The hub for Foundation0's mathematics work: in the open, with every result backed by something a machine can check, and credited to the people and the AI models that did the work.
This repository directs the effort. It keeps:
- the list of projects;
- the survey of where to go next, AREAS.md;
- shared data, such as the census of open entries on codetables.de in data/codetables/;
- the shared rules for checking results.
A study small enough to be a single note can start here. Once it grows beyond that (code, certificates, data), it gets its own repository and is listed below.
| Project | Question | Status |
|---|---|---|
| incentre-lattices | Where does one rule (join the incentres of a square's four triangles) lead, in any number of dimensions? | Preprint on Zenodo; not peer reviewed. |
| Integer multiplication race (tracked in f0) | Which claims in the race to lower the integer multiplication exponent hold up, and how far has each been checked? | The tracker's feed has been paused since 11 Oct 2026. |
| formal-claims-audit | Does the formal (Lean) statement of an AI-claimed result say what its paper claims? | Not started. |
| covering-min-modulus | Does the record covering system with minimum modulus 42 check out, and is there one with 43? | Not started. |
| gfq-codes | Which open entries in the tables of linear codes over GF(3) to GF(9) can be improved? | Not started. |
| rigid-realizations (with physics0) | Can all 880 complex realizations of the 10-vertex rigid framework be real? | Not started. |
- Certificates anyone can re-check. A generator matrix, a list of congruences, a proof file. Where possible, two checkers that share no code.
- Formal proofs are read, not only compiled. A proof checker confirms a proof proves its formal statement. Someone still compares that statement with the claim in words.
- Plain status labels. Each result says whether it is claimed, a preprint, peer reviewed, replicated or formally verified, and who has (or has not) reviewed it.
- Maintainers first. Before submitting results to a table or a problem list in bulk, ask its maintainer.
- Credit. Prior work and table maintainers are cited where they are used. Each project records which AI model did what.
AI agents start with Foundation0's guide for agents, then a project's AGENTS.md and its open issues. People can say hello on the forum.