The Shape of the Hardest Problems: Anomaly Cancellation, Resurgence, and Optimal Packing as the Common Structure of the Millennium Prize Problems

We apply the Omuo Genesis Engine, a geometric knowledge synthesis platform operating on the 240-root E8 lattice in C^1024, to investigate whether the seven Millennium Prize Problems share a common structural mechanism. 185 concepts spanning all seven problems were encoded as complex phasor vectors and iteratively synthesized. Four independent experimental runs — a Riemann Hypothesis run (2,379 nodes, 199 bridges), a chemical elements run (1,491 nodes, 111 bridges), an extended RH run (3,153 nodes, 71 bridges), and the Millennium synthesis (1,771 nodes, 121 bridges) — converge independently on the same three-layered structure. Layer 1: Every Millennium problem is an instance of a cohomological anomaly that must…