This record archives version v1.3 of the manuscript “Unified Residual Classicality Criterion for the Quantum-to-Classical Transition” and its full reproducibility package. This version is the repository companion to the journal-submission version prepared for Quantum Studies: Mathematics and Foundations. It includes the main manuscript, supplementary mathematical notes, supplementary validation report, figure source archive, LaTeX/source archive, benchmark CSV files, Python scripts, manifest files, citation metadata, license file, checksums, and author declarations. The work proposes a falsifiable, comparator-dependent residual-vector criterion for assessing quantum-to-classical behaviour. Classicality is certified only when predeclared residual channels — dynamical, semiclassical, operational, coarse-graining, and open-system — simultaneously pass their declared tolerances for a specified comparator, observable class, resolution, norm, and finite time interval. The work does not claim a universal solution to the measurement problem or a universal proof of quantum-to-classical emergence; it provides a finite-time certification framework with sufficient error-control conditions and controlled benchmark validation. Version-specific DOI: 10.5281/zenodo.20750070Previous version DOI: 10.5281/zenodo.20682081
This record archives version v1.3 of the manuscript “Unified Residual Classicality Criterion for the Quantum-to-Classical Transition” and its full reproducibility package. This version is the repository companion to the journal-submission version prepared for Quantum Studies: Mathematics and Foundations. It includes the main manuscript, supplementary mathematical notes, supplementary validation report, figure source archive, LaTeX/source archive, benchmark CSV files, Python scripts, manifest files, citation metadata, license file, checksums, and author declarations. The work proposes a falsifiable, comparator-dependent residual-vector criterion for assessing quantum-to-classical behaviour. Classicality is certified only when predeclared residual channels — dynamical, semiclassical, operational, coarse-graining, and open-system — simultaneously pass their declared tolerances for a specified comparator, observable class, resolution, norm, and finite time interval. The work does not claim a universal solution to the measurement problem or a universal proof of quantum-to-classical emergence; it provides a finite-time certification framework with sufficient error-control conditions and controlled benchmark validation. Version-specific DOI: 10.5281/zenodo.20750070Previous version DOI: 10.5281/zenodo.20682081
This repository contains the computational reproducibility and verification package accompanying the frozen Version v1.0 manuscript: “Phase Curvature and Assumption-Budgeted Certification in Gravity-Mediated Entanglement.” The associated manuscript develops an operational certification framework for gravity-mediated entanglement experiments. Its central aim is to quantify when an observed entanglement signal excludes a specified neighborhood of local classical-mediator models under explicit assumptions and separately controlled nuisance channels. The package supports the manuscript’s analytical and numerical results concerning: gauge-invariant nonseparable phase curvature for diagonal two-path interactions; exact concurrence and separability-distance formulas for pure two-qubit outputs; assumption-budgeted exclusion bounds around the classical-mediator free class; primal and dual PPT/semidefinite-program certification; finite-shot confidence bounds for experimentally accessible Pauli correlators; certified residual bounds for physically compensated coherent nuisance interactions; stochastic geometry and Casimir–Polder uncertainty budgets; matter-bypass and common-auxiliary-channel bookkeeping; circular-shield mode analysis, including the azimuthal matched-null obstruction; thermal shield-channel factorization; finite-footprint high-mode suppression; an analytic positive high-mode tail bound for the shield benchmark; and a conservative outward-rounded audit of the finite numerical mode block. The frozen manuscript does not claim that a particular experimental apparatus has already closed every systematic-error channel. Quantities such as preparation error, matter-channel leakage, shield-model discrepancy, control error, and readout error remain apparatus-dependent inputs to the certification framework. Package contents The archive includes: the frozen Version v1.0 manuscript source; deterministic verification scripts for the theorem-core identities; finite-shot and Casimir–Polder statistical/geometry checks; shield-mode and analytic-tail verification; conservative floating-point interval/audit checks; submission-interface regression checks; machine-readable verification reports; and a SHA256 manifest for file-integrity verification. All verification scripts distributed with the Version v1.0 package return PASS under the documented software environment. The numerical audit is intended as a transparent reproducibility layer for the stated model calculations. It should not be interpreted as a formal interval-special-function proof or as certification of a realized experimental apparatus.
Description: This work presents a quantitative framework for describing the quantum–classical transition as a continuous dynamical process governed by open quantum system interactions. A normalized Quantum Persistence Function is introduced to measure residual quantum coherence, allowing classical emergence to be characterized through a scale-dependent suppression criterion. The model is constructed using a microscopic spin–boson open-system foundation and extends decoherence analysis to inflationary cosmology. The framework connects dynamical decoherence bounds with observational constraints derived from primordial statistics measured by the Planck Collaboration. The formulation builds conceptually on decoherence theory associated with Wojciech H. Zurek and provides a diagnostic criterion for residual coherence survival across cosmological scales. The results aim to provide a practical quantitative tool for evaluating classicalization efficiency in inflationary models and for relating open-system quantum dynamics to empirical cosmological observations. KEYWORDS: Quantum–classical transition; decoherence theory; open quantum systems; inflationary cosmology; residual quantum coherence; spin–boson model; classicalization dynamics; primordial perturbations; cosmological quantum mechanics
This work formulates classical physics as a stable residual-rigid macroscopic phase of quantum dynamics. The central thesis is not that classical mechanics is an independent fundamental theory, nor that decoherence alone solves the measurement problem, but rather that classical behavior arises conditionally when quantum states belong to a protected small-residual basin around a regular classical stratum. Let ρ denote a quantum state and let Mcl denote a regular classical stratum in the quantum state space. The non-classicality residual is defined as the multi-component map Rcl(ρ) = (Roff(ρ), Rloc(ρ), REhr(ρ), Rdyn(ρ), Rred(ρ)), where the components measure, respectively, off-diagonal coherence in a pointer decomposition, failure of semiclassical localization, Ehrenfest defect, transverse dynamical instability, and lack of redundant environmental records. The associated residual energy is ηcl(ρ) = woff ‖Roff‖² + wloc ‖Rloc‖² + wEhr ‖REhr‖² + wdyn ‖Rdyn‖² + wred ‖Rred‖², with positive weights determined by the macroscopic resolution scale of the physical model. The mathematical structure is residual-quadratic. If R(u*) = 0, η(u) = ‖R(u)‖², and L = DR(u*), then the canonical second variation satisfies D²η(u*)[h,h] = 2 ‖Lh‖², and the associated stability operator is A = L∗L. Applied to the classicality residual, this gives the transverse stability operator Acl = DRcl∗ DRcl. The principal rigidity statement is conditional: if the linearized residual has a coercive transverse spectral gap and if small residual energy cannot occur far from the classical stratum, then ηcl(ρ) ≤ ε* implies dist(ρ,Mcl)² ≤ C ηcl(ρ). Thus classical physics is interpreted as a protected low-residual basin in quantum state space: a stable macroscopic regime in which decoherence, semiclassical localization, Ehrenfest control, dynamical invariance, and environmental redundancy jointly enforce rigidity of classical behavior. The framework also identifies the main failure modes of classicality: closing of the transverse spectral gap, absence of decoherence, loss of localization, failure of redundant records, tunneling, revivals, mesoscopic superpositions, and concentration-like escape channels. Consequently, the classical regime is not asserted as a universal limit of all quantum states, but as a gapped residual-rigid phase valid under explicit stability and anti-concentration hypotheses.
ECEG V9: the submitted manuscript, editable LaTeX source and computational supplement. This repository deposit was created on 31 October 2026 to preserve a dated, DOI-identified copy. The manuscript and accompanying scientific files are unchanged from the Quantum Information Processing submission of 10 October 2026. This is a preprint, not an accepted or peer-reviewed publication. Full text and supplementary files are restricted; bibliographic metadata are public. AbstractQuantum records can encode different source observables while sharing the same reduced states and energy statistics. We determine the optimal fidelity for converting a family of such records using local diagonal controls on an arbitrary interaction hypergraph. The answer depends only on the branch overlap and the smallest unsupported interaction. A weighted phase inequality proves the optimum and supplies an attaining control. We also derive limits on shared access to records, distinguish equal endpoint marginals from stationary evolution, and extend the fidelity bound to mixed preparation errors and integrated control deviations. All results concern a specified finite-dimensional quantum model. FilesECEG_V9_QIP_Submitted.pdf: submitted English manuscript (18 pages).ECEG_V9_QIP_Source.zip: editable LaTeX source and template files.ESM_1.zip: numerical verification scripts, machine-readable results, reproducibility instructions and file manifest. The statement in the submitted manuscript that no public repository identifier was claimed describes the submission on 10 October 2026; the present DOI identifies this later archival deposit.
Correction in version 1.1 (2026-10-18) The Decimal/Fraction interval engine distributed with version 1.0 used context-sensitive Decimal unary negation and absolute value on interval endpoints. These operations can round inward, so the recorded P02G certificate in v1.0 should not be treated as a rigorously outward-rounded enclosure. Version 1.1 repairs those operations using exact copy_negate() and copy_abs(), hardens the second interval implementation's row-bound selection, and regenerates the interval reports, checksums, and reproducibility manifest. The certified rectangle, theorem scope, and all 34 mathematical environments in the manuscript remain unchanged. Repaired P02G and the separately implemented mpmath.iv P02J both pass the original theorem gates. The result remains conditional computer-assisted mathematical evidence, not formal machine verification or external peer review. Previous version (v1.0): https://doi.org/10.5281/zenodo.23438614 This unrefereed research preprint establishes a computer-assisted, quantitatively certified non-identifiability result for fragment-size-averaged Holevo information in an N=4 environment with two equiprobable pure pointer-conditioned branches. For every point in an explicitly specified closed rational rectangle of coordinate area 4 × 10^-14, two realizations of the complete averaged Holevo information curve exist: one with minimum pure-common-rest carrier size two and another with carrier size four. The proof combines a uniform parameterized contraction mapping, directed interval arithmetic with a second interval implementation, and an intermediate-value construction. Reproducibility materials include the certification programs, frozen numerical certificates, SHA-256 checksums, and a standalone 200-state numerical comparison against direct 16-dimensional partial traces. Both interval implementations share the underlying analytic Holevo reduction and do not constitute independent symbolic proofs. The conclusions are restricted to N=4, equiprobable pure branches, fragment-size-averaged Holevo information, and the specified carrier definition. They do not establish non-identifiability for arbitrary N, mixed states, unequal priors, or individual labeled-fragment information. This is an unrefereed preprint, not a formally verified or peer-reviewed mathematical theorem. Comprehensive novelty priority is not claimed. Licensing: The manuscript and original documentation/data are provided under CC BY 4.0 where applicable. Original Python research code is provided under the MIT License. The accompanying reproducibility archive specifies licenses on a per-file basis. AI assistance disclosure: OpenAI ChatGPT assisted with mathematical analysis, Python implementation, numerical and interval verification, manuscript preparation, and quality assurance. Claude contributed critical assessment and adversarial review assistance. Neither AI system is a coauthor or an external scientific referee. The human author, Yoichi Tsujisawa, assumes responsibility for the research and its publication.
The quantum-to-classical transition is often operationally identified through one preferred indicator, such as coherence loss, classical record formation or measurement stability. This paper develops a different reconstruction test: classicality is treated as a witness-indexed, observer-explicit and recoverability-sensitive cross-scale transition rather than as a single hard boundary inserted by assumption. Starting from a fine description X, a candidate effective state Γ and a future observable family Y, we define a predictive-retention ratio η_pred=I(Γ;Y)/I(X;Y) and residual ε_cl=I(X;Y|Γ). We distinguish raw relation count from record-forming capacity K_rec^(δ), introduce relation-to-record efficiency κ_R, define a transition spectrum T_C={t_W} across a declared witness family and its width ΔT_C=max_W t_W−min_W t_W, and require observer counterfactuals so that conditioning or readout cannot manufacture a physical transition. An observer-conditioned recoverability diagnostic separates information destroyed, information dispersed into wider system–environment relations and information inaccessible to a restricted observer. The resulting classicality vector is deliberately non-compensatory unless a physical model proves otherwise. The construction is a falsifiable physical-regression architecture, not a derivation of quantum mechanics from Ω₀/A2, and it makes explicit the calculations and counterexamples required before any stronger claim is admissible.