openmath-open-theorem

Queries open formal verification theorems from the OpenMath platform. Use when the user asks for a list of open theorems, wants Lean or Rocq-specific theorems, needs full detail for a theorem ID, or wants to download a theorem and scaffold a local proof workspace.

Instructions

Query the OpenMath library to discover and scaffold open theorems. The discovery scripts use OPENMATH_SITE_URL and OPENMATH_API_HOST when set, and otherwise fall back to the default production endpoints.

First-run gate

Before discovery on a new machine or workspace, check the shared openmath-env.json. Auto-discovery only checks ./.openmath-skills/openmath-env.json and ~/.openmath-skills/openmath-env.json.

This gate is mandatory. If openmath-env.json is missing, or if it exists but preferred_language is missing, stop. Do not query the OpenMath theorem list, theorem detail, or download APIs until setup is complete.

If no config exists, stop and ask the user where to create it, then collect at least:

• preferred_language: lean or rocq
• config visibility / save scope: ./.openmath-skills or ~/.openmath-skills
• the submit/authz fields only if the user wants end-to-end submission later

Command:

bash

python3 scripts/check_openmath_env.py

Workflow checklist

• Env: Run check_openmath_env.py. If openmath-env.json is missing from ./.openmath-skills and ~/.openmath-skills, or preferred_language is missing, ask the user to finish setup before continuing.
• Explore: Run fetch_theorems.py [language] only after the first-run gate passes. If no language is passed, it uses preferred_language from openmath-env.json and must not fan out to other languages automatically.
• Detail: Run fetch_theorem_detail.py <id> only after the first-run gate passes.
• Download: Run download_theorem.py <id> only after the first-run gate passes.
• Prove: Use the openmath-lean-theorem skill for environment setup, preflight checks, and proving.
• Submit: Use the openmath-submit-theorem skill to hash and submit the proof.
• Verify: Run fetch_theorem_detail.py <id> and confirm your address is the prover and status is verified.
• Claim: Use the openmath-claim-reward skill to generate the withdrawal command.

Scripts

Script	Command	Use when
Shared env check	python3 scripts/check_openmath_env.py [--config <path>]	Mandatory first-run gate; validates shared config, preferred language, and the resolved OpenMath website/API endpoints.
List open theorems	python3 scripts/fetch_theorems.py [--config <path>] [language]	Listing or filtering open theorems after the first-run gate passes. language: optional lean or rocq. Without an explicit CLI language, query only the configured preferred_language.
Theorem detail	python3 scripts/fetch_theorem_detail.py [--config <path>] <id>	Need description, metadata, and formal definition (source) for a theorem ID; refuses to run until the first-run gate passes.
Download & scaffold	python3 scripts/download_theorem.py [--config <path>] <id> [--output-dir <path>] [--force]	Creating a local Lean or Rocq proof workspace after the first-run gate passes.

openmath_api.py is the shared API client. openmath_env_config.py reads shared user preferences from openmath-env.json.

Notes

• Endpoints: Default website is https://openmath.shentu.org; default API host is https://openmath-be.shentu.org. Runtime overrides: OPENMATH_SITE_URL, OPENMATH_API_HOST.
• Language: User-facing and API language naming is rocq.
• No fallback: If preferred_language is lean, query only Lean by default. If no theorems are found, report that result and stop; do not automatically query Rocq, and vice versa.
• Lean scaffold: Pins Lean and mathlib4 to v4.28.0. Rocq scaffold is _CoqProject-based.
• After download: Use the openmath-lean-theorem skill for Lean environment setup, preflight, external skill installation, and the proving workflow.

References

Load when needed (one level from this file):

• references/init-setup.md — Discovery-first setup flow for shared openmath-env.json, preferred language, and config visibility.
• references/reward_overview.md — How rewards are calculated and how to claim them.