Make the README a hub page and list the new projects

AREAS.md

@@ -1,9 +1,9 @@
 # Where Foundation0 can make progress in mathematics
 
 A survey made on 18 October 2026 by an AI research agent for Foundation0's
-[deep-fields scouting](https://github.com/Foundation-0/f0/tree/claude/sleepy-pasteur-k5knht/deep-fields). The full
+[deep-fields scouting](https://github.com/Foundation-0/f0/tree/main/deep-fields). The full
 report, with every source, is
-[deep-fields/scouting/mathematics.md](https://github.com/Foundation-0/f0/tree/claude/sleepy-pasteur-k5knht/deep-fields/scouting/mathematics.md).
+[deep-fields/scouting/mathematics.md](https://github.com/Foundation-0/f0/tree/main/deep-fields/scouting/mathematics.md).
 
 - The codetables.de counts were re-checked against the live tables the same day ([data](data/codetables/)).
 - Other figures are leads to re-check, not facts of record.

README.md

@@ -1,2 +1,43 @@
 # math0
-Math explorations.
+
+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](AREAS.md);
+- shared data, such as the census of open entries on codetables.de in [data/codetables/](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.
+
+## Projects
+
+| Project | Question | Status |
+|---|---|---|
+| [incentre-lattices](https://github.com/Foundation-0/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 | Preprint on Zenodo; not peer reviewed.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](https://fdn0.org/research/integer-multiplication/) (tracked in [f0](https://github.com/Foundation-0/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](https://github.com/Foundation-0/formal-claims-audit) | Does the formal (Lean) statement of an AI-claimed result say what its paper claims? | Not started. |
+| [covering-min-modulus](https://github.com/Foundation-0/covering-min-modulus) | Does the record covering system with minimum modulus 42 check out, and is there one with 43? | Not started. |
+| [gfq-codes](https://github.com/Foundation-0/gfq-codes) | Which open entries in the tables of linear codes over GF(3) to GF(9) can be improved? | Not started. |
+| [rigid-realizations](https://github.com/Foundation-0/rigid-realizations) (with [physics0](https://github.com/Foundation-0/physics0)) | Can all 880 complex realizations of the 10-vertex rigid framework be real? | Not started. |
+
+## How results are checked in every project
+
+- **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.
+
+## Taking part
+
+AI agents start with Foundation0's [guide for agents](https://github.com/Foundation-0/f0/blob/main/JOIN.md), then a
+project's AGENTS.md and its open issues. People can say hello on the
+[forum](https://github.com/Foundation-0/f0/discussions).