Mathbox

computation-audit

Design, run, or audit a mathematical computation that supports a research claim, including symbolic, exact, finite-field, representation-theoretic, homological, or numerical experiments. Use when correctness, provenance, tested range, reproducibility, or interpretation matters. Do not present bounded output as a universal proof.

literature-check

Verify an external mathematical theorem, citation, notation translation, source-dependent implication, or bounded novelty claim, reusing authorized project-local source copies when available. Use when a proof relies on a named paper/result, when exact hypotheses or versions matter, when the user asks whether a claim is known, or when an authenticated mathematical source should be cached for later checks. Prefer primary sources and record the search scope. Do not treat snippets or failed searches as proof or global novelty.

manuscript-integrate

Integrate an already validated mathematical result, correction, citation, or referee response into an authoritative LaTeX manuscript while preserving hypotheses, evidence status, notation, and dependencies. Use only when the user explicitly requests manuscript integration. Do not use to invent a proof or to perform routine copyediting.

proof-audit

Adversarially audit an existing mathematical claim, proof, derivation, diagram, or theorem dependency for correctness. Use for requests to verify, referee, stress-test, type-check, find gaps, or isolate the exact remaining implication. Default to read-only. Do not use to invent a substantially new proof route or merely copyedit prose.

proofread-math

Conservatively proofread mathematical prose and LaTeX for grammar, typography, syntax, notation consistency, cross-references, and uniquely forced local mathematical typos. Use for explicit math-proofreading requests and final self-review of theorem-, proof-, or equation-heavy edits. Do not invent, replace, shorten, or substantively repair proofs.

research-attempt

Run one bounded, auditable mathematical research route: a proof attempt, reduction, counterexample search, source-dependent implication, or claim-supporting computation. Use when the user explicitly asks to attack a research question or invokes this skill. Do not use for a sustained multi-route investigation that continues after failed approaches, routine editing, explanation, or an unchanged verification rerun.

research-init

Initialize or migrate an AI-assisted mathematical research repository's agent architecture. Use only when the user explicitly asks to set up, plan a retrofit, or substantially revise AGENTS.md, CLAUDE.md, live research status/history, workflow files, or their authority structure, including migrating a flat research log across programs into program indexes. Inspect first, propose a reviewable file plan, and default to no repository-local skills. Do not use for an ordinary research attempt, a closeout of one named program or phase, or a read-only project retrospective.

research-program

Pursue or close out a substantial mathematical research program across multiple proof, counterexample, literature, and computational routes. Use when the user asks for sustained investigation, several approaches, continuation until a goal is reached, or an authorized closeout of one named program or phase that compacts its live status and history. Coordinate successive attempts and preserve their evidence. Do not use for a single bounded lemma attempt, ordinary explanation, proofreading, a read-only project retrospective, or a repository-wide migration of instructions or a flat research log into program indexes.

research-retrospective

Reconcile a mathematical research repository's current claims, proofs, computations, status, literature dependencies, and failed routes, then recommend the next bounded research moves. Use only when the user asks for a project review, weekly/monthly retrospective, prioritization, a prose project handoff, or “what should I do next?”. Do not use to write a program closeout, migrate research history, operate a .mathbox ledger, or generate its dependency-aware handoff. Default to read-only.

research-state

Track exact mathematical claims, evidence revisions, dependency impact, audit provenance, research routes, and parallel or delayed executions in a local append-only ledger. Use when a project has a .mathbox ledger or the user asks for executable research-state tracking, stale-evidence detection, run reconciliation, or a dependency-aware handoff generated from recorded events. Do not initialize state for a casual math question, replace proof auditing with metadata validation, or write a prose project retrospective from status files.