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 V_err(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 V_err 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 N^0.1326 near γ₁ = 14.13 and N^0.1555 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.