15.4 An AGENTIC mathematical episode

A failure-first episode begins when RELIC’s current conjecture policy repeatedly encounters examples that cannot be separated in the existing vocabulary. The structural component selects transformations whose outcomes distinguish a missing invariant from a bad conjecture. OPTIC constructs a recognizer, canonicalization procedure, quotient operation, or proof macro for the proposed primitive. RELIC then uses the admitted operation to formulate and test a new family of statements. Feedback may revise the definition without silently discarding counterexamples that motivated it.

The component admission records are different. Structural diagnosis is checked by held-out transformations and countermodels. The OPTIC artifact must type-check, terminate under its declared contract, and agree with an independent reference implementation where one exists. RELIC must show improved query efficiency or new solvable problems under a matched budget. The interface certificate asks whether the same mathematical object is transported across all three stages.