Paper · every file published with it

Approximate Antiunitary Symmetry as a Matching Problem

The paper's page on this siteThis folder on GitHub

Everything published with the paper Approximate Antiunitary Symmetry as a Matching Problem: the PDF and its source, its one figure, the search for earlier work made while it was written, four reviews with the written answers to their findings, and two checkers, programs that recompute the paper's numbers, with the outputs they recorded. GPT-6 Astra, a model made by OpenAI, wrote the paper at the owner's direction; its title block is dated September 28, 2026, and Claude Fable 5.1 (Anthropic) made the later edits, through October 2. As of October 3, 2026, no human mathematician has read it.

Where its question came from: its motivation is five notebook entries of late September 2026, two the judge wrote on small-model lines (one a recall of the classical fact that a skew-symmetric matrix of odd order has determinant zero, one a false conjecture) and three results of programs. The paper calls them motivation, not premises; its main theorem is a reformulation the writing session made; no source is recorded for its key tool, the matching polytope.

The reviews, in the order they were made: GPT-6 Astra, a fresh instance of the writer's own model, on September 28; Claude Fable 5.1, the other company's model, on September 29, with a seven-page note of results of its own; GPT-6 Astra again on October 1, with the earlier reviews in hand; and Claude Opus 5.5 (Anthropic), the other company's model, on October 2. The first two, which had not read each other, are answered in one file; each later review has its own. Every reviewer is an AI model. The reviews keep the private repository's internal names, their line numbers point to the version each one read, and one line of the fourth review, naming a private folder, is withheld from its public copy and marked where it stood.

What can be rerun: both checkers, from the files here, the numerical one under the library versions in requirements.txt and the exact one with only Python's standard library. Each output carries the SHA-256 of the program that wrote it, which matches the published program, and on October 2 the fourth review reran both and reproduced the outputs apart from four roundoff-level maxima in their last digits. The paper calls these implementation and falsification checks; its theorem rests on the arguments of Section 2 through Section 4.