Hypnos Math

Note · every file published with it

A dividing-plane barrier in the OpenAI forced Navier-Stokes blow-up construction

The note's page on this siteThis folder on GitHub

Everything published with the note A dividing-plane barrier in the OpenAI forced Navier-Stokes blow-up construction: the PDF and its source, its figure, four reviews with the written answers to their findings, the checker, a program that recomputes the note's numbers, with its recorded output, its tests and the program that draws the figure, and, under lane/, the material of the line of work the note came from. Claude Fable 5.1, a model made by Anthropic, wrote the note at the owner's direction on October 1, 2026, the date on its title block, and its text was revised through October 2. As of October 3, 2026, no human mathematician has read it.

Where its question came from: a separate line of work the owner ran with frontier-model sessions on the OpenAI forced Navier-Stokes blow-up manuscript. On September 30, 2026, Claude Opus sessions wrote section digests and eleven explanations, from which a Claude Fable 5.1 session assembled a ledger of the construction's moves; the explanation of the manuscript's Appendix B asked whether the bias on the dividing plane is forced, and sketched the answer. On October 1 a Claude Fable 5.1 session ranked that question first on its map of open questions and wrote the note. No small model's line is among the note's sources, and the material has not been filed into the notebook.

The reviews, in the order they were made: GPT-6 Astra, the other company's model, on October 1, of the write-up that preceded the note, which found the flux identity already in Duraiswami's paper; Claude Fable 5.1, a fresh instance of the writer's own model, the same evening; GPT-6 Astra again on October 2; and Claude Opus 5.5, a different model from the writer's company, on October 2, which found that the explanation of Appendix B had sketched the barrier the day before. 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, in about one second, and three reviewers reran it. Its test file loads it from a path of the private repository, so the tests do not run from the published folder as it stands. The note's theorem rests on its Section 3, not on the program.

Under lane/: an index written when the work began; the ledger, a move-by-move account of the construction in 183 entries, as readable text (version 1.1, of October 1) and as two data files, version 1.1 and version 1.0 of September 30, which is kept frozen as exactly what the three small models were shown in a one-time test with the reasons withheld (their 16,018 lines never recovered the reason for a move); and eleven explanations, ten of the manuscript's sections and appendices and one of its companion on the Euler equation, each by a fresh Claude Opus session on September 30. These files keep the project's internal names.

The paper

Reviews

Checks

Other material