desargues-hf/annals-math-rl-sample

Desargues Formal Reasoning Sample

Two Lean 4 theorem-proving tasks spanning textbook algebra and research mathematics, packaged by Desargues with execution environments and automated verification for Harbor.

RL environments: We convert formal theorem statements into RL tasks with executable verification. Our Lean-GAP example is derived from open-source statements authored by contributors in our network. This sample pairs a textbook algebra exercise with an AnnalsChallenge research theorem, using the same reproducible Lean and Mathlib environment and separate submission verifier.

Expert-authored data: Our contributors have worked on research-level formalizations, including AnnalsFormalization. We can recruit experts to produce new, mathematically reviewed formal statements tailored to labs' research goals.

Included tasks

Task	Task ID	Mathematical level
Kernel and image of a linear map are submodules	lean_gap_df_10_2_1	Textbook algebra (Lean-GAP, exercise 10.2.1)
Absolute profinite rigidity and hyperbolic geometry	annals_absolute_profinite_rigidity	Research mathematics (AnnalsChallenge)

Each task has one theorem target and includes instructions, an environment recipe, starter workspace inputs, and a verifier. manifest.json, manifest.parquet, and registry.json describe both tasks. The levels describe the mathematics; agent solving difficulty has not been empirically calibrated. Reference proofs are not included.

Agent workflow and grading

1. Initialize /workspace using the command in the task's instructions.
2. Complete Submission.lean, adding Lean helper files under Submission/ as needed. Lean and Mathlib are available; task execution runs without network access.
3. Harbor collects the submitted Lean files and sends them to a fresh verifier sandbox. Comparator checks the proof against the original trusted statement.

Reward is 1 for a fully accepted proof and 0 for an incomplete, invalid, or timed-out submission. There is no partial credit. Infrastructure failures are reported separately. Lean compilation alone does not establish success: unfinished sorry proofs are rejected by the verifier.

Solution.lean connects the submitted declarations to the verifier; it contains no reference proof. The submitted answer is the workspace files.

Run a task

Requires Python 3.12+, the Hugging Face CLI, and a Daytona account. Set DAYTONA_API_KEY, DAYTONA_API_URL, and the credentials required by your agent. Replace AGENT_NAME and MODEL_NAME below with your chosen agent and model.

hf download desargues-hf/annals-math-rl-sample --repo-type dataset --local-dir annals-math-rl-sample
cd annals-math-rl-sample

python3 -m venv .venv
source .venv/bin/activate
python -m pip install -e './generator[run]'
python -m annals_challenge_harbor.snapshot
SNAP=$(python -m annals_challenge_harbor.snapshot --print-name)

harbor run -p tasks -e daytona --ek snapshot_template_name="$SNAP" \
  -a AGENT_NAME -m MODEL_NAME -i lean_gap_df_10_2_1 -n 1

The snapshot command builds the shared environment in your Daytona account. Initial setup requires network access; agent execution and grading are offline. To run the research task, use -i annals_absolute_profinite_rigidity.

Each task requests 4 CPUs, 8 GiB memory, and 10 GiB storage, with a four-hour agent budget and a three-hour-fifteen-minute verifier budget.

Environment

The sample includes a shared Docker build recipe and a Daytona snapshot helper. See the environment documentation for local Docker builds, dependency versions, and regeneration.