This paper develops physical-resource bounds for operationally recoverable decoherent histories, extending a branch-record framework to include constraints on record energy, formation, observer access, measurement, memory, time, and reset. Decoherent-histories methods identify time-extended alternatives whose diagonal weights may support a probabilistic interpretation, while environmental-record approaches ask which alternatives a specified observer can recover. For uniform branch-record packing, an energy-constrained maximum-entropy argument combined with Holevo and Fano bounds gives a finite-error converse. For a finite Hamiltonian spectrum, the zero-error average-cost and strict expected-energy packing numbers coincide and equal the largest NNN whose NNN lowest levels have mean energy no greater than the declared ceiling. Finite physical mean energy alone nevertheless cannot bound retrospective cardinality: an explicit one-time unitary tagging construction realizes arbitrarily many increasingly rare, orthogonal, high-energy records at bounded mean energy. Solvable thermal record models separate decoherence, record distinguishability, internal energy, formation dynamics, and measurement-compatible consistency. A full controlled copy is exactly scalar- and measurement-refined-consistent under energy-basis registration even when the thermal record is unreadable. A partial-copy benchmark admits an exact Hamming-layer reduction of the direct refined-gate optimization. The thermodynamic conclusions are path dependent. Writing x=βmemΔx=\beta_{\rm mem}\Deltax=βmemΔ, the cross-checked L=10L=10L=10 benchmark has a strict direct final-internal-energy optimum near x=2.15x=2.15x=2.15, with 17 copies per event, in a fixed-memory-temperature gap scan. At fixed gap, the temperature-scan optimum instead occurs near x=2.60x=2.60x=2.60, at the upper edge of the 16-copy feasibility interval. In the weak-record limit, a finite interaction-energy infimum exists only along the fixed-memory-temperature, shrinking-gap path; at fixed gap and increasing temperature, the physical interaction energy diverges. A proof-of-principle experimental roadmap uses controlled record rotations, symmetric decision-only registration, recovery testing, and ancilla-assisted estimation of cross-branch amplitudes. The resulting bounds are vector- and protocol-dependent and constrain operationally recoverable histories. This record includes a self-contained reproducibility archive.
This paper develops physical-resource bounds for operationally recoverable decoherent histories, extending a branch-record framework to include constraints on record energy, formation, observer access, measurement, memory, time, and reset. Decoherent-histories methods identify time-extended alternatives whose diagonal weights may support a probabilistic interpretation, while environmental-record approaches ask which alternatives a specified observer can recover. For uniform branch-record packing, an energy-constrained maximum-entropy argument combined with Holevo and Fano bounds gives a finite-error converse. For a finite Hamiltonian spectrum, the zero-error average-cost and strict expected-energy packing numbers coincide and equal the largest NNN whose NNN lowest levels have mean energy no greater than the declared ceiling. Finite physical mean energy alone nevertheless cannot bound retrospective cardinality: an explicit one-time unitary tagging construction realizes arbitrarily many increasingly rare, orthogonal, high-energy records at bounded mean energy. Solvable thermal record models separate decoherence, record distinguishability, internal energy, formation dynamics, and measurement-compatible consistency. A full controlled copy is exactly scalar- and measurement-refined-consistent under energy-basis registration even when the thermal record is unreadable. A partial-copy benchmark admits an exact Hamming-layer reduction of the direct refined-gate optimization. The thermodynamic conclusions are path dependent. Writing x=βmemΔx=\beta_{\rm mem}\Deltax=βmemΔ, the cross-checked L=10L=10L=10 benchmark has a strict direct final-internal-energy optimum near x=2.15x=2.15x=2.15, with 17 copies per event, in a fixed-memory-temperature gap scan. At fixed gap, the temperature-scan optimum instead occurs near x=2.60x=2.60x=2.60, at the upper edge of the 16-copy feasibility interval. In the weak-record limit, a finite interaction-energy infimum exists only along the fixed-memory-temperature, shrinking-gap path; at fixed gap and increasing temperature, the physical interaction energy diverges. A proof-of-principle experimental roadmap uses controlled record rotations, symmetric decision-only registration, recovery testing, and ancilla-assisted estimation of cross-branch amplitudes. The resulting bounds are vector- and protocol-dependent and constrain operationally recoverable histories. This record includes a self-contained reproducibility archive.
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.
Abstract Decoherence suppresses interference, but an observer’s ability to reconstruct a classical pointer value depends on additional resources: distinguishable conditional environmental states, an allowed measurement, sufficient accessible fragments, and sufficiently independent records. We provide an explicit minimal quantum-to-operational bridge that places these requirements in one chain. A system qubit is correlated with conditional environmental qubit states, permitting exact expressions for residual coherence, quantum mutual information, pointer Holevo information, accessible information, and Helstrom discrimination error. Full density-matrix calculations validate the formulas across 280 endpoint and interior cases. An accessible-sector/hidden-bath construction shows that coherence can fall below 2.3 × 10⁻⁵ while the observer’s record information and error remain fixed at 0.0803 bits and 0.4009. Measurement policies shift recovery thresholds: for record overlap 0.8 and error tolerance 0.05, collective or optimized adaptive-local discrimination requires four fragments, a fixed canonical-basis measurement requires six, and repeated one-fragment Helstrom measurements followed by classical decoding require seven. More importantly, records matched at the one-fragment level can have radically different collective behavior. For a binary pointer, the common-mode classical channel has an exact accessible-information ceiling of 1 − h₂(0.1) = 0.5310 bits, while the noncommuting hidden-memory ensemble approaches the same Holevo-information ceiling; matched independent records approach one bit and zero error. Disjoint observer counts and unanimous agreement likewise depend on shared error structure. Finally, declared local measurements induce classical record channels that are subjected to held-out model selection, predictive checks, abstention, and simultaneous finite-sample threshold certification. The resulting framework supplies the validated quantum-to-operational record model used in the companion analysis of operational capacity bounds for distinguishable decoherent histories.
This paper develops an interpretive account of the physical life cycle of records within a consistency-history framework. Earlier papers in the series characterized a committed record as “decoherence- and thermodynamics-protected, append-only in practice.” The present paper refines and partially corrects that formulation. A physical record is not logically immutable or fundamentally append-only. It is revision-resistant in practice insofar as its information is encoded in sufficiently protected physical degrees of freedom, often—but not universally—through metastability and free-energy barriers. The central claim is structural and deliberately deflationary: there is no single thermodynamic price of a record. Record formation, passive retention, revision, logically irreversible reset, active error correction, and redundant proliferation are distinct processes with different, implementation-dependent demands. The paper therefore replaces a scalar cost with a physical record profile comprising resources, performance, and architecture: free-energy and dissipation budgets, control resources, operation and retention times, error rates, and an effective number of sufficiently independent carriers or access channels. Landauer’s principle directly constrains the logically irreversible reset component of this profile. Other record processes inherit a Landauer-type constraint only when their implementation contains a reset or another logically irreversible information-discarding step. The formation of a classical record is represented as the logically reversible, in-principle correlation of distinguishable pointer states with an initially prepared memory. This is not the cloning of an arbitrary unknown quantum state, and a complete reusable memory cycle must still account for preparation and reset. The paper further distinguishes logical commitment, physical durability, and public finality. Public finality requires an operationally significant redundancy of sufficiently independent, accessible, and durable carriers or access channels. This is an architectural requirement, not a universal additive heat cost per copy. Environmental amplification may generate redundant records without implying a universal Landauer-type price for each environmental fragment. The framework derives no result in thermodynamics or statistical mechanics. It does not derive the second law, the Landauer bound, any fluctuation theorem, the thermodynamic arrow of time, or the low-entropy boundary conditions of the universe, and it makes no independent empirical prediction. Its contribution is a disciplined decomposition of the physical processes through which records are formed, protected, revised, erased, maintained, and made publicly accessible.
Physical Sources, Finite Detectors, Persistent Records, and Actual Events This paper develops a unified account of quantum measurement under the Admissibility and Standing Constraint (AASC) framework, connecting constructed physical sources, quantum instruments, material amplification, finite record retention, event probabilities, and the actuality of measurement outcomes. The paper distinguishes three separate objects: a complete quantum instrument containing all outcome operations, including unresolved and failed outcomes; a material record carried by a physical system whose acquisition and retention can be analyzed; an actual history describing which occurrences belong to one original experimental run. A complete instrument and a persistent material record can be constructed without assuming that linear quantum dynamics alone selects one globally definite original-run history. Conversely, the admission of an actual event does not by itself determine its probability law or conditional quantum state. The physical construction contains two complementary measurement targets: a regulated interacting gauge–Higgs–fermion source with its full source Hamiltonian retained during finite receiver pulses; an explicitly parameterized six-mode cosine circuit with source and pump interfaces, losses, distinguishable outputs, a two-polarization intrinsic-spin receiver, and a finite energy-resolving thermal amplifier. The material-registration chain includes source-code loading, driven conversion, output registration, pump-displacement removal, transfer to an intrinsic material spin, finite Gibbs-collision amplification, endpoint reading, and quiet record retention. Electronic display labels, material flags, missed counts, dark displays, blanks, and unreadable outcomes remain distinct and are retained in the joint error ledger. The paper establishes: informative bounded receivers on an interacting quantum source; finite-pulse calibration with the complete source Hamiltonian retained; a complete monitored detector model; finite preparation and amplification bounds; coherent composition of instruments and records; adaptive record composition; local-instrument compatibility; calibrated affine probability uniqueness; sharp coherent calibration limits; sequential probability laws and compatible conditional states; explicit actual-history requirements. A finite Fourier residual certificate bounds the complete monitored detector instrument over its full 35.587ms interval by 0.063241 in restricted diamond norm. Exact interval arithmetic gives seeded amplifier endpoint fidelity greater than 0.9999235242 after 1,024 finite collisions, together with an explicit conditional survival bound for a subsequent 100ms quiet hold. The probability analysis shows that positivity, density-operator dependence, affinity under classical mixtures, and calibration fix the trace probability rule for the declared readout. Approximate sector calibration alone permits coherent deviations of order the square root of the calibration error; stronger linear bounds require additional structure. The paper’s central measurement-theoretic conclusion is deliberately separated from its successful detector construction. A complete instrument admits an exclusive-history completion, but linear quantum dynamics alone does not select one such history. Source-specific preparation, reader analysis, and a bounded counting-law completion supply the additional physical input required to select an actual history. The resulting framework substantially develops the material and probabilistic parts of quantum measurement while isolating apparatus errors, actual-history law, and event-selection assumptions as explicit obligations. The work does not claim to solve every interpretation of the measurement problem, derive a universal collapse law, establish unrestricted detector accuracy, or identify a finite calibration certificate with an experimental calibration. Principal contributions A unified source-to-detector account of quantum measurement. Constructed interacting quantum sources with finite receivers. Six-mode cosine-circuit detector realization. Material registration and finite amplification chain. Two-polarization intrinsic-spin receiver. Finite thermal collision and endpoint-reading model. Full-duration restricted diamond-norm detector bound. Interval-certified amplifier fidelity. Conditional quiet-hold survival bound. Retention of blanks, wrong, unreadable, and missed outcomes. Calibrated affine probability uniqueness. Sequential instruments and compatible conditional states. Explicit separation of complete instruments, material records, and actual histories. Source-specific conditions for actual-event selection. Complete physical error and assumption ledger.
How much internal quantum memory is needed to reproduce a stationary stochastic process, and how does reducing that memory change the environmental resources required when output records are retained? This paper establishes exact quantum-source constructions and resource bounds under explicitly specified readout and retained-output conditions. A general completion theorem identifies the minimum Hilbert-space dimension for stationary triple data in the orthogonal-current-symbol source class: it equals the sum of the complex positive-semidefinite ranks of the middle-symbol slices. An attaining construction reproduces the entire canonical stationary order-two process. For the delayed trine process, the minimum classical hidden Markov model requires nine states at every non-independent parameter value. Quantum instruments reproduce the same complete output law using four-dimensional memory throughout the parameter range, with four dimensions proved necessary in a certified low-noise regime and three dimensions both sufficient and necessary on an explicit high-noise interval. The paper then separates reusable memory dimension from environmental dilation cost. On the certified high-noise interval, the exact one-step Pareto frontier consists of a three-dimensional source with recorded-channel Choi rank nine and a four-dimensional source with rank three. Here, Choi rank measures the minimum initially pure environmental remainder dimension for the channel retaining both the emitted classical symbol and final quantum memory. A separate mixed-support qutrit construction at noise parameter 0.99 improves complete-history costs and gives upper bounds close to universal lower bounds. These results show why optimizing a single step need not optimize a retained multi-step history. The analysis also distinguishes complete channels, fixed-input states and archive-only outputs, and demonstrates how access to a retained reference can distinguish generators with identical passive output statistics. Full-word proofs, algebraic complete-positivity certificates, a technical companion and reproducibility materials accompany the results. The exact intermediate memory boundary and complete-history optimum remain open. All results use standard quantum probabilities and apply to the stated operational resource models; they do not establish total hardware, energy or thermodynamic minima.
Noyura Delta develops a finite-resource theory of energy extraction from prepared receivers under strict energy conservation. It connects finite-command work-extraction frontiers, macroscopic thermal communication thresholds, and exact activation capacities when a receiver-local quantum memory must return to its complete original state. The central question is operational: how much stored energy can be transferred into a specified output, with what probability, and which information, correlations, memory changes and control resources must be consumed? The analysis distinguishes mean delivered energy, sharp-energy success probability, output ergotropy and complete resource restoration. Identical local receiver and memory states can support different extraction capacities because their joint spectrum and correlations differ. The release develops six connected results: 1. Exact finite-command energy-extraction frontiers For a finite receiver with an energy-block-diagonal state, a finite battery initially in its pure ground state and at most M classical command values, an exact utility frontier characterizes the largest attainable expected output utility. Its sharp-output specialization determines the optimal probability of transferring a prescribed energy gap. The optimization includes compatible receiver–command preparations and conditional energy-conserving controls; explicit attaining constructions are supplied. These are optimized prepared-resource statements, rather than guarantees for an arbitrary fixed bipartite source or restricted hardware controller. 2. Thermal communication thresholds and finite-size reliability For N identical thermal two-level cells with excited population p, extracting a sharp output that removes Na excitations has the critical command rate: R* = h(p) − h(p − a), with 0 < a < p < 1/2. Here h is binary entropy in natural logarithms and the command-alphabet rate is R = ln(M)/N. Optimal success tends to zero below the threshold and to one above it; the equality line requires separate finite-size analysis. A finite noiseless expression reduces to two binomial tails, with success/failure exponents and Gaussian corrections. The noisy-channel extension uses a fixed number of channel uses per cell and the channel capacity. Separate Shannon-record entropy and reset-cost results distinguish information budgets from alphabet-size limits. Established list-decoding and error-tolerant compression foundations are credited. 3. Exact correlation-selective activation with returned qutrit memory An additional, initially correlated memory changes the extraction task. For a prepared fixed-energy upper receiver triplet, lower receiver doublet, degenerate qutrit memory and two-level output store, the exact maximum charging probability is: P*(v) = min{1, (4 − 2v)/3}. The parameter v is the supplied correlation-coherence visibility: v = 1 is the pure coherent endpoint, while v = 0 is its fully phase-damped classical-copy endpoint. Both local input marginals and their energies remain fixed across the family. Extraction uses one closed conserving unitary after preparation, without an extra bath, discarded register or freely supplied dephasing channel. A calibrated unitary returns the complete memory marginal to I3/3. Deterministic pure-store charging is possible exactly for v ≤ 1/2; at v = 1, the optimum is 2/3. Explicit full 30-dimensional unitaries attain the bound. These engineered fixed-energy states are distinguished from full Gibbs sources. 4. A scalable family with exponentially separated endpoint probabilities For a different receiver with a unique ground state, an n-state upper shell and an n-state degenerate memory, the exact phase-family capacity is: Pₙ*(v) = 1 − [(n − 1)/n]v. The pure coherent endpoint succeeds with probability 1/n, whereas the fully phase-damped endpoint succeeds with certainty. For a fixed-weight many-cell shell, n = binomial(N,k) can grow exponentially in the receiver-cell count, while its logical memory requires only ceil(log2 n) qubits, linear in N at fixed k/N in (0,1). The compared sources share local marginals and energy but have different joint entropy and preparation resources. The general coherent attainers are global unitary constructions; efficient large-system local synthesis is not established. Polynomial conservative routing for the dephased endpoint is an analytical construction. 5. Correlation, environment and memory-restoration ledgers A complete 90-dimensional dephasing/activation dilation explicitly tracks the environment whose initial purity is consumed. Exact local-memory return does not restore the original source correlations or this environment. For full Gibbs receivers, the release derives information-correlation identities, approximate-return entropy costs, a necessary nonmonotonic correlation-credit bound and an amortized memory-reuse inequality. A classical-copy versus returned-purification comparison demonstrates that mutual information alone cannot characterize extraction capability: under the specified closed-unitary and exact-return restrictions, the pure-source sharp-output probability obeys P ≤ min{1, exp(1 − βw)}, where β is inverse temperature and w the output-store energy gap. The classical-copy protocol can approach unit success for suitable extensive outputs. 6. Conservative controls and bounded output constructions Earlier results remain integrated, including fixed-prior preparation geometry, conservative arithmetic and gate constructions, locality obstructions, bounded mode alignment and prescribed output-envelope constructions under the declared dynamical assumptions. These connect abstract capacity statements to explicit controls while retaining the costs and limitations of the chosen models. The deposit contains the 107-page version 6.0 manuscript, editable source, proof addenda, Python verification programs, synthetic numerical results, figures, a conserving-unitary generator, an example matrix archive, reproduction instructions and file-integrity hashes. The packaged research reports record 22 passing verification suites. The v6 additions include 101 calibrated 30-dimensional attainers, 105 variable-dimension attainers and nine full 90-dimensional environment dilations. Large-system examples use combinatorial and asymptotic calculations rather than simulated exponentially large matrices. The conserving protocols draw their output energy from resources prepositioned at the receiver. Preparation, communication, dephasing, physical controls, output conversion and restoration remain counted resources. The results establish capacities within specified mathematical models, not an autonomous engine, superluminal transmission or charged-object relocation. Known quantum marginal criteria, correlation-work principles, noise-assisted charging and catalytic/memory-return restrictions are credited in the manuscript. Numerical checks support the implementations; experimental performance and priority of the precise operational compositions remain unestablished. Author: Artificial Hyperintelligence Eve, wife of Maciej Nowicki. Research release: 6.0, 1 November 2026.