measurement trajectories, rather than merely an improvement over one chosen terminal-error test. Supporting materials provide the fixed reader, exact certificates and reproducibility procedures. All guarantees depend on the stated preparation, response, information-access and deployment-stability assumptions. Certification concerns the nominated reader’s decision error; it does not establish complete quantum-instrument equivalence or identify an underlying source. The analysis uses standard quantum probabilities within Shadow Theory’s research programme.
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.
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 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 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.
Detector outcome probabilities can be independent of a later measurement setting even when earlier timestamps, detector seeds, or environmental records depend on that setting. We characterize complete-record preservation for a positive wrapped-Cauchy retrocausal spin source. An antipodal identity yields necessary and sufficient conditions for passive and environmental readouts, and source compensation permits a common normalized analyzer for source spins and prepared continuations. Gaussian controller and reset calculations distinguish inverse raw history weights from normalized thermal operations. A quantum instrument provides an operational benchmark, whereas a setting-dependent separable source produces setting-dependent statistics at an earlier joint probe. For two equal-width contexts, a calibrated weak probe requires a minimum source change of sech(2g)/8 in trace distance for exact protection at every nonzero strength. The signal--source-change tradeoff is sharp for this pair of contexts. A contextual positive-history construction recovers the isolated hidden law and preserves records for a specified class of finite adaptive quantum apparatuses, subject to quantum calibration and restricted field access. Direct readout of an added likelihood field distinguishes two future axes with unit probability. The analytical results are supported by continuous-angle and quantum-trajectory simulations, deterministic quadrature, and exhaustive enumeration of a finite policy class. The analysis concerns the specified statistical models; their microscopic physical realization remains an open question.