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Computational Composite Methodology

Computational Composite Methodology · Under construction

Unlike the other cases here, CCM doesn't target any one specific conjecture — it's a methodological theory about how the mathematical research process itself should be organized. Its core claim is methodological, not ontological: mathematical research can be represented as a continuously evolving state, in which multiple representations, search operators, certificate languages, obstructions, cost models, and path histories all interact. CCM formally separates four concepts that are often conflated — truth, method coverage, search success, and verification — and proves a core firewall theorem: as long as every final positive/negative verdict is gated by a sound verifier, and every representation transformation preserves certificate semantics, the routing process itself can be fully heuristic or even AI-generated, and the conclusion remains rigorous.

13 "calibration benchmarks" (Benchmarks 01-13) span extremal graph theory, number-theoretic semigroups, recursion, SAT/combinatorics, matrix algebra, linear-programming duality, Farkas' lemma, convexity, polynomial nonnegativity, composite routing, certificate-library expansion, cost-aware routing, and online adaptive routing — the documents explicitly state these are "empirical witnesses to the theory, not the theory itself." There is also a separate 18-round deep-application series applying CCM to the modern Hilbert's third problem (scissors congruence / Dehn invariant).