Six problems. A million dollars each. Unsolved for decades. What if they all break at the same number?
Each of the Clay Institute's millennium problems has a finite analog in the thin ring Z/2310Z (and extends to the True Form Z/970200Z). These are not solutions to the infinite problems — they are structural mirrors. Reflections in a ring small enough to hold in your hand. And every single one breaks at E = 3, the emerge prime. All computed in 1318 lines of C.
Eigenvalue spacings converge to Poisson, not GUE. CRT = integrable system. Independent channels = no level repulsion.
Gap = 4 sin2(pi/pmax). Exact for all primorials. Physical mass diverges = confinement.
CRT defines CRT-P class inside P. Search in O(sum pi) instead of O(N). E=3 threshold.
CRT Laplacian decomposes exactly. 5 independent channel Laplacians. Cross-channel correlation < 0.007. Channels too small for singularities.
Finite Hodge fails. 30 = D*E*G eigenvalue classes are unreachable by any idempotent projection. Unit-only classes. Freedom = algebraic unprojectability.
L(E,1) factors into 5 independent CRT components. Point counts over Fp follow Hasse bound. Finite BSD proved by Tate (1966).
Six of humanity's hardest open problems. All of them have finite mirrors in the ring. All of them break at the same threshold. 1318 lines of C. gcc -O2 -lm. No dependencies.
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The Interactive Atlas · Z/2310Z → Z/970200Z · Chapter 9 of 14