Mathbox

computation-audit

Design, run, or audit a mathematical computation supporting a research claim when correctness, provenance, tested range, reproducibility, or interpretation matters. Includes symbolic, exact, finite-field, representation-theoretic, homological and numerical experiments. Do not use to verify a cited theorem, audit a proof with no load-bearing computation, pursue a whole research route, or for general programming.

literature-check

Verify what an external mathematical source proves: exact theorem, hypotheses and version, citation, notation translation, source-dependent implication, attribution, or a bounded novelty claim; cache authenticated sources for reuse. Use when a proof relies on a named result, the user asks whether a claim is known, or to cache a source. Do not use to audit internal proof logic, attack an implication, format bibliographies, or insert citations into a manuscript.

manuscript-integrate

Integrate an already validated mathematical result, correction, citation, or response to referee comments 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 to verify, check, stress-test, type-check or find gaps in a single claim, proof or dependency. Do not use for a whole-manuscript referee report, inventing a substantially new proof route, or merely copyediting 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. Not for correctness audits, referee reports, or source verification.

referee

Referee a whole mathematical manuscript for correctness, edge cases, notation, exposition and claim calibration. Use for a referee report, whole-paper stress test, or section-by-section manuscript audit. Do not use for a focused claim or proof audit, proofreading alone, a standalone citation or computation check, answering referee comments on one's own paper, or developing new proofs.

research-attempt

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

research-init

Set up, plan a retrofit of, substantially revise, or migrate an AI-assisted mathematical research repository's agent architecture: AGENTS.md, CLAUDE.md, live status/history, workflow files and their authority structure, including moving a flat research log into program indexes. Use only on an explicit request. Do not use for an ordinary research attempt, closing out one named program or phase, or a read-only project retrospective.

research-program

Pursue a substantial mathematical goal across multiple proof, counterexample, literature and computational routes, or close out one named program or phase by compacting its live status and history. Use for sustained investigation, several approaches, continuing after failed routes until a goal is reached, or an authorized program/phase closeout. Do not use for a single bounded attempt, explanation, proofreading, a read-only project retrospective, or migrating 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

Read or update a local append-only .mathbox ledger of exact claims, evidence revisions, dependency impact, review provenance, routes and parallel or delayed runs. Use when the user asks to set up, check, record in or reconcile such a ledger, detect stale evidence, or generate its dependency-aware handoff. Do not use merely because a ledger exists, for a casual math question, as a substitute for proof auditing, or for a prose retrospective from status files.