Contract

• Input: a mathematical statement to prove (or a set of statements to evaluate).
• Output: a Markdown proof artifact saved to the repo, with statement, strategy, steps, verification, and theorem citations.
• Side effects: none.
• Dependencies: none.
• Stop condition: all proof steps justified; verification passed; artifact saved.
• Risk: low — reasoning-only, no code execution.
• Boundary: generates reasoning only; no code execution, no file system writes beyond the Markdown artifact.

Pure-Math Proofs

Construct a proof — an airtight argument from accepted axioms to a stated statement — using the strategy that fits the shape of the claim.

When to use

• User asks to "prove", "demonstrate", "show rigorously" a mathematical statement.
• The statement lives in number theory, algebra, analysis, combinatorics, or topology.
• A claim from another skill (e.g. cs-formal-methods) needs a mathematical underpinning.