Note · every file published with it

Maximal Coherence for Prescribed Intrinsic Populations and Youla Values: Two Questions of Gil

The note's page on this siteThis folder on GitHub

Everything published with the note Maximal Coherence for Prescribed Intrinsic Populations and Youla Values: Two Questions of Gil: the PDF and its source, four reviews with the written answers to their findings, and one checker, a program that recomputes the note's numbers, with its recorded output, kept as two identical files. Claude Fable 5.1, a model made by Anthropic, wrote the note at the owner's direction; its title block is dated September 29, 2026, and its text was revised through October 2, when its title was also shortened. As of October 3, 2026, no human mathematician has read it.

Where its questions came from: they are J. J. Gil's own, from his paper in Entropy 28(8):877 (August 4, 2026). They surfaced while frontier models reviewed the paper on approximate antiunitary symmetry, whose lemma on skew-symmetric contractions the note reuses; GPT-6 Astra's review of that paper answered the free-value question first, on September 28, before this note's first draft. No step of the note's mathematics came from the harness.

The reviews, in the order they were made: Claude Opus 5.5, a different model from the writer's company, on September 29, which supplied the example now in Remark 4.5; GPT-6 Astra, the other company's model, the same day, kept from reading the first review, which showed that Theorem 4.1 follows from an inequality of Horn (1950), now the note's second argument for it; GPT-6 Astra again on October 2; and Claude Opus 5.5 on October 2, whose two major findings were about credit and sources. Every reviewer is an AI model. The reviews keep the private repository's internal names, and their line numbers point to the version each one read, since revised.

What can be rerun: the checker, from the files here, with NumPy and SciPy; a run takes about four minutes. On October 2 the fourth review ran it with the library versions its output records and got that output byte for byte. The note calls its checks implementation controls, not part of its arguments; the searches are local, and each records its worst shortfall so that a miss would show.