Prompt 11 — Mathematical concept-invention candidate miner

Inputs

SESSION_BUNDLE: {{SESSION_BUNDLE_JSON}}
CURRENT_LEARNER_LIBRARY: {{CURRENT_LEARNER_LIBRARY_JSON}}
VISIBLE_CURRICULUM_ONLY: {{VISIBLE_CURRICULUM_ONLY_JSON}}
REFERENCE_LIBRARY_ACCESS: {{REFERENCE_LIBRARY_ACCESS_POLICY_JSON}}
MIN_REUSE_COUNT: {{MIN_REUSE_COUNT}}
MIN_HELDOUT_GAIN: {{MIN_HELDOUT_GAIN}}

Task

Analyze verified and failed learner episodes for recurring structures that may deserve a reusable concept, lemma, algorithm, representation, invariant, or strategy.

You may propose a candidate only when the archive shows a concrete pressure, such as:

• repeated predicates or cumbersome descriptions;
• repeated proof fragments;
• repeated transformations;
• repeated conserved quantities;
• a recurring equivalence class;
• a representation that shortens several solutions;
• a procedure that solves a family rather than one instance;
• a physical relationship that predicts held-out observations.

For each candidate, produce:

• candidate ID and type;
• gap brief;
• originating episode IDs;
• positive, negative, borderline, adversarial, and counterexample cases;
• candidate definition or procedure;
• nearest learner-library concepts;
• dependencies;
• expected compression gain;
• expected held-out solve gain;
• transfer domains;
• complexity and brittleness costs;
• falsification plan;
• independent verification obligations;
• contamination assessment;
• status candidate only.

Do not consult the modern reference library unless REFERENCE_LIBRARY_ACCESS explicitly allows the historian-comparison phase. Do not call a candidate “new” except new_to_agent or new_to_current_library after comparison.

Return concept-invention artifacts compatible with the existing general.concept-invention capability chain plus native MathGenesis candidate objects. Wrap native candidate objects in JSON matching schemas/library-batch.schema.json; keep existing general.concept-invention artifacts in metadata.compatibility_artifacts until dedicated schemas are wired.