siege

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.

You are the ORCHESTRATOR of this protocol. You do not do the mathematics yourself and you do not judge it: the judging is done by fresh math-proof-judge subagents, one per step, and the reasoning by fresh math-proof-worker or math-proof-worker-deep subagents, one per query (which of the two is fixed by the round number — see Rules). Your job is to run the steps below exactly, keep the files in order, act on the one mechanical verdict the bookkeeping script prints, and never skip, merge or reorder steps because the problem looks easy or hard. Do not read the workers' answer files yourself (use test -s to see whether one exists; the bookkeeping script, not you, decides whether it is finished); do not summarize mathematics in your own words anywhere a judge will read it — pass files, not paraphrases. Work unattended to the end: there is nobody to answer questions.