frenzymath

Write a high-signal mathematical synthesis from global memory and the fact graph for the Codex main agent's own strategy and worker dispatch.

Write a human-readable mathematical progress report (compiled PDF) on a project for the operator / the mathematician who posed the problem. This is NOT `elaboration` (the internal strategy synthesis) and NOT the dashboard. Render from the fact graph's…

First-run setup interview for a Danus deployment. Run it on the FIRST session, whenever runtime/.danus-initialized is absent or OPERATOR.md is still the blank template, or when the operator asks to set up / initialize / onboard / re-configure. It greets the…

Screen a decomposition plan by first trying to prove all of its subgoals directly, then identifying the key stuck points if the plan does not fully go through. Use when a decomposition plan is created.

Synthesize the common stuck points across failed decomposition plans. Use when the current batch of decomposition plans has failed — whether they failed already at direct proving or only after further attempts.

Verify a result and, on acceptance, write it as a fact — via the fact_submit tool. Use for the full target theorem AND for every sharply-delimited intermediate result, lemma, construction, or formula you intend to build on. The verifier is the sole authority…

Turn a project's verified fact graph into a publishable LaTeX paper in a configurable house style — a standalone amsart .tex with a real bibliography, compiled to PDF. Use when a project's target theorem is established and the operator wants the paper, or…

Validate externally referenced theorems by querying arXiv theorem search first and Codex's built-in web search second. Use when a markdown proof cites statements from external papers.

Screen a decomposition plan by first trying to prove all of its subgoals directly, then identifying the key stuck points if the plan does not fully go through. Use when a decomposition plan is created.

Find relevant math results, constructions, examples, counterexamples, and background references for a statement. Use when you need context for a new problem, supporting references for constructing examples or counterexamples, or external results while proving…

Validate externally referenced theorems by querying arXiv theorem search first and Codex's built-in web search second. Use when a markdown proof cites statements from external papers.

Verify a markdown proof in the order it is written. Use when the task is to check local correctness, theorem applicability, and reasoning gaps statement by statement through a paper-style proof.

Launch one sub-agent per decomposition plan after direct screening has identified the key stuck points for each plan. Use when all current plans have been screened by direct proving, none fully solves the problem, and parallel recursive work is needed.

Construct candidate counterexamples to test a proposed conjecture, lemma, or intermediate claim by keeping the assumptions true while making the claimed conclusion fail. Use when you are stuck in reasoning and want to see where the assumptions take effect and…

Generate and analyze simpler examples that satisfy both the assumptions and the conclusion of a theorem statement or subgoal. Use when you are stuck in reasoning and need simpler examples to regain traction, when you need simpler examples that satisfy both…

Synthesize the common stuck points across failed decomposition plans and recursive sub-agent reports. Use when the current batch of decomposition plans has failed.

Use when editing .lean files, debugging Lean 4 builds (type mismatch, sorry, failed to synthesize instance, axiom warnings, lake build errors), searching mathlib for lemmas, formalizing mathematics in Lean, or learning Lean 4 concepts. Also trigger when the…