Spectral Disjointness and Cumulative Boundedness in the Prime Gravity Manifold

This paper establishes an empirical and theoretical framework connecting the spectral properties of the Prime Gravity fluctuation sequence Vₑrr (n) to the unconditional boundedness of its cumulative potential W (N). The central observation is domain-theoretic: Riemann zeta zeros generate log-periodic Ingham waves incommensurable with the linear Fourier basis, so projecting Vₑrr onto linear frequencies constitutes a disjointness test rather than a zero-detection apparatus. FFT peak amplitudes measured across eleven scales (N = 5, 000 to N = 10, 000, 000) grow as N⁰. 1326 near γ₁ = 14. 13 and N⁰. 1555 at the global maximum — both dramatically sub-random-walk (α ≪ 0. 5) — while the cumulative potential W (N) scales at α ≈ 0. 49, consistent with a Central Limit Theorem accumulation of √N incoherent channels. A companion Power Spectral Density experiment confirms a flat white-noise plateau across four decades of linear frequency, with no low-frequency energy accumulation. These results are interpreted as empirical evidence of hyperuniformity: the Sieve of Eratosthenes is maximally disjoint from linear oscillations, preventing any rogue-wave constructive interference in W (N). The paper identifies three algebraic bridges — zero topological entropy of the integer sieve, linear disjointness via Sarnak's Möbius Disjointness framework, and a CLT bound on W (N) — which together constitute a complete proof architecture. Combined with Paper 5's topological equivalence theorem (DOI: 10. 5281/zenodo. 19430053), closing all three bridges would unconditionally prove the Riemann Hypothesis.