Verify and repair algebra

Use the user's chosen tools when specified. Otherwise, use an available ResiMind MCP connection or its JSON-lines CLI to check polynomial work independently of the proposing model. Read the interface reference for setup, request syntax and result interpretation.

Preserve the original expression, declared variables and assumptions. ResiMind accepts integer literals, +, -, *, nonnegative integer powers and division by a nonzero integer literal. Do not silently discard conditions or turn a variable denominator into an unconditional polynomial identity.

For a proposed equality, call verify_identity. For a multi-step derivation, check adjacent steps in order and report the first rejected step. If a preceding step is unresolved, report that uncertainty instead of certifying the prefix.

• verified: report the exact coefficient evidence for this equality.
• rejected: use the mismatch to propose a correction. For an expansion task, expand_polynomial can provide independently checked sparse terms.
• unresolved: report the unsupported operation or work limit. Use another appropriate method if available; this result is not a disproof.

Recheck a proposed repair against the original source. At most three repair attempts are useful for this workflow; if they do not verify, return the remaining mismatch or uncertainty. Do not describe an exact algebra check as a Lean proof. Sparse coefficients are decimal strings: keep their exact values.

Use learn_polynomial only when the task includes retaining or learning rules. Inspect learning.new_rule_ids: a verified solution alone does not establish that a new rule was learned. Keep one server process alive for learning and recall; restart clears this interface's memory. A recall miss permits another solver, but should not be reported as successful rule reuse.

Return the corrected result, the verification outcome and any unresolved conditions. The workflow does not require publishing user inputs, modifying project configuration, or sending data to an external model.