leanscreen

A calibrated faithfulness screen for informal↔Lean 4 statement pairs, served over MCP so Claude (Code, Desktop, or any MCP client) can check statements while you draft them.

The one thing to understand before using it: this screen may only reject. passed_screening means "no defect found by this harness" — it is not a certification of faithfulness. Measured against 886 frozen human verdicts, statements a human reviewer had rejected still passed the full screen 17.0% of the time for theorems and 35.6% for definitions; statements a human had certified faithful were flagged 15–18% of the time. Every response carries this calibration verbatim.

Two tools

check_fast — deterministic only: lints (unused binders, trivially satisfiable existentials, pinned ∃! witnesses, suspicious ℕ-arithmetic, …), vacuity checks (reflexive goals, True goals, withheld declarations), and Lean 4 elaboration against your own mathlib environment. Zero API calls, no key needed, ~0.1s per statement once the REPL is warm. Call it constantly while drafting.

check_deep — everything in check_fast, plus two independent LLM judges under strict consensus (a back-translation judge and a clause-by-clause checklist judge on separate models) and an adversarial counterexample probe. Runs on your ANTHROPIC_API_KEY; measured cost is roughly $0.17–0.27 per statement (the response reports actual spend as actual_cost_usd), 30–60 seconds. Call it deliberately, before something ships.

Both take informal (the natural-language statement), lean (the Lean 4 statement), and an optional kind (theorem | definition, inferred from the declaration head when omitted). Responses rank their evidence — counterexample > deterministic > two-judge-consensus > single-judge — and a single-judge flag is explicitly labeled as below the reporting bar.

Related MCP server: Chiasmus

Install

pip install git+https://github.com/ibrahimmian36/leanscreen

Requires Python ≥3.12. Runtime dependencies: httpx, pydantic, pydantic-settings, mcp — nothing else.

Lean setup (optional but recommended)

Without a Lean project, the server still runs — check_fast does lints + vacuity and says plainly that elaboration was skipped. With one, statements are elaborated for real:

1. A Lean 4 project with mathlib, built: lake build inside it.

2. The community REPL, built against the same toolchain: lake build inside the repl repo gives you .lake/build/bin/repl.

3. lake on the server's PATH.

mathlib imports once at server startup (~100 seconds, in the background — calls arriving mid-warm-up answer immediately with a "still warming" note), then each check takes ~0.1s.

Configuration

Environment variables (or a .env in the working directory), all LEANSCREEN_-prefixed:

Claude Code (.mcp.json in your project) or Claude Desktop (claude_desktop_config.json):

{
  "mcpServers": {
    "lean-faithfulness-screen": {
      "command": "leanscreen",
      "env": {
        "LEANSCREEN_LEAN_PROJECT_PATH": "/path/to/your/lean-mathlib-project",
        "LEANSCREEN_LEAN_REPL_PATH": "/path/to/repl/.lake/build/bin/repl",
        "ANTHROPIC_API_KEY": "sk-ant-…"
      }
    }
  }
}

What this does not guarantee

The judge configuration was calibrated 2026-07-15 against 886 frozen human verdicts (595 faithful / 291 unfaithful) from a production research-math corpus. Under strict two-judge consensus, human-rejected pairs still passed 17.0% (theorems) / 35.6% (definitions) of the time, and human-certified pairs were flagged 15–18% of the time. Both judges are Anthropic-family models, so correlated blind spots cannot be ruled out. The counterexample probe confabulates: on one PutnamBench sample its counterexamples were wrong 4 times out of 5. Treat every flag as a candidate for human confirmation and every pass as "nothing found", never "faithful."

Human certification — an expert reviewer confirming that the Lean means the informal statement — is what this screen deliberately does not automate. We offer it as a service: contact ibrahimnmian@gmail.com.

License

FSL-1.1-Apache-2.0 (the Functional Source License): free to use, copy, modify, and redistribute — including internal commercial use, non-commercial education and research, and professional services — but not to offer as a competing commercial product or service. Each version automatically becomes Apache 2.0 two years after its release (the same license as mathlib). Not OSI-approved until the conversion — read it before building on it commercially.

Provenance

Extracted from Millennium Research's private formalization platform (2026-07-28); the detector stack, judge prompts, and calibration figures are the ones used in our published benchmark audits (miniF2F, ProofNet#, PutnamBench, ProofNetVerif, CLEVER). The calibration data is not included.

Project page: millenniumresearch.ai/leanscreen