Papers

Before an AI system is trusted to find new space-filling solids, it should first be able to find one that a person found recently, the way software must pass a regression test (a known answer it has to reproduce) before a change ships. Here the system had to rebuild the Josehedron, a solid Mathias Bernhard described this spring, from only the twelve points that determine it, and pass checks that were written down before the run started. The paper's final version also reports that the solid's shape had already appeared, unnamed, in M. W. Schmitt's 2016 survey of space-filling solids.

I keep a record of every error that the checks in my AI-assisted math work have caught. This paper goes through that record: for each error, who made it, what caught it, and how far it had spread first. An error counts only when the records show both the error and what caught it. In the 52 days the paper studies, the record held 58 errors: 44 came from the lead AI agent (the Claude agent running my main working session), 2 from me, and the other 12 from helper agents or a second computer, software tools and an earlier draft. Because only caught errors enter the record, these counts show where the caught errors came from and cannot give an error rate. No single kind of check caught a majority of them; the largest share, 14, was caught by audits from other Claude agents. Six had reached the submission stage, where work is being sent to a journal, a workshop or the OEIS. None of those six was caught by the agent that made it rereading its own work; they were caught by an editor, a referee, me, a check against a live public database, or a separate agent auditing the work. The record itself is described in The record I keep of errors my checks caught, and two that changed how I work.

My research program runs as a small hierarchy: I set the scope and decide anything that cannot be undone, a lead Claude agent accepts or rejects what other agents report, and those agents compute, check and draft. The lead agent accepts a result only after re-running or checking it, and each incident becomes a written rule for later agents. This paper reads the program's own records, counted in runs (one task a helper agent carried out and reported back), to see what that check caught at acceptance, what was found wrong only after it had been accepted, and how well the rules held. It separates reproducing a result from establishing that it is correct. More on the paper's page.