Descripción en inglés para v3.9.6, ajustada al alcance del manuscrito y lista para pegar en Zenodo: [2743] This version of A Categorical Functorial Framework for Phenomenal Structure in Open Physical Systems develops the proposed correspondence between open physical systems and phenomenal structures, retaining the five-component target of content, quality, unity, temporality, and subjectivity. Version 3.9.6 introduces Distributional and Orbit-Coverage Obstructions to Invariance-Only Sufficiency. The revision examines whether distributional balance and organizational symmetries are sufficient to establish the original scalar bridge. It distinguishes equality in distribution, pointwise invariance under a group action, and constancy on descriptor fibers. Main contributions Distributional-to-pointwise obstruction: equality of scalar distributions under a measure-preserving transformation does not generally imply preservation of individual values. Orbit-coverage criterion: for unrestricted real-valued assignments, group invariance guarantees descriptor sufficiency exactly when each descriptor fiber is a single group orbit. Comparison-graph criterion: within an equality-based proof route, connectedness of the graph of orbit comparisons characterizes when additional equalities force constancy throughout a fiber. Restricted-class and topological limits: the revision explains why conclusions for arbitrary functions must not be transferred automatically to continuous, measurable, or phenomenologically admissible quantities. A sufficient orbit-closure result identifies a possible regularity-based alternative and its limitations. Fixed-reference application: the AB model has two kernel-automorphism orbits within a single constant-descriptor fiber. This illustrates the missing interorbit argument even when pointwise group invariance is granted. Contribution relative to earlier versions The orbit data, variable-contrast examples, and distinction between population balance and individual equality were already present in earlier developments. They are not presented as new empirical discoveries. The increment is an explicit analysis of the relevant implications, their proofs, their quantifier boundaries, and their consequences for the proposed proof strategy. The mathematical ingredients are standard; no claim of worldwide priority for new general mathematics is made. Scientific status This is an incremental theoretical and methodological revision. It excludes an unqualified invariance-only inference route; it does not refute Q or exclude every possible theoretical justification of the original bridge. No experience is attributed to the AB model. No new human dataset, validated original-degree instrument, independently justified individual phenomenal comparison, completed calibration, or fresh Lean verification is reported. The broader theoretical demonstration remains a research objective, not a premise. Files and production note The materials provide the complete LaTeX source and a complete 80-page PDF. The PDF uses alternative programmatic typesetting rather than a TeX-engine compilation; some complex expressions appear in linear notation. The LaTeX source remains authoritative for conventional compilation. The manuscript retains the Creative Commons Attribution 4.0 International License. Generative AI assisted drafting, literature checks, finite computation, and document preparation. Responsibility for the final content remains with the author.
Descripción en inglés para v3.9.6, ajustada al alcance del manuscrito y lista para pegar en Zenodo: [2743] This version of A Categorical Functorial Framework for Phenomenal Structure in Open Physical Systems develops the proposed correspondence between open physical systems and phenomenal structures, retaining the five-component target of content, quality, unity, temporality, and subjectivity. Version 3.9.6 introduces Distributional and Orbit-Coverage Obstructions to Invariance-Only Sufficiency. The revision examines whether distributional balance and organizational symmetries are sufficient to establish the original scalar bridge. It distinguishes equality in distribution, pointwise invariance under a group action, and constancy on descriptor fibers. Main contributions Distributional-to-pointwise obstruction: equality of scalar distributions under a measure-preserving transformation does not generally imply preservation of individual values. Orbit-coverage criterion: for unrestricted real-valued assignments, group invariance guarantees descriptor sufficiency exactly when each descriptor fiber is a single group orbit. Comparison-graph criterion: within an equality-based proof route, connectedness of the graph of orbit comparisons characterizes when additional equalities force constancy throughout a fiber. Restricted-class and topological limits: the revision explains why conclusions for arbitrary functions must not be transferred automatically to continuous, measurable, or phenomenologically admissible quantities. A sufficient orbit-closure result identifies a possible regularity-based alternative and its limitations. Fixed-reference application: the AB model has two kernel-automorphism orbits within a single constant-descriptor fiber. This illustrates the missing interorbit argument even when pointwise group invariance is granted. Contribution relative to earlier versions The orbit data, variable-contrast examples, and distinction between population balance and individual equality were already present in earlier developments. They are not presented as new empirical discoveries. The increment is an explicit analysis of the relevant implications, their proofs, their quantifier boundaries, and their consequences for the proposed proof strategy. The mathematical ingredients are standard; no claim of worldwide priority for new general mathematics is made. Scientific status This is an incremental theoretical and methodological revision. It excludes an unqualified invariance-only inference route; it does not refute Q or exclude every possible theoretical justification of the original bridge. No experience is attributed to the AB model. No new human dataset, validated original-degree instrument, independently justified individual phenomenal comparison, completed calibration, or fresh Lean verification is reported. The broader theoretical demonstration remains a research objective, not a premise. Files and production note The materials provide the complete LaTeX source and a complete 80-page PDF. The PDF uses alternative programmatic typesetting rather than a TeX-engine compilation; some complex expressions appear in linear notation. The LaTeX source remains authoritative for conventional compilation. The manuscript retains the Creative Commons Attribution 4.0 International License. Generative AI assisted drafting, literature checks, finite computation, and document preparation. Responsibility for the final content remains with the author.
A versioned collection of twenty-one distinct AI-assisted research manuscripts on quantum information and quantum computation. Each manuscript is supplied as a separate PDF, identified by title, author, date, scope, website and QIQC report in README.md and MANUSCRIPTS.json. Sources for manuscripts 1–20 remain in sources-and-verification.zip; the new Chernoff manuscript's source and checking records are in chernoff-two-pass-source.zip. Collection version 1.3, 16 October 2026. This version adds Yuxuan Zhang, Two-pass local measurements beat the measured Chernoff exponent, manuscript version 1.0, 16 October 2026, 10 pages, file chernoff-two-pass.pdf. Theorem 1 gives faithful noncommuting four-dimensional states and a two-pass copywise LOCC counterexample to the universal equality in Eq. (4): the measured Chernoff exponent is below 0.677144, while the displayed protocol's exact exponent exceeds 0.68250256. The optimal unrestricted LOCC and SEP exponents, convergence of their optimal exponent sequences, and possible equality between the two classes remain unresolved. All twenty earlier manuscript PDFs and the earlier source archive are unchanged. Human and AI contributions. The author set the research directions, designed the harness that coordinated model tasks, tools, memory, and checking, supplied physical and mathematical intuitions and proof skeletons, and guided the development and revision of the research ideas. AI models developed detailed candidate arguments and derivations, searched the literature, wrote and ran computational checks, and drafted and revised the manuscripts under this supervision. This is an independently authored collection, not an official publication of the QIQC catalog. Archival publication does not establish novelty, external proof validation or catalog acceptance. Individual verification qualifications remain in each manuscript and index. Background references are distinguished from the manuscripts reporting the results. Withdrawn partial results and research logs are excluded. The eleven-qubit manuscript retains its individual DOI, 10.5281/zenodo.22968593. Prefer that individual DOI when citing that manuscript alone. Research website: https://yuxuanzhang1995.github.io/agentic-research/
Anyones, generalizaciones de bosones y fermiones en espacios bidimensionales, son campos cuánticos topológicos materializados como excitaciones de partículas de energía finita en fases topológicas de la materia. Hay dos formas matemáticas equivalentes de modelar sistemas anyon. Podemos centrarnos en el colector del estado fundamental, entonces el sistema anyon es modelado en baja energía por un unitario (2 + 1) -TQFT. Una alternativa es considerar la estructuras de fusión y trenzado de todas las excitaciones elementales en el plano. El anyon El sistema es entonces modelado de manera equivalente por una categoría modular (unitaria). Esta tesis se centra en las matemáticas de la Computación Cuántica Topológica (TQC). La noción fundamental para la descripción matemática de TQC es la categoría de tensor modular. El físico define las teorías de cualquiera como categorías modulares en coordenadas. Algo que, como primera impresión, parece no tener nada que ver con teoría de categorías. Para describir los anones y su comportamiento, primero definimos álgebras de fusión y presentar algunos ejemplos clave. Después de esto, presentamos la teoría de categorías, declarando el definiciones basicas. En consecuencia, definimos categorías semisimples de forma abstracta. Aquí nosotros Presente nuestro ejemplo principal, la categoría de espacios vectoriales graduados sobre un campo fijo. El Se introduce el producto Deligne de categorías semisimple como parte técnica esencial, análogo al producto tensorial de espacios vectoriales. De las definiciones anteriores, vamos a Desarrollar la noción de categorías modulares en coordenadas. Específicamente, construimos un Categoría de tensor trenzado basada en espacios vectoriales graduados sobre un campo fijo. Finalmente, el Se da la relación entre la computación cuántica topológica y la teoría de categorías.
RTCG-P5, version 1.0, establishes finite-count passing guarantees for a target-centered certificate of a prescribed quantum instrument on a specified family of imperfect preparations. Six rank-two states share one signed, support-preserving parameter epsilon in [-10^(-6),10^(-6)]. The diagnostic instrument is fixed; actual readouts and trusted references remain nominal. Both the new rule and the old scalar rule use the same acquired preparation allowances. An explicit doubled fixed allocation of 636776064000000000000 attempted trials yields the upward-reported sufficient upper 0.000098454319447, strictly below 10^(-4). For every fixed parameter in the family and every allowed coupling between settings, the new rule passes with probability at least 1 - 873 exp(-12), approximately 0.994636102615544. Trials are iid within each setting; independence across settings is not assumed. The original allocation's sufficient envelope is 0.000108332505187 and does not close. This does not establish failure of the actual rule or a necessary acquisition cost. A separate single-analyzer argument proves an actual-output obstruction for the unchanged scalar preparation-penalty rule. At either signed endpoint, its reported upper is at least 0.00672 except on an event of probability at most 2 exp(-12), for every fixed valid allocation retaining that conversion. The obstruction is specific to this rule. It is not an information-theoretic lower bound or a lower bound on the physical instrument error. The universal false-certification bound, 889 exp(-12), remains a separate inherited guarantee for complete complex CP competitors under the stated trusted-reference and shared-world contract. The family-specific power guarantee does not restrict that competitor class, and the two probability statements are not combined into one 99-percent event or a posterior correctness assertion. The manuscript and mathematical supplement provide the physical construction, concentration proofs, all signed response coefficients, whole-interval argument and exact arithmetic. The companion provides editable sources, byte-preserved numerical programs and data, supporting Lean sources, actual execution/type/axiom evidence and reader instructions. The retained Lean 4.19.0 execution supports the stated deterministic and conditional probability implications. Physical-source realization, concentration/Holder arguments, inherited unrestricted physical coverage, complete raw-count linkage and general Python refinement retain their explicit formal boundaries. Packaging the public release is not a new Lean execution. This is a new finite-count extension of RTCG-P4, Target-Centered Preparation Calibration for Outcome-Resolved Instrument Certification (10.5281/zenodo.23789860). No experimental acquisition, practical sample efficiency, fewer-shot result or optimal acquisition cost is claimed. Manuscript, supplement, documentation and author-owned mathematical data use CC BY 4.0; original numerical, checking, build and Lean code use MIT. Inherited and third-party notices remain authoritative for their material.
This preprint develops a refinement–compatibility–stability (RCS) framework in which finite process occurrences generate rational calibration readouts indexed by a directed refinement system, and studies when such readouts determine a stable continuum value. Throughout, a continuum-valued observable means the completion class determined by an admissible stable refinement thread; no operator-algebraic or quantum-mechanical notion of observable is presupposed. Main results. Every stable rational thread determines a unique value in the Cauchy completion of the internal rational field. Equality of completed values is equivalent to asymptotic thread equivalence; realization preserves the induced algebraic operations; and the value is invariant under cofinal changes of refinement schedule. For bounded occurrence ratios, asymptotically negligible perturbations to the numerator and denominator preserve the completed value. Nested rational enclosures of vanishing width provide a sufficient, independently checkable stability certificate. The mathematical completion is distinguished from the physically realizable spectrum selected by a declared class of admissible protocols. Occurrence-ratio generation and stability alone do not determine a unique physical spectrum; additional assumptions about admissible channel composition can induce corresponding algebraic structure. A Pell-type recursion yields a stable irrational completion value using finite positive-integer counts, while an oscillatory model shows that qualitative refinement assumptions alone do not guarantee quantitative stability. Computability is treated conditionally: if the refinement system and protocol count functions are computable, and the stability thresholds are effectively obtainable, the completion value is a computable real. The paper does not assume that every physically admissible protocol is effective, and does not claim that physical observables must be computable. Scope. Apart from standard algebraic and topological facts cited in Sections 2 and 4, the results depend only on the definitions, axioms, postulates and additional conditions stated in this manuscript. No linear, geometric, temporal, or topological realization developed in the broader Observation–Feedback programme is assumed here. The readout is compared with the partial observables of relational physics, and stability, invariance and physical admissibility are treated as logically distinct requirements. The framework originates in the finite-occurrence and refinement-stability sector of the Observation–Feedback (OF) Closure programme (companion manuscript: Observation–Feedback Closure I, v1.5.0, doi:10.5281/zenodo.21859450), which supplies the broader relational motivation. The paper makes no empirical predictions and does not identify the physically realizable spectrum with the full mathematical completion. Version note. Version v1.1 is a clarificatory revision of v1.0. It states the provenance of the “OF”-labelled arithmetic, separates calibration protocols, readout threads and completion values, and sharpens the distinction between quantitative stability and physical admissibility. The only changes inside numbered equations are notational (κ_T → Read_T and N_eff → N_eff,i*); no theorem statement, proof, or mathematical conclusion has been changed. The PDF lists the full set of changes immediately before the Acknowledgments. Status. Preprint; not peer reviewed. The deposit includes the manuscript PDF, LaTeX source and BibTeX bibliography.