Ultrametric and Adelic Structure in a Hierarchical Model of Emergent Space-Time: A Research Programme
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| Natura: | Recurso digital |
| Lingua: | inglese |
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2026
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| author | Carlos Herrero González |
| author_facet | Carlos Herrero González |
| contents | <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">We propose a mathematical framework for the emergence of space-time from a discrete hierarchy of physical regimes, called Levels of Existence, characterised by the propagation velocity of their constituent entities relative to the invariant constant c. The correspondence between this hierarchy and established mathematical structures is articulated by systematically distinguishing between verified results, working conjectures with specified verification protocols, and open questions.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">Verified results include: the existence valuation v_p(E) = -floor(log_p(E)) is a rigorous non-Archimedean valuation (Theorem 1); Ostrowski's theorem independently motivates four types of completions of Q; the spectral parameter of the Vladimirov operator alpha_p = log(p+1)/log(p) is geometrically determined by the Bruhat-Tits tree without free adjustment; the primordial state is formally the zero element of the tropical semiring; the series defining the vacuum form factors Z_p converges for m_p > 0 and diverges for m_p = 0.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">Working conjectures with specified verification protocols include: the transformation matrices are isomorphic to Iwahori subgroups of GL(n,Q_p); the tropicalisation of the flag variety Fl(2) over the adele ring is isomorphic to the light cone. Appendix A establishes that the Hecke algebra for p=5 admits representations whose eigenvalue field contains Q(sqrt(5)). Appendix B provides the first verified quantitative computation: vacuum form factors Z_p for the first eight primes, with a rigorous convergence proof and the negative result that isolated minimisation of Z_p does not select the spectral parameter.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19794253 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Ultrametric and Adelic Structure in a Hierarchical Model of Emergent Space-Time: A Research Programme Carlos Herrero González p-adic analysis, ultrametric geometry, adele ring, Bruhat-Tits building, Iwahori subgroup, Vladimirov operator, tropical geometry, Mikhalkin-Payne theorem, emergent space-time, p-adic mathematical physics, Hecke algebra, form factors <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">We propose a mathematical framework for the emergence of space-time from a discrete hierarchy of physical regimes, called Levels of Existence, characterised by the propagation velocity of their constituent entities relative to the invariant constant c. The correspondence between this hierarchy and established mathematical structures is articulated by systematically distinguishing between verified results, working conjectures with specified verification protocols, and open questions.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">Verified results include: the existence valuation v_p(E) = -floor(log_p(E)) is a rigorous non-Archimedean valuation (Theorem 1); Ostrowski's theorem independently motivates four types of completions of Q; the spectral parameter of the Vladimirov operator alpha_p = log(p+1)/log(p) is geometrically determined by the Bruhat-Tits tree without free adjustment; the primordial state is formally the zero element of the tropical semiring; the series defining the vacuum form factors Z_p converges for m_p > 0 and diverges for m_p = 0.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">Working conjectures with specified verification protocols include: the transformation matrices are isomorphic to Iwahori subgroups of GL(n,Q_p); the tropicalisation of the flag variety Fl(2) over the adele ring is isomorphic to the light cone. Appendix A establishes that the Hecke algebra for p=5 admits representations whose eigenvalue field contains Q(sqrt(5)). Appendix B provides the first verified quantitative computation: vacuum form factors Z_p for the first eight primes, with a rigorous convergence proof and the negative result that isolated minimisation of Z_p does not select the spectral parameter.</p> |
| title | Ultrametric and Adelic Structure in a Hierarchical Model of Emergent Space-Time: A Research Programme |
| topic | p-adic analysis, ultrametric geometry, adele ring, Bruhat-Tits building, Iwahori subgroup, Vladimirov operator, tropical geometry, Mikhalkin-Payne theorem, emergent space-time, p-adic mathematical physics, Hecke algebra, form factors |
| url | https://doi.org/10.5281/zenodo.19794253 |