Learn from Math Agent Trajectories

Extract reusable Jacobian lessons from a completed or paused investigation; do not resume solving the problem. A correct answer can expose workflow defects, and an unsuccessful search can reveal useful mathematical vocabulary.

Establish the evidence

Record the intended and actual outcome, stopping condition, transcript coverage, and available revision/catalog context. Use observable sources, calls, code, artifacts, corrections, and final claims. Narration alone is not execution evidence; current-main capabilities were not necessarily available in the trace.

Reconstruct decisions that changed correctness, cost, progress, or confidence. For a finding that depends on mathematical claims, numerical or symbolic work, solver semantics, or bespoke code, consult mathematical evidence. Preserve decisive claims and later corrections, with their hypotheses and evidence scope.

Attribute the lesson

Distinguish working capabilities, environment limitations, discovery/selection, execution friction, representation/interoperability, contract/scale defects, missing operations, handoff failures, and caller reasoning. Compare needed postconditions with the session-visible catalog when available; check current source before proposing new work. Handwritten code and tool non-use are leads, not automatic evidence of missing operations.

Separate a reusable operation gap from public-catalog admission. An existing postcondition with a narrow envelope is a scale/backend question. A convenience or theorem-specific assembly does not become a public operation solely because it occurred in the trace. Use the admission contract when proposing publication.

Route only when the requested follow-up needs a deeper workflow:

• evaluate-mcp-tool-adoption for controlled availability, discovery, or selection;
• audit-mcp-tool-friction for problems after selecting a tool;
• audit-public-operation-contracts for a particular mathematical contract; or
• recent-conjecture-evaluations for a new held-out reliability probe.

An unresolved conjecture is generally unsuitable as an evaluation oracle. Extract frozen, independently checkable finite obligations when proposing an evaluation, and preserve contamination boundaries.

Report actionable learning

For each material finding, give the source evidence, implication, proportionate repair, and uncertainty. Include a compact claim/correction ledger when it helps explain a changed conclusion; include ownership and success criteria when proposing implementation. Search narrowly for an existing issue before suggesting a new one. External mutations require user authorization.

Prefer discovery, contract, representation, or scale repairs when they explain the failure. Update skills only for reusable decision guidance and product docs only for durable public behavior. An isolated agent slip may need no repository change. Stop when the requested trace is accounted for and the supported lessons and remaining proof gaps are clear; report coverage rather than implying that the underlying mathematical problem is solved.