What Primes Are: A Recognition Science Perspective on the Atoms of Arithmetic and Why Zeros Lie on a Line
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| Natura: | Recurso digital |
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Zenodo
2026
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| _version_ | 1866901790945968128 |
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| author | washburn, jonathan |
| author_facet | washburn, jonathan |
| contents | <p>We present an expository account of prime numbers as they appear in Recognition Science (RS), a framework that derives physical structure from a single primitive: the Recognition Composition Law. Within RS, primes are not mysterious random objects but the irreducible events in a universal ledger—the fundamental "atoms" of multiplicative accounting. This perspective illuminates the Riemann Hypothesis: zeros of the zeta function must lie on the critical line because any other configuration would violate the conservation constraints imposed by the ledger's eight-tick structure. We give an intuitive proof outline that builds geometric understanding before introducing technical machinery, making the underlying mechanism transparent. The central insight is that prime-frequency observables are bandlimited by the ledger's Nyquist cutoff, which bounds prime sums uniformly and forces zeros onto the symmetry axis through an energy-budget argument.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18133411 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | What Primes Are: A Recognition Science Perspective on the Atoms of Arithmetic and Why Zeros Lie on a Line washburn, jonathan <p>We present an expository account of prime numbers as they appear in Recognition Science (RS), a framework that derives physical structure from a single primitive: the Recognition Composition Law. Within RS, primes are not mysterious random objects but the irreducible events in a universal ledger—the fundamental "atoms" of multiplicative accounting. This perspective illuminates the Riemann Hypothesis: zeros of the zeta function must lie on the critical line because any other configuration would violate the conservation constraints imposed by the ledger's eight-tick structure. We give an intuitive proof outline that builds geometric understanding before introducing technical machinery, making the underlying mechanism transparent. The central insight is that prime-frequency observables are bandlimited by the ledger's Nyquist cutoff, which bounds prime sums uniformly and forces zeros onto the symmetry axis through an energy-budget argument.</p> |
| title | What Primes Are: A Recognition Science Perspective on the Atoms of Arithmetic and Why Zeros Lie on a Line |
| url | https://doi.org/10.5281/zenodo.18133411 |