The φ-Field Structure of the Prime Numbers,
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| Formato: | Recurso digital |
| Lenguaje: | inglés |
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Zenodo
2025
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| _version_ | 1866902179479027712 |
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| author | Angell, Harald |
| author_facet | Angell, Harald |
| contents | <p><strong>Abstract</strong><br>This work introduces the φ-Field framework, a resonance-based geometric law that unifies the apparent randomness of prime numbers with deterministic structural patterns. Using large-scale computational analysis and φ-ribbon geometry, the study demonstrates that primes align with predictable field structures rather than stochastic processes. The implications extend beyond number theory, suggesting vulnerabilities in randomness-dependent cryptographic systems and opening pathways toward new deterministic frameworks for encryption, physics, and biological codes such as DNA. Supplementary data and figures provide computational evidence, cross-domain visualizations, and reproducibility scripts.</p> <p> </p> <p><strong>Note on validation:</strong><br>This result is part of the Harald Wave Field Theory (HWFT) program. Evidence is presented in parallel tracks:</p> <ol> <li> <p><strong>Open, classical validation</strong> — φ-law oblateness and c²-form law, tested directly on NASA/IAU datasets.</p> </li> <li> <p><strong>Controlled-access validation</strong> — randomness/prime structure results under a 12-month responsible disclosure embargo (auto-open 2026-09-27).</p> </li> </ol> <p>See the <strong>Golden Framework community</strong> for cross-linked works:<br> <a href="https://zenodo.org/communities/golden-framework/" target="_new" rel="noopener">https://zenodo.org/communities/golden-framework/</a></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17138847 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The φ-Field Structure of the Prime Numbers, Angell, Harald Prime numbers φ-Field Deterministic randomness Cryptography Number theory Wave resonance Hardy–Littlewood Riemann hypothesis Randomness collapse DNA field geometry <p><strong>Abstract</strong><br>This work introduces the φ-Field framework, a resonance-based geometric law that unifies the apparent randomness of prime numbers with deterministic structural patterns. Using large-scale computational analysis and φ-ribbon geometry, the study demonstrates that primes align with predictable field structures rather than stochastic processes. The implications extend beyond number theory, suggesting vulnerabilities in randomness-dependent cryptographic systems and opening pathways toward new deterministic frameworks for encryption, physics, and biological codes such as DNA. Supplementary data and figures provide computational evidence, cross-domain visualizations, and reproducibility scripts.</p> <p> </p> <p><strong>Note on validation:</strong><br>This result is part of the Harald Wave Field Theory (HWFT) program. Evidence is presented in parallel tracks:</p> <ol> <li> <p><strong>Open, classical validation</strong> — φ-law oblateness and c²-form law, tested directly on NASA/IAU datasets.</p> </li> <li> <p><strong>Controlled-access validation</strong> — randomness/prime structure results under a 12-month responsible disclosure embargo (auto-open 2026-09-27).</p> </li> </ol> <p>See the <strong>Golden Framework community</strong> for cross-linked works:<br> <a href="https://zenodo.org/communities/golden-framework/" target="_new" rel="noopener">https://zenodo.org/communities/golden-framework/</a></p> |
| title | The φ-Field Structure of the Prime Numbers, |
| topic | Prime numbers φ-Field Deterministic randomness Cryptography Number theory Wave resonance Hardy–Littlewood Riemann hypothesis Randomness collapse DNA field geometry |
| url | https://doi.org/10.5281/zenodo.17138847 |