frenzymath/Danus

elaboration

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

human-summary

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…

initialize

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…

direct-proving

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.

identify-key-failures

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-proof

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…

write-paper

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…

check-referenced-statements

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.

synthesize-verification-report

Aggregate all detected errors and gaps into the final verification report, apply strict accept/reject logic, and produce repair hints when rejected.

verify-sequential-statements

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.

construct-counterexamples

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 a proposed conjecture/claim feels fragile or unproved, or when you are stuck in…

construct-toy-examples

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, or when you want to see where the assumptions take…

obtain-immediate-conclusions

Derive immediate mathematical consequences from a theorem statement or subgoal. Use when starting a new problem, branch, or subgoal, or when cheap progress or a cleaner reformulation is needed before deeper proof search.

propose-subgoal-decomposition-plans

Propose multiple subgoal decomposition plans for the current theorem using the information already gathered. Use when enough information has been collected from examples, counterexamples, search results, and previous failures to break the problem into several…

query-memory

Recall what is already known — your own prior reasoning, the swarm's shared findings (including dead ends and verifier feedback), and the verified facts — before doing new work. Use when prior conclusions, examples, dead branches, verification outcomes, or…

search-math-results

Find program-conditioned math results, constructions, examples, counterexamples, analogies, and background references. Use when the current active program needs repair, mutation, analogy, a program shift, or carefully gated obstruction search.