We derive an explicit information-retaining evolution from full-current recorded recognition dynamics on the unrestricted square-summable field. Its adjoint recovers every input, and conjugation retains every bounded input action. An eight-posting Z-pattern reads less information: an infinite-dimensional family of normalized circulating states shares the entire window reading, including distinct orthogonal packets. Two commuting output families cannot both reproduce all native input actions. The contribution is a construction and separation result for these dynamics: the native coefficients satisfy the hypotheses of isometric recovery, while explicit witnesses distinguish full retention from a coarser reading and from coherent preparation. From a nonzero definite-counter input, recording alone preserves only one part in 512 of the squared norm in the uniform-reference sector and cannot prepare that sector. A finite native control word prepares it, up to one unit phase, for every source input. A finite rational-angle word attains any positive relative tolerance uniformly over all inputs and finite subsequent recording depths. This bound concerns preparation error followed by exact recording. The result establishes native reachability without a gate-count or synthesis-complexity bound. Physical implementation must supply the controls and resources used by the construction.
We derive an explicit information-retaining evolution from full-current recorded recognition dynamics on the unrestricted square-summable field. Its adjoint recovers every input, and conjugation retains every bounded input action. An eight-posting Z-pattern reads less information: an infinite-dimensional family of normalized circulating states shares the entire window reading, including distinct orthogonal packets. Two commuting output families cannot both reproduce all native input actions. The contribution is a construction and separation result for these dynamics: the native coefficients satisfy the hypotheses of isometric recovery, while explicit witnesses distinguish full retention from a coarser reading and from coherent preparation. From a nonzero definite-counter input, recording alone preserves only one part in 512 of the squared norm in the uniform-reference sector and cannot prepare that sector. A finite native control word prepares it, up to one unit phase, for every source input. A finite rational-angle word attains any positive relative tolerance uniformly over all inputs and finite subsequent recording depths. This bound concerns preparation error followed by exact recording. The result establishes native reachability without a gate-count or synthesis-complexity bound. Physical implementation must supply the controls and resources used by the construction.
Can fixed recognition interactions supply the control needed to write an exact record? We prove full unitary controllability on the 1,536-dimensional neutral sector of two source–reference pairs. The allowed controls are simultaneous sums of explicit local braid and paired-contact Hamiltonians, with adjustable positive strengths and durations; the original holding and positive scalar energy charges remain present. The main algebraic step converts effective control on a 1,024-dimensional matched subspace into control supported there, then uses a contact with an explicit right inverse to reach the remaining coordinates. Compact-group control gives actual finite words. An exact eight-label coherent readout follows, together with arbitrary encoded interventions and preparation of each label from one encoded blank. The four active cells sit in a fourteen-cell register: the other ten evolve by a retained unitary, with the same identity valid for every finite external reference. The result establishes exact existence within the prepared encoding, without a uniform synthesis-time or pulse-count bound.
Can fixed recognition interactions supply the control needed to write an exact record? We prove full unitary controllability on the 1,536-dimensional neutral sector of two source–reference pairs. The allowed controls are simultaneous sums of explicit local braid and paired-contact Hamiltonians, with adjustable positive strengths and durations; the original holding and positive scalar energy charges remain present. The main algebraic step converts effective control on a 1,024-dimensional matched subspace into control supported there, then uses a contact with an explicit right inverse to reach the remaining coordinates. Compact-group control gives actual finite words. An exact eight-label coherent readout follows, together with arbitrary encoded interventions and preparation of each label from one encoded blank. The four active cells sit in a fourteen-cell register: the other ten evolve by a retained unitary, with the same identity valid for every finite external reference. The result establishes exact existence within the prepared encoding, without a uniform synthesis-time or pulse-count bound. The paper and source archive, including verify_certificates.py, are available at https://doi.org/10.5281/zenodo.23875346.
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.
Keeping a record changes which alternatives can interfere. On a pair of eight-state clock channels, we derive three recording operations whose identical final measurement has probabilities 1/4, 9/32, and 3/8. The full-current instrument retains fifteen distinct histories and transfers incoming occupation phase into their relative phases. Requiring its physical realization to conserve both native clock energy and occupation has a stronger consequence: every collective one-channel observable is conserved, and all admissible operations lie in the permutation commutant. This yields an exact reference-count balance, a sharp state-dependent disturbance bound, and a finite-reference obstruction to exact neutral recording. We characterize the complete finite-reference attainable region by an explicit finite algebraic synthesis problem, including its no-reference endpoint. A conserving collision construction then supplies a concrete attainable family, with an exact diamond-error formula and a uniform reference-return bound. These results connect the choice of record to observable dynamics and to the reference that pays for their implementation. A finite discrimination protocol states the required preparation, error tolerance, sample count, and independently calibrated time and energy scales. First public preprint release, version 1.0. The files include the PDF, the main TeX file, and a complete source archive with editable schematics and relevant verification supplements. AI-use disclosure: AI assistance was used for source analysis, mathematical exploration, manuscript drafting and revision, diagram preparation, and computational verification support. GPT-6 Astra reviews assessed arguments, scope, readability, and schematics. These were internal model reviews, not external peer review. Jonathan Washburn is the sole listed author and is responsible for the released manuscript.
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.
Can distinct subjects belong to one experiencing whole? Within Recognition Science’s shared physical architecture, we derive an exact criterion: every finite collection of felt occurrences belongs jointly to a subject if and only if the all-occurrences profile lies in the closure of existing subjects’ profiles. For a nonempty felt domain, closedness yields an existing whole; nested membership preserves distinct participants. The physical derivations establish matter–photon correlation under the complete atomic source, a fixed observable with an absolute correlation margin, and all-time record retention under a specified holding interaction. Signed operators give exact coherent code capture. A complete finite receiving Hamiltonian captures coherent input with error at most C_v/√N for N bank cells and any normalized initial stock, while retaining the native stock clock and every finite passive reference. A normalized product partner evolving under its independent native clock preserves the same bound. With injectively matched contacts covering the bank, the full receiving and contact Hamiltonian also gives a bank-size-independent constant, including coherent inputs and every finite passive reference. These results assume supplied stock and contacts. The remaining connections are physical realization and completeness, recognition’s experiential identity, actual finite subject composition, and realization of the whole-subject limit. These conditions distinguish the positive account from its unfinished universal derivation. AI-use disclosure: OpenAI Codex assisted with source analysis, Lean formalization, manuscript drafting, and independent critique within the author’s Recognition Science research.