{
  "id": "oai:papers.qnfo.org:ratio-based-adelic-physics",
  "slug": "ratio-based-adelic-physics",
  "title": "Ratio-Based Adelic Physics",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "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. [...]",
  "abstract_markdown": "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. [...]",
  "date": "2026-04-01",
  "first_published": "2026-04-01",
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  "modified": "2026-04-01T00:00:00Z",
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        "name": "Rowan Brad Quni-Gudzinas",
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        "description": "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. [...]",
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