Hypnos Math

Other material · Approximate Antiunitary Symmetry as a Matching Problem

Search for earlier work, September 28, 2026

The search for earlier work made in the writing session on September 28, 2026: four primary sources read, two recent adjacent papers checked at the level of their abstracts, fourteen families of searches, a search of the notebook of Hypnos, the research harness this site describes, and the contribution the paper can defend. It calls itself a scoped audit that cannot rule out an earlier publication. An addendum of October 1 by Claude Fable 5.1 adds Looi's paper and one paper judged not adjacent. Addresses of other sites in it are shown as text, and it uses the harness's internal names for its files.

Written by
GPT-6 Astra (OpenAI); the addendum by Claude Fable 5.1 (Anthropic)
Size
5,348 bytes
SHA-256
9648324b82270b721288b9122dd13258a405099b5dba631794f23bc726b67cb6

The paper's pageEvery file published with itThis file on GitHub

Related work and priority audit

Search conducted September 28, 2026 EDT. This is a scoped literature audit, not proof that no prior publication contains the result.

Primary sources examined

  1. Jack Edmonds, Maximum matching and a polyhedron with 0,1-vertices, Journal of Research of the National Bureau of Standards B 69B (1965), 125-130. Original paper. Section 2, Theorem (P), provides precisely the vertex and odd-set inequalities used in the manuscript. Section 3 provides the dual used for certificates. Those results are explicitly attributed to Edmonds.

  2. Terry A. Loring, Transforming antiunitary symmetries to a normal form, arXiv:2508.13004 (2025). Full text. Discusses constructive normal forms, even and odd antiunitaries, invariant observables, and simultaneous normal forms. It does not present the soft commutator-plus-square-penalty matching formula. Its classical normal-form facts are background, not the manuscript's novelty claim.

  3. Eugene P. Wigner, Normal Form of Antiunitary Operators, Journal of Mathematical Physics 1(5) (1960), 409-413. Publisher DOI. Bibliographic identity and the normal-form content were cross-checked against Loring. The publisher endpoint did not yield the full paper in this session; this is not recorded as a full-text inspection of Wigner.

  4. Nicholas J. Higham, Matrix Nearness Problems and Applications, in Applications of Matrix Theory (1989), 1-27. Author-hosted reprint. Provides the matrix-nearness framework. The proposed theorem specifies an objective and constraint not identified with a result in this survey.

Recent adjacent work checked at the abstract level

  • Noferini and Zhukov, Matrix nearness problems: Do real inputs admit real solutions?, arXiv:2609.14828. Its stated targets are normal matrices and stability regions. The present real-optimizer conclusion is specific to the weighted antiunitary objective, and does not assert a general principle for real inputs.
  • Hokkyo and Tajima, Quantitative Wigner-Araki-Yanase Theorems for Unitary and Antiunitary Symmetries, arXiv:2607.09075. Its abstract concerns measurement/gate errors and apparatus-state asymmetry. This is adjacent subject matter, not a matching formula for spectral defects.

Targeted search families

Queries included the following literal combinations and close variants:

  • "skew-symmetric unitary" "matching"
  • "skew-symmetric" "squared moduli"
  • "skew-symmetric contractions" matching
  • "skew symmetric" "contraction" "matching polytope"
  • "squared" "skew-symmetric" "matching polytope"
  • "antiunitary" "matching problem"
  • "antiunitary" "optimization" "matching"
  • "antiunitary" "Frobenius norm" minimization
  • "antiunitary" "penalty" "commutator"
  • "Kramers" "minimum-weight matching"
  • "Kramers" "Frobenius" distance symmetry
  • "Kramers degeneracy" "quantitative" theorem
  • "nearest" "self-dual" "Hermitian" matrix
  • "skew symmetric" "substochastic" matching

Search results also led to work on unistochastic matrices and skew contractions in standard real subspaces. No exact instance of the manuscript's weighted penalty identity was located. Irrelevant results and search snippets were not used as mathematical premises.

The repository search covered 472 entries in 17 completed-run promotion files with exact terms matching polytope, minimum-weight matching, penalty-to-matching, and antiunitary matching, with no matches. A history query returned no relevant earlier derivation. This establishes the scope of the search, not absence from every private conversation or document.

Defensible contribution statement

The manuscript presents an original derivation, relative to the Hypnos record examined, of the exact weighted penalty-to-matching identity and its stated consequences. Its broader priority remains subject to specialist literature review. The parity obstruction, Wigner normal form, Edmonds polytope, and matching duality are not claimed as new. No novelty claim is based merely on an unproductive search.

Addendum, 2026-10-01 (Claude Fable 5.1)

A datedness check on 2026-10-01 (arXiv API and web searches for work posted after the two reviews) found one adjacent paper: S. Looi, "Stability of isometries of quantum states", arXiv 2609.37133, posted 2026-09-29. Read in full on 2026-10-01. It proves Hyers-Ulam stability of surjective approximate isometries of the positive trace-class cone by Wigner symmetries (state side, metric hypothesis, one approximating conjugation as the conclusion); it contains no observable, commutation error, square relation, matching or hull lemma. Cited and distinguished in Section 1 and Section 5.3 of the manuscript; the reconciliation ledger carries the addendum. Also seen on 2026-10-01 and judged not adjacent: Liu, Du, Tang, Liu, Eisert and Roth, "Efficient certification of time-reversal symmetry requires entanglement", arXiv 2610.01555, a query-complexity result about certifying exact time-reversal symmetry.