We assess 18 chapter-specific reviews of the ten mathematical results announced by OpenAI on 1 August 2026, alongside review standards, Lean formalizations, subsequent research, and mathematical references. The article audits this review record without claiming a complete reconstruction of all ten proofs. No confirmed substantive mathematical error in a principal result remains in the examined assessments, although review depth varies and some dependencies remain partly checked. Chapter 8 presents the strongest reservation: a specialist review requests major revision of compressed analytic arguments. In Chapter 6, an apparent polarity error was withdrawn after an overbar lost during PDF extraction was recovered from the typeset source. Subsequent research independently reuses the Chapter 3 proof mechanism and confirms that Connes's rigidity conjecture is false, without independently reproducing Chapter 4's stronger infinite-family result. Among the cited follow-ups, Chapter 7 receives the strongest direct theorem-level corroboration through a stronger hardness theorem. Related equality results in Chapter 8 do not verify the analytic inequality proof. Some follow-ups disclose material AI assistance. We argue that confidence should combine formal checking, human reconstruction, independent mathematical use, and a public record supporting correction of both proofs and reviews.
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8 pages, 5 references. V2: 11 pages, 8 references. V3. 13 pages, 27 references. Revised and updated version
We assess 18 chapter-specific reviews of the ten mathematical results announced by OpenAI on 1 August 2026, alongside review standards, Lean formalizations, subsequent research, and mathematical references. The article audits this review record without claiming a complete reconstruction of all ten proofs. No confirmed substantive mathematical error in a principal result remains in the examined assessments, although review depth varies and some dependencies remain partly checked. Chapter 8 presents the strongest reservation: a specialist review requests major revision of compressed analytic arguments. In Chapter 6, an apparent polarity error was withdrawn after an overbar lost during PDF extraction was recovered from the typeset source. Subsequent research independently reuses the Chapter 3 proof mechanism and confirms that Connes's rigidity conjecture is false, without independently reproducing Chapter 4's stronger infinite-family result. Among the cited follow-ups, Chapter 7 receives the strongest direct theorem-level corroboration through a stronger hardness theorem. Related equality results in Chapter 8 do not verify the analytic inequality proof. Some follow-ups disclose material AI assistance. We argue that confidence should combine formal checking, human reconstruction, independent mathematical use, and a public record supporting correction of both proofs and reviews.
Large language models can accelerate scientific exploration, but generated arguments are not evidence. We report a human–AI research workflow in which model outputs are treated as conjectures and claims are admitted only after proof or deterministic, independently checked computation. The workflow is illustrated by a connected sequence of results in mathematical physics. An exhaustive exact search of 19,683 rotation-symmetric ternary process functions finds 111 logically consistent cases, of which 108 are noncausal, and yields a projection-rigidity result over 432 source completions and 5,184 coarse-grainings. These structures generate qutrit product bases. For all 108 noncausal cores, exact orthogonality-preserving measurement calculations certify local rigidity and therefore impossibility of perfect finite-round local-operations-and classical-communication discrimination. An independent exact sweep of all 744 consistent binary tripartite process functions reproduces the qualitative causality/QNLWE boundary implied by recent general theory while additionally certifying local orthogonality-preserving rigidity for all 64 noncausal binary cases. We further obtain a closed-form rigidity spectrum and quantitative finite-round error bounds. Three of four pre-run structural predictions in the first campaign were falsified, and subsequent conjectures were retained when killed. We use this record to distinguish final-answer verification from discovery provenance, contrasting our control-first architecture with the large-scale multi-agent search and Lean verification reported in OpenAI’s September 2026 Navier–Stokes announcement. The general process-function/product-basis correspondence and its qualitative causality/QNLWE equivalence are credited to prior work; the contribution here is the audited research architecture together with the exact ternary census, projection rigidity, stronger local measurement-rigidity certificates, and quantitative results.
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/
AI agents are increasingly capable of constructing quantum algorithms and proofs, yet machine-checked proofs alone cannot guarantee that the intended problem is solved or that resource claims match the verified computation. Here we introduce Lean-QuantumAlg, a Lean 4 framework for trustworthy AI-assisted development of quantum algorithms. Its Algorithm-Solves-Problem contract binds correctness, success probability, borrowed-state restoration and quantum and classical resource bounds to a single execution, while separating the guarantees that Lean checks from the problem specifications and execution models that humans review. We demonstrate the framework on nine AI-formalized quantum algorithms, from Grover search to quantum attacks on RSA-2048 and P-256, with less than 1% of each algorithm's imported source code requiring statement-level human review once the shared framework has been audited. By integrating reusable mathematical foundations, certified algorithmic primitives and execution-grounded verification, Lean-QuantumAlg provides a basis for AI agents to construct and certify quantum algorithms, opening a path toward scalable AI-driven discovery of quantum algorithms.
This record preserves the current working state of From Geometric Closure to Physical Test: An Operational and Falsification Audit of the ENSO Framework. The package contains the 41-page audit paper, the nine ENSO papers included in the audited corpus, their TeX source files and associated validation suites, the complete audit-side script collection, and the reports, ledgers, and supporting outputs generated during the project. The materials are organised so that the internal audit suite can be run from a single folder, while the individual predecessor validators remain available with the papers to which they belong. The purpose of the audit is to distinguish, claim by claim, what is mathematically proved, what is conditionally established within ENSO, what reconstructs standard quantum mechanics, what is numerically supported, what remains an identification, and what is still open to empirical test. The audit reports that the load-bearing mathematical architecture survives separate re-derivation and computational testing within the project. It verifies the reciprocal closure invariant, the canonical reciprocal-phase amplitude map under its stated assumptions, conjugation and quadratic closure, the quadratic-weight result, the binary closure projection theorem, the log-affine edge-closure proposition, the mathematical golden-ratio attractor, and the geometric derivation of the Resolution Gap. The framework also reconstructs twenty standard quantum-mechanical cases and obtains the Born-rule route through a non-circular stochastic argument within an imported Hilbert-space and measurement setting. These results are classified as reconstruction rather than as independent empirical confirmation. The audit also states plainly that the standard quantum-mechanical baseline remains ontologically incomplete, particularly at measurement, and that ENSO’s atemporal intrinsic-closure ontology is therefore being assessed against a framework that does not itself provide a settled account of the transition from propagation to recorded outcome. The present package is an author-side, AI-assisted internal audit and should not be treated as external peer review or independent replication. It is deposited as a working research project rather than as the final completed audit. The current version preserves the research record, publication sequence, scripts, corrections, provenance notes, and claim classifications while further work proceeds on the operational discriminator, the measurement-rate identification, and the empirical conditions under which ENSO may be distinguished from standard continuous-measurement quantum mechanics. The package retains both positive and negative results. The audit-side suite contains no unresolved failures, while a deliberately retained predecessor negative result is preserved rather than removed. The operational frontier remains open: the mathematical and reconstructive architecture is established within its stated premises, but a fully developed and experimentally validated discriminator is the next stage of the research programme. For further information about the ENSO Framework, please contact Eric Needham: ensotheory1@gmail.com
Withdrawn by the author. This document was produced in an exploratory project with AI language models (2025–2026). An independent check in September 2026 found that it contains mathematical errors and novelty claims that cannot be upheld. Its correct mathematical content is either standard theory or is covered, with complete proofs, in:C. Hartmann, Second-order generators with quadratic Leibniz defect on M_n: a self-contained study of ½[H,[H,·]] + [K,·], Zenodo (2026), DOI: [https://doi.org/10.5281/zenodo.22967633].Please cite that text instead. This version is kept for the record only.
A 20-chapter beginner's guide to quantum computing that starts with an honest question — why don't we have quantum computers yet? The guide teaches the standard curriculum accurately, explains why the standard approach faces a thermodynamic wall (a 20,000-fold cooling gap that is Carnot-limited), and introduces the ultrametric alternative: passive geometric fault tolerance on Bruhat-Tits trees, with DOI-registered evidence, computationally validated error thresholds 75 times higher than surface codes, and three falsifiable predictions. This is the v1.2 edition (August 2026). Five quantitative statements from the May 2026 edition are corrected, each verified by an independent computation deposited with this record (artifacts/verification/verify_guide_claims.py, 35 checks, all passing; see Appendix B). Appendix A records the research program's progress since May 2026, including a trapped-ion falsifiability register, an audit of a 2026 no-go theorem on quantum error correction and quantum Darwinism, and the program's own correction on prime-valuation readings of quantum codes. This deposit includes the complete source set: manuscript, HTML, PDF, references (BibTeX), citation audit, project plan, license, and verification artifacts. v1.2.1 (August 2026): post-publication audit corrections. Chapter 20's summary now lists seven open problems (including the QEC–Darwinism tradeoff); the LHC temperature comparison is marked approximate (95×, rounded); Appendix A correction #5 completed; the citation audit's internal-reference count corrected; open problem 7 carries its numeric bound (F_L > 0.874). No quantitative claims changed. v1.2.2 (August 2026): deposit-file corrections. LICENSE now contains the full CC BY 4.0 International legal code, and README.md is the deposit manifest (a project-blueprint README was attached in v1.2.1 by an automation error). No content changes.