Even the full outcome distribution of a specified diagonal Hamiltonian does not determine where a quantum memory stores readable information or how a probe can resolve it. We construct environmental encodings with identical populations and source states: one distributes a binary label across individual fragments, whereas the other conceals it from every proper subset. Established observable-algebra methods certify an exact probe null when the complete dynamics accesses only the matched algebra. A complementary coupling saturates a restricted trace-distance bound, yet its response is largest when neither encoding records the source and vanishes when their local-record contrast is maximal. For states matched only on low-degree interaction words, we derive a time-dependent Dyson-tail bound on probe distinguishability. A separate GHZ pair realizes an order-N onset, D_P(t) = |sin(2gt)|^N, despite identical energy populations and proper-subset reductions. Its phase can be perfectly distinguishable even at equal interference visibility. Preparation, leakage and statistical certificates connect these analytic results to a proposed measurement protocol. The benchmark separates energy statistics, record location and dynamical accessibility within ordinary quantum mechanics; it reports mathematical and numerical results, not experimental confirmation. Research status and contentsThis is an unreviewed preprint by Ahmet Faruk Arapoglu, Independent Researcher, Türkiye. It contains the English article with complete supplementary mathematical proofs, a Turkish translation of the same main article, and portable LaTeX sources, code and synthetic numerical outputs. Version 6 is the internal manuscript release number, not a claim of six previous public Zenodo releases. No external funding or competing interests are declared. No journal acceptance, new force, gravitational law, or established theory of everything is claimed. Author contribution and use of generative AIAhmet Faruk Arapoglu is the sole author and originator of the underlying ECEG proposal. The initial concept and mathematical framework originated with the author, who also established the research contexts, questions, investigative steps, conceptual branches and methodological objectives. These author-defined ideas and directions form the starting point of the work. Within this research programme, generative AI tools assisted with critical examination and literature research, development and checking of subsequent finite-dimensional formulations and derivations, computational implementation and verification, figures, and manuscript drafting, editing and translation. This assistance extended to the main text, mathematical supplement and reproduction code. The author retains authorship and responsibility for the final content, research claims and their interpretation. Türkçe açıklamaBu kayıt, aynı çalışmanın İngilizce ana metnini ve ayrıntılı kanıt ekini, Türkçe ana metin çevirisini ve yeniden üretim dosyalarını içerir. Sonuçlar açık varsayımlara dayanan analitik çıkarımlar ve sentetik hesaplamalardır; deneysel doğrulama ya da hakemli dergi kabulü değildir. Yazar katkısı ve üretken yapay zekâ kullanımıAhmet Faruk Arapoglu, çalışmanın temelindeki ECEG önerisinin tek yazarı ve özgün fikir sahibidir. Başlangıçtaki özgün fikir ve ilk matematiksel çerçeve yazarın kendisine aittir; araştırma bağlamları, soruları, inceleme basamakları, kavramsal dallanmaları ve yöntemsel hedefler de yazar tarafından belirlenmiştir. Çalışmanın çıkış noktasını yazarın bu fikirleri ve araştırma yönlendirmesi oluşturur. Bu araştırma programı kapsamında üretken yapay zekâ araçlarından eleştirel inceleme ve kaynak araştırmasında, sonraki sonlu boyutlu formülasyon ve türetimlerin geliştirilmesi ve kontrolünde, hesaplamaların kodlanması ve doğrulanmasında, şekillerde ve metnin yazımı, düzenlenmesi ve çevirisinde destek alınmıştır. Bu destek ana metni, matematiksel eki ve yeniden üretim kodunu kapsamaktadır. Nihai içeriğin, araştırma iddialarının ve bunların yorumlanmasının yazarlığı ve sorumluluğu Ahmet Faruk Arapoglu'ya aittir.
Even the full outcome distribution of a specified diagonal Hamiltonian does not determine where a quantum memory stores readable information or how a probe can resolve it. We construct environmental encodings with identical populations and source states: one distributes a binary label across individual fragments, whereas the other conceals it from every proper subset. Established observable-algebra methods certify an exact probe null when the complete dynamics accesses only the matched algebra. A complementary coupling saturates a restricted trace-distance bound, yet its response is largest when neither encoding records the source and vanishes when their local-record contrast is maximal. For states matched only on low-degree interaction words, we derive a time-dependent Dyson-tail bound on probe distinguishability. A separate GHZ pair realizes an order-N onset, D_P(t) = |sin(2gt)|^N, despite identical energy populations and proper-subset reductions. Its phase can be perfectly distinguishable even at equal interference visibility. Preparation, leakage and statistical certificates connect these analytic results to a proposed measurement protocol. The benchmark separates energy statistics, record location and dynamical accessibility within ordinary quantum mechanics; it reports mathematical and numerical results, not experimental confirmation. Research status and contentsThis is an unreviewed preprint by Ahmet Faruk Arapoglu, Independent Researcher, Türkiye. It contains the English article with complete supplementary mathematical proofs, a Turkish translation of the same main article, and portable LaTeX sources, code and synthetic numerical outputs. Version 6 is the internal manuscript release number, not a claim of six previous public Zenodo releases. No external funding or competing interests are declared. No journal acceptance, new force, gravitational law, or established theory of everything is claimed. Author contribution and use of generative AIAhmet Faruk Arapoglu is the sole author and originator of the underlying ECEG proposal. The initial concept and mathematical framework originated with the author, who also established the research contexts, questions, investigative steps, conceptual branches and methodological objectives. These author-defined ideas and directions form the starting point of the work. Within this research programme, generative AI tools assisted with critical examination and literature research, development and checking of subsequent finite-dimensional formulations and derivations, computational implementation and verification, figures, and manuscript drafting, editing and translation. This assistance extended to the main text, mathematical supplement and reproduction code. The author retains authorship and responsibility for the final content, research claims and their interpretation. Türkçe açıklamaBu kayıt, aynı çalışmanın İngilizce ana metnini ve ayrıntılı kanıt ekini, Türkçe ana metin çevirisini ve yeniden üretim dosyalarını içerir. Sonuçlar açık varsayımlara dayanan analitik çıkarımlar ve sentetik hesaplamalardır; deneysel doğrulama ya da hakemli dergi kabulü değildir. Yazar katkısı ve üretken yapay zekâ kullanımıAhmet Faruk Arapoglu, çalışmanın temelindeki ECEG önerisinin tek yazarı ve özgün fikir sahibidir. Başlangıçtaki özgün fikir ve ilk matematiksel çerçeve yazarın kendisine aittir; araştırma bağlamları, soruları, inceleme basamakları, kavramsal dallanmaları ve yöntemsel hedefler de yazar tarafından belirlenmiştir. Çalışmanın çıkış noktasını yazarın bu fikirleri ve araştırma yönlendirmesi oluşturur. Bu araştırma programı kapsamında üretken yapay zekâ araçlarından eleştirel inceleme ve kaynak araştırmasında, sonraki sonlu boyutlu formülasyon ve türetimlerin geliştirilmesi ve kontrolünde, hesaplamaların kodlanması ve doğrulanmasında, şekillerde ve metnin yazımı, düzenlenmesi ve çevirisinde destek alınmıştır. Bu destek ana metni, matematiksel eki ve yeniden üretim kodunu kapsamaktadır. Nihai içeriğin, araştırma iddialarının ve bunların yorumlanmasının yazarlığı ve sorumluluğu Ahmet Faruk Arapoglu'ya aittir.
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.
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.
STATUS (18 October 2026). The physics programme that motivated this work was concluded in October 2026 and its claim of a unified derivation withdrawn. The results in this paper do not depend on that programme and stand as stated. Can an exact account of recorded events also determine what happens next? We examine this question in a finite quantum model with 48 preparations and an apparatus with ten distinguishable outcomes. Two reversible evolution rules reproduce exactly the same first-use specification but predict different results when the apparatus is used again. A separate example fixes one evolution rule: two possible histories then have identical counts of reads, commits and service events, yet different probabilities for the next outcome. Counts alone are therefore insufficient for prediction in this model. What remains visible depends on the observation. At eight preparations, even the complete individual-read distributions agree between the two rules, while correlations between the reads distinguish them. We classify two explicitly specified families of observations and determine exact ranges for the simpler family, showing both how distinctions are lost and how they can survive. The results separate event accounting, the choice of evolution, retained memory and the conversion of records into measured responses. They are conditional finite-model results, not a derivation of a physical dynamics or a measured coupling. The contribution is a set of exact counterexamples and classifications, rather than new principles of quantum theory. Exact computations and explicit proofs identify the additional response, weighting and sampling choices that a predictive physical interpretation must supply. Version 0.2 incorporates corrections following an author-requested preprint review. The deposit supplies the PDF, editable LaTeX with three TikZ figures, bibliography, exact fixture data for 96 two-read processes over 48 preparations, and a portable Python/SymPy verifier. The revised verifier passes 2,926 exact assertions. These are conditional finite-model results; no physical law, bridge, weighting or sampling measure is selected. The unchanged historical audit sources are available in a separately linked companion archive. Frozen audit sources and INT99 result dossier: https://doi.org/10.5281/zenodo.22541080.
A physical identification requires a domain of experiments, a realization, and an observation that distinguishes competing mechanisms. We construct these for the δ framework. Within finite causal quantum experiments, computable Choi data are equivalent to finite arithmetic programs producing valid instrument approximations at every requested accuracy. A separate pointer reader preserves the quantum posterior and supports adaptive composition. For the native two-atom census, the actual join update and common-mode retention select golden scaling and a signed contraction. Coherent return selects its minimal conserving completion; an independently calibrated spectral band then selects its constant interaction. A bright-mode construction and a stable short-time calibration procedure supply an explicit realization and uncertainty budget; measured duration and frequency supply the dimensional units. We derive a general endpoint identity between stored record energy and comparison imbalance, and distinguish the monotone fresh-record trajectory from coherent recurrence. The logical-to-physical bridge also has a sharp boundary: an explicit instance of the proposed completion generator has no effective value-reflecting physical reader or numerical comparison receipt. Sequence completion requires precisely the corresponding halting-oracle resource, not an unexplained scalar cost. This obstructs operational completion while leaving purely proof-language transport distinct. Native implementations of identical logical strength nevertheless carry different physical receipts. Joint covariance and the exact endpoint law state the valid relationship between those quantities. Finally, calibrated return and three-outcome tests distinguish the relevant phase and recording alternatives, with quantitative error bounds. First public preprint release, version 1.0. The files include the PDF and the main TeX file. 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.
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.