The Evolution Machine: Turning Proof Friction into Systematic Progress

Enterprise agent systems generate candidate claims, plans, and proofs at a rate that exceeds human verification capacity. This shifts the bottleneck from generation to promotion: what can be safely accepted, replayed, and defended under dispute. Our work presents the Evolution Machine, a triadic architecture composed of Solvers, Math Machines, and Learner Machines. Solvers explore candidate solutions; Math Machines enforce promotability under explicit regimes, admissible transforms, falsifiers, and verification budgets; and Learner Machines distill reusable motifs and repairs from the bidirectional interaction, generating improved candidates and bridge proposals without altering promotion rules. We define a computable notion of evolution as increasing variation of wisdom and show how systematic progress can occur even when raw problem-solving capability does not increase, provided that promotability discipline and repair knowledge accumulate. We evaluate the thesis on a suite of settled truth domains spanning short proofs, foundation-sensitive arguments, long and formal proofs, and computer-assisted proofs, using motifs and receipts as portable learning artifacts. The suite is constructed to force generalization across regimes and verification substrates: each case is treated as a different representation of promotability under explicit admissibility, and each run produces a comparable set of outputs — regime cards, Circle-of-Equivalence bridges, HOLD ledgers, and repair receipts — that can be replayed under substitution. Across the suite, the Learner Machines accumulate a motif atlas and a repair library that transfer between domains, so progress is measured as reduced recurrence of the same failure patterns and faster convergence to PASS(well-formed protocol) under bounded verification budgets, rather than as narrative confidence in any single proof.