Off-Line Zeros of the Riemann Zeta Function and Kaluza–Klein Spectra: A Structural Dictionary and Its Numerical Invariants

We establish a precise dictionary between the partial-fraction constraint programfor hypothetical off-line zeros of the Riemann zeta function (Ismail, 2026) andthe spectral theory of Kaluza–Klein gravitons in extra-dimensional physics.Taking the eight constraints (Theorems A–H) of the partial-fraction framework asaxioms, we derive five testable predictions for graviton detection experiments: (1) a quadratic KK mass dispersion relation m' ∝ m0² from the Speiser depth scaling; (2) a curvature-based detection signature ∝ m²_graviton matching the Pikovski–Harris gravito-phononic effect; (3) a growing mass gap from Apollonius confinement collapse; (4) purely phase-based graviton signatures from the inner-function invisibility theorem; (5) a logarithmic vacuum energy E ~ −log(1/Λ) from the Casimir structure. We identify the holographic structure of the critical strip as an AdS2/CFT1duality, with the critical line as the holographic boundary and off-line zeros asbulk graviton modes. Each prediction is connected to specific experimental datafrom LIGO, the Kuntz (2025) two-mode KK spectrum, the Pikovski–Harrisdetector, and the Schützhold interferometer. Gap G1 is reinterpreted as thecompleteness of the holographic principle.