Benchmarks 01-13 Theory Extraction Map

The document positions itself immediately at the top: ‘records what each benchmark contributes to the foundational theory. Benchmarks are evidence and calibration artifacts, not CCM's definitions.’ Includes a complete cross-reference table, laying out each of the 13 benchmarks' mathematical ecosystem and main methodological contribution in turn: 01 Mantel (extremal graph theory, finite evidence → structural compression → global lift), 02 Frobenius (number-theoretic semigroups, exact symbolic reconstruction and residue thresholds), 03 Zeckendorf (recursion/greedy, recursive partition and mutation-necessity testing), 04 Ramsey (SAT/combinatorics, falsification as constraint, impossibility patterns), 05 Cayley–Hamilton (matrix algebra, the distinction between general and minimal certificates), 06 Primal–Dual LP (optimization, cross-representation coupling and certificate hierarchy), 07 Farkas (convex cones, positive certificates of nonexistence), 08 Jensen (nonlinear convexity, defect decomposition and the sign domain), 09 SOS/Motzkin (polynomial nonnegativity, coverage-vs-truth, method-obstruction certificates), 10 Composite Routing (mixed polynomial objectives, three-state semantics), 11 Certificate Expansion (fixed target set, library coverage monotonicity and conservative expansion), 12 Cost-Aware Routing (overlapping certificates, vector cost and routing regret), 13 Online Routing (non-stationary streams, dynamic state and switching delay). The document splits the 13 papers into two phases: Phase I (01-09) is ‘certificate-ecosystem calibration,’ with the recurring structure ‘controlled representation → compression/coupling/separation/decomposition → proof-bearing certificate → generalization lift’ — the document emphasizes: ‘the domain-specific proof-bearing objects will change; the control architecture will persist’; Phase II (10-13) formally shifts the research focus from individual certificate languages to the policy for choosing a certificate language itself. The document also lists theoretical elements jointly observed across more than one benchmark (defect decomposition appears in both LP duality/Jensen-variance/SOS; positive nonexistence certificates appear in both SAT-UNSAT/Farkas separation; obstruction preservation appears in both the failed Ramsey deletion hypothesis and the Motzkin non-SOS obstruction). It closes by explicitly drawing the ‘benchmark claim boundary’: this project only supports the existence and reproducibility of the CCM workflow skeleton, not universal superiority, completeness, or convergence of the unresolved region to zero.