math-proof: siege

The approach

The skill works on one problem in at most MAX_ROUNDS rounds. Each round a judge writes a few self-contained questions, at most WAVE of them before round ESC_ROUND. The steps below call them queries. Each question goes to a fresh worker that sees only that question and the problem statement. The judge reads the answers, rewrites the running summary, and adds to a ledger of claims marked PROVED, REFUTED or OPEN. One claim is the goal, set in round 1; the judge may set a new goal at a later round, and in particular may raise it to a more significant statement once it is proved (the proved goal then stays in the ledger as the fallback result, to which the judge returns if two waves bring the raised goal no nearer; when the goal is raised you tell the user and copy the proved result to DIR/result-so-far.md). When an answer holds a complete written proof or disproof of the goal, two more workers check that exact text line by line. Once both pass, the judge concludes or raises the goal. Before round MIN_ROUNDS, that is the only way to conclude. From round ESC_ROUND on, if no complete proof or disproof is in hand, a round may hold up to WAVE_DEEP questions for higher-effort workers. All but at most two of them aim at the one statement still missing from the proof. After the rounds end, the judge writes a self-contained proof.md, a worker checks it, and the judge finalizes it. Unless the goal the run ends on was both proved and checked twice during the rounds, there are also extra revision passes and a last wave of full proof attempts before finalizing. proof.md has a Status section that says plainly what is and is not proved. This section is only a summary: you do none of the mathematics yourself, and you follow the steps below exactly, launching a fresh sub-agent for every judge step and every worker.