The Prime Gravity Constant: Blind Frequency Selection and Structural Confirmation of Ω_PG = π/log(5) in the Hilbert–Pólya Operator
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2026
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| _version_ | 1866901881279741952 |
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| author | Gleason, Timothy |
| author_facet | Gleason, Timothy |
| contents | <p>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 Ω_PG = 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 — Ω_PG 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 Ω_PG, 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.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19519372 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Prime Gravity Constant: Blind Frequency Selection and Structural Confirmation of Ω_PG = π/log(5) in the Hilbert–Pólya Operator Gleason, Timothy Prime Gravity Prime Gravity Constant Omega_PG pi/log(5 Frequency Selection Hilbert–Pólya Conjecture Blind Falsification Valley Landscape Arithmetic Frequency Riemann Zeros Boundary Oscillation Geodesic Schrödinger Operator Number Theory Mathematical Physics Zeta Function Spectral Theory Prime Distribution <p>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 Ω_PG = 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 — Ω_PG 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 Ω_PG, 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.</p> |
| title | The Prime Gravity Constant: Blind Frequency Selection and Structural Confirmation of Ω_PG = π/log(5) in the Hilbert–Pólya Operator |
| topic | Prime Gravity Prime Gravity Constant Omega_PG pi/log(5 Frequency Selection Hilbert–Pólya Conjecture Blind Falsification Valley Landscape Arithmetic Frequency Riemann Zeros Boundary Oscillation Geodesic Schrödinger Operator Number Theory Mathematical Physics Zeta Function Spectral Theory Prime Distribution |
| url | https://doi.org/10.5281/zenodo.19519372 |