frenzymath
- 18 skills
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- 6 hours ago last updated
- ▌ Lean4 · frenzymath bundleUse 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 user asks for help with Lean 4, mathlib, or lakefile. Do NOT trigger for Coq/Rocq, Agda, Isabelle, HOL4, Mizar, Idris, Megalodon, or other non-Lean theorem provers.
- ▌ Recursive Proving · frenzymath bundleLaunch 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.
- ▌ Initialize · frenzymathFirst-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 operator, explains Danus, asks the critical choice (codex backend) plus a few free-text fields (how to address them, language, git branch, spend ceiling), then provisions everything (branch, config/danus.env, OPERATOR.md, codex login, verify service) and marks runtime/.danus-initialized. The system cannot run without these answers, so do not skip it.
- ▌ Elaboration · frenzymathWrite a high-signal mathematical synthesis from global memory and the fact graph for the Codex main agent's own strategy and worker dispatch.
- ▌ Write Paper · frenzymath bundleTurn 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 asks to write/revise/audit references for the paper for a project. NOT human-summary (a reader-facing progress report with no bibliography); this is the publication artifact, with verified citations, headed for arXiv / a LaTeX git repo.
- ▌ Human Summary · frenzymath bundleWrite 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 verified statements/proofs into a clean, self-contained report — precise problem statement, essential partial results with REAL proof sketches, the one major obstacle, a neutral approach timeline, and the single remaining lemma written out in full — then output a compiled PDF.
- ▌ Query Memory · frenzymath bundleRecall 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 verified results may inform the current question, claim, subgoal, or branch decision.
- ▌ Verify Proof · frenzymath bundleVerify 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 on mathematical correctness.
- ▌ Direct Proving · frenzymath bundleScreen 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.
- ▌ Search Math Results · frenzymath bundleFind 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.
- ▌ Identify Key Failures · frenzymath bundleSynthesize 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.
- ▌ Construct Toy Examples · frenzymath bundleGenerate 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 effect and gain intuition.
- ▌ Construct Counterexamples · frenzymath bundleConstruct 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 reasoning and want to see where the assumptions take effect and gain intuition.
- ▌ Check Referenced Statements · frenzymath bundleValidate 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 Sequential Statements · frenzymath bundleVerify 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.
- ▌ Obtain Immediate Conclusions · frenzymath bundleDerive 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.
- ▌ Synthesize Verification Report · frenzymath bundleAggregate all detected errors and gaps into the final verification report, apply strict accept/reject logic, and produce repair hints when rejected.
- ▌ Propose Subgoal Decomposition Plans · frenzymath bundlePropose 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 materially different plans.