The Origin of Zeta: Emergence of the Partition Function from Arithmetic Equilibrium
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2025
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| author | DELATORRE, JOHN ChatGPT (OpenAI Collaborative Research) |
| author_facet | DELATORRE, JOHN ChatGPT (OpenAI Collaborative Research) |
| contents | <p> We invert the traditional “Gibbs ⇒ ζ” narrative. Instead of assuming the Riemann<br> zeta function as a given analytic object or postulating a Gibbs ensemble with energies<br> En = lnn, we show that a discrete arithmetic medium—the primeon ensemble in<br> logarithmic p-space—forces an equilibrium measure with weights n−s. The normalizer<br> is then n≥1n−s = ζ(s) by necessity. Thus, ζ is not merely a convenient partition<br> function; it is the statistical shadow of a stable arithmetic equilibrium. The nontrivial<br> zeros acquire a physical meaning as phase-resonance conditions of the lattice; the critical<br> line ℜ(s) = 1/2 is a stability boundary</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17555113 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
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| spellingShingle | The Origin of Zeta: Emergence of the Partition Function from Arithmetic Equilibrium DELATORRE, JOHN ChatGPT (OpenAI Collaborative Research) Riemann zeta partition function primeon lattice p-space equilibrium measure inverse-square law <p> We invert the traditional “Gibbs ⇒ ζ” narrative. Instead of assuming the Riemann<br> zeta function as a given analytic object or postulating a Gibbs ensemble with energies<br> En = lnn, we show that a discrete arithmetic medium—the primeon ensemble in<br> logarithmic p-space—forces an equilibrium measure with weights n−s. The normalizer<br> is then n≥1n−s = ζ(s) by necessity. Thus, ζ is not merely a convenient partition<br> function; it is the statistical shadow of a stable arithmetic equilibrium. The nontrivial<br> zeros acquire a physical meaning as phase-resonance conditions of the lattice; the critical<br> line ℜ(s) = 1/2 is a stability boundary</p> |
| title | The Origin of Zeta: Emergence of the Partition Function from Arithmetic Equilibrium |
| topic | Riemann zeta partition function primeon lattice p-space equilibrium measure inverse-square law |
| url | https://doi.org/10.5281/zenodo.17555113 |