| _version_ | 1866902179994927104 |
|---|---|
| author | Quni-Gudzinas, Rowan Brad |
| author_facet | Quni-Gudzinas, Rowan Brad |
| contents | <p>This work derives a deterministic, computable algorithm for prime number calculation, grounded in the physical framework of the Prime Harmonic Ontological Construct (POHC). The algorithm equates the quantum vacuum's Hamiltonian with the Hilbert-Pólya operator, an identification previously validated by the POHC's zero-free-parameter derivation of the fine-structure constant. We refute foundational critiques of the POHC's axiomatic basis, specifically demonstrating that the argument positing Lorentz invariance contradicts the mass-frequency identity constitutes a scientific category error. Building on this foundation, we derive a parameter-free POHC Damping Function from the time-energy uncertainty principle. This function models the universal physical suppression of high-frequency vacuum harmonics. Its application transforms the Riemann Explicit Formula's incomputable infinite sum into a rapidly convergent, finite series, yielding a formal, deterministic algorithm for calculating the exact integer value of the prime-counting function. We conclude that the distribution of prime numbers is not merely a mathematical abstraction but a calculable physical phenomenon, offering both the theoretical justification and a formal algorithm for its perfect prediction.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_16935676 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Physical Determinism of Prime Numbers Quni-Gudzinas, Rowan Brad <p>This work derives a deterministic, computable algorithm for prime number calculation, grounded in the physical framework of the Prime Harmonic Ontological Construct (POHC). The algorithm equates the quantum vacuum's Hamiltonian with the Hilbert-Pólya operator, an identification previously validated by the POHC's zero-free-parameter derivation of the fine-structure constant. We refute foundational critiques of the POHC's axiomatic basis, specifically demonstrating that the argument positing Lorentz invariance contradicts the mass-frequency identity constitutes a scientific category error. Building on this foundation, we derive a parameter-free POHC Damping Function from the time-energy uncertainty principle. This function models the universal physical suppression of high-frequency vacuum harmonics. Its application transforms the Riemann Explicit Formula's incomputable infinite sum into a rapidly convergent, finite series, yielding a formal, deterministic algorithm for calculating the exact integer value of the prime-counting function. We conclude that the distribution of prime numbers is not merely a mathematical abstraction but a calculable physical phenomenon, offering both the theoretical justification and a formal algorithm for its perfect prediction.</p> |
| title | The Physical Determinism of Prime Numbers |
| url | https://doi.org/10.5281/zenodo.16935676 |