The Prime Gravity Constant: Blind Frequency Selection and Structural Confirmation of ΩPG = π/log (5) in the Hilbert–Pólya Operator

Paper 9 identified an oscillatory correction to the Prime Gravity Hilbert–Pólya boundary law with empirical frequency ω = π/log (5). The present paper asks whether this frequency is structurally selected by the Prime Gravity manifold or an artifact of the W values chosen for testing. We introduce the Prime Gravity Constant ΩPG = π/log (5) ≈ 1. 95198 and subject it to a blind frequency falsification test: a dense scan maps actual coll=0 valley positions at each W with no formula guidance, and candidate frequencies are scored by their ability to predict those positions. Across 12 W values spanning three orders of magnitude — including both structured (round) and adversarial (prime-valued) cutoffs — ΩPG achieves the lowest mean prediction error (0. 097) among all tested candidates and remains stable under ±5% perturbation, while competing frequencies degrade under irregular W sampling. The error landscape exhibits a clear global minimum at ΩPG, supporting structural rather than coincidental selection. π/log (2) emerges as a meaningful harmonic competitor on structured W values but collapses on prime-valued W, ruling it out as the dominant frequency in this framework.