15.2 Historical and generated worlds

Historical controls test reconstruction under carefully restricted evidence. Generated mini-worlds test invention where memorized names and standard proof templates cannot supply the answer directly.

Historical cases such as Galois theory or the development of group theory are motivation, not benchmarks of autonomous rediscovery. Their surrounding languages, failed attempts, and later interpretations are difficult to freeze. They are best used to ask whether AGENTIC’s audit vocabulary—obstruction, new primitive, transport, consequence, and reuse—describes the episode without claiming that the historical mathematician literally executed DIAL.

Generated worlds permit a stronger test. The evaluator can sample a finite algebraic presentation, hide one generator, quotient, symmetry, or invariant, and release only typed queries. Novel names prevent direct retrieval, while a machine-held model supplies exact counterexamples. The frozen reference space specifies which concepts and constructors the system already possesses.