Ratio-Based Adelic Physics: Reconciling Continuous Topology and Ultrametric Complexity across Spin Glasses, Linguistics, and Cosmology
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Zenodo
2026
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| author | Quni-Gudzinas, Rowan Brad |
| author_facet | Quni-Gudzinas, Rowan Brad |
| contents | <p>The tension between continuous Archimedean spacetime paradigms and discrete, non-Archimedean topological realities constitutes the central mathematical bottleneck in modern complexity science, hindering the unification of quantum mechanics, spin glass phase dynamics, and cognitive psychophysics. This manuscript resolves these disparities by introducing a ratio-based adelic framework, utilizing generalized scaling ratios ($q$) and Bruhat-Tits tree topologies to replace traditional integer-prime models. By formulating the Vladimirov fractional derivative operator natively for arbitrary transcendental values and deriving the corresponding $q$-adic product formulas, this methodology actively maps discrete states onto continuous metrics using the Monna projection. Simulated integrations verify that linguistic c-command parsing, passive quantum error correction scaling, and thermodynamic barrier thresholds all adhere to identical ultrametric properties dictated by these scaling parameters. Consequently, the results demonstrate that logical error suppression scales exponentially as $q^{-d}$, that spatial dimensionality fundamentally bounds replica symmetry breaking, and that the Hubble parameter analytically resolves to a positive $H=+1/2$ natively from tree navigation depths modeling expansion. By resolving the dimensionality dispute within 3D Ising models and formally deducing an emergent Lorentz symmetry directly from tree automorphisms, this generalized adelic ontology successfully projects discrete computational substrates onto continuous observables. This ratio-centric paradigm directly addresses the gaps within canonical quantum gravity, presenting testable log-periodic predictions while dissolving the theoretical divide between physical mechanics and hierarchical cognitive processing.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19440081 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Ratio-Based Adelic Physics: Reconciling Continuous Topology and Ultrametric Complexity across Spin Glasses, Linguistics, and Cosmology Quni-Gudzinas, Rowan Brad <p>The tension between continuous Archimedean spacetime paradigms and discrete, non-Archimedean topological realities constitutes the central mathematical bottleneck in modern complexity science, hindering the unification of quantum mechanics, spin glass phase dynamics, and cognitive psychophysics. This manuscript resolves these disparities by introducing a ratio-based adelic framework, utilizing generalized scaling ratios ($q$) and Bruhat-Tits tree topologies to replace traditional integer-prime models. By formulating the Vladimirov fractional derivative operator natively for arbitrary transcendental values and deriving the corresponding $q$-adic product formulas, this methodology actively maps discrete states onto continuous metrics using the Monna projection. Simulated integrations verify that linguistic c-command parsing, passive quantum error correction scaling, and thermodynamic barrier thresholds all adhere to identical ultrametric properties dictated by these scaling parameters. Consequently, the results demonstrate that logical error suppression scales exponentially as $q^{-d}$, that spatial dimensionality fundamentally bounds replica symmetry breaking, and that the Hubble parameter analytically resolves to a positive $H=+1/2$ natively from tree navigation depths modeling expansion. By resolving the dimensionality dispute within 3D Ising models and formally deducing an emergent Lorentz symmetry directly from tree automorphisms, this generalized adelic ontology successfully projects discrete computational substrates onto continuous observables. This ratio-centric paradigm directly addresses the gaps within canonical quantum gravity, presenting testable log-periodic predictions while dissolving the theoretical divide between physical mechanics and hierarchical cognitive processing.</p> |
| title | Ratio-Based Adelic Physics: Reconciling Continuous Topology and Ultrametric Complexity across Spin Glasses, Linguistics, and Cosmology |
| url | https://doi.org/10.5281/zenodo.19440081 |