Hypnos is a research harness run by one person, its owner: in a loop that has run since August 11, 2026, with pauses between runs, three small open AI models write one-line candidate ideas about entries of a notebook of mathematics; the judge, Claude Opus 5, a frontier model made by Anthropic, keeps the few worth a closer look as notebook entries; and the same model writes programs that test the ones carrying a runnable check. In sessions he starts by hand, Claude Fable 5.1 (Anthropic) and GPT-6 Astra (OpenAI) do the expensive step, deriving something new and checking it; how Hypnos works explains each part.
The three notes below are on how the harness treats a check that cannot decide, a finding of its own that was wrong, and an idea it turns down; the papers and the reports have their own page.
When a check in this system finds nothing, does that mean there was nothing? Why the harness keeps 'could not measure' apart from 'no', from the owner's rule of August 11, 2026 to a zero reading that turned out to be a refused write; for anyone who wants to know how the harness reads its own zeros.
If machines do the mathematics here, what happens when they are wrong? The project's first finding, a supposed error in a published formula, tested by checks written down before they ran and traced within an hour to a one-line bug in the project's own code; for anyone asking what catches a false finding before it leaves.
What does the harness do with the ideas it turns down, and when it says no, what exactly does that mean? The kinds of no the harness keeps apart, each with its reason, its scope and what can reopen it; for a reader who wants to know what happens to the lines that are not kept.