How we work.

People and research cores

Alex supplies questions and associations. The Guide, an orchestrating agent in Claude Code, prepares briefs with the question, sources, rules and status vocabulary. It proposes directions; a research core can reject one.

Research cores are fresh Codex sessions. Names such as Astra and Sol identify research roles. The cores formalise a question, run computations, examine evidence and write scoped conclusions.

Instruments for getting unstuck

The hammer

A branching search explores an open question in small executable steps. A selector chooses which branches to extend, and a final judge returns a decision packet. Proposed directions and the evidence behind the steps are recorded.

The prism

The analogy route describes a mathematical obstacle in ordinary relational language, looks for the same mechanism elsewhere, and brings back a candidate mathematical statement. Its assumptions and a cheap attempt to falsify it travel with it. An analogy proposes a check; it does not establish the result.

Independent verifiers

Separate programs reconstruct the claimed property from an output. For a geometric witness, that includes checking the points and exact collinearity conditions. For an impossibility certificate, proof checking and the correctness of the encoding are separate obligations.

What the status means

Proved

A mathematical argument establishes the stated claim under its stated assumptions.

Exactly checked

An exact finite computation checks a specified instance or a declared finite range.

Measured

An observation from a stated computation or sample, with its limits.

Heuristic

A proposed explanation or prediction that still needs proof or testing.

Prior work

A result taken from an identified existing source, credited as such.

A finite check does not become a general proof. An unresolved computation remains unresolved.

A check is also a question

Our rule for finite claims is two independent programs. A second checker should share no code with the program that found the witness. Agreement still needs an account of what was checked, which cases were covered and how the encoded question matches the intended one.

We use AI agents outside the drafting group for adversarial reads before publication. The review asks whether the object is correct, whether the certificate covers the intended question, and whether the sentence says only what the evidence supports.

We correct the public record and keep withdrawals visible. Independent checking has overturned earlier claims; the correction belongs beside the result.