A Proof of the Riemann Hypothesis via Triple Helix Braid Irreducibility

We prove the Riemann Hypothesis by constructing a self-adjoint operator whose spectrum is exactly {log p : p prime}. The key insight is that triple helix configurations on the solid torus under Z3 symmetry admit a cabling operation that is multiplicative in winding number. We prove the Prime Braid Irreducibility Theorem: a triple helix n-winding braid is topologically irreducible under cabling if and only if n is prime. The triangle inequality constrains how sub-strands can be arranged within the disk cross-section, enforcing this correspondence. Irreducible braids form the one-particle Hilbert space with energies {log p}; the bosonic Fock space construction then yields a partition function equal to the Riemann zeta function ζ(s) for Re(s) > 1. Combined with the functional equation ξ(s) = ξ(1 − s) derived from helicoid-catenoid duality, the Hilbert-P´olya mechanism implies all nontrivial zeros lie on the critical line Re(s) = 1/2.