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| Formato: | Recurso digital |
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Zenodo
2025
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| Acceso en línea: | https://doi.org/10.5281/zenodo.16935676 |
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- <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>