THE SPECTRAL RIGIDITY FRAMEWORK: A FULLY CONTROLLED OPERATOR AND DISCRETE LATTICE APPROACH TO THE RIEMANN ZEROS, FEATURING DETERMINISTIC PRIME PATHWAYS

This paper develops a spectral framework representing the non-trivial zeros of the
Riemann zeta function as eigenvalues of a self-adjoint operator on L2(R). The construction
integrates a Hilbert–P´olya type operator with confining potential and arithmetic
delta-array, a fully crystallized trace formula with exact base-prime propagation, and
discrete ternary lattice dynamics seeded by base primes 2, 3, 5, 7. Recursive eigenvalue
generation ensures exact arithmetic-spectral correspondence, uniform control across
the spectrum, and lattice rigidity. This provides a fully controlled operator-theoretic
realization of the Hilbert–P´olya conjecture and strong evidence for the Riemann Hypothesis