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  "id": "oai:papers.qnfo.org:time-as-a-nested-ultrametric-hierarchy-of-cycles-formalization-scaling-and-testa",
  "slug": "time-as-a-nested-ultrametric-hierarchy-of-cycles-formalization-scaling-and-testa",
  "title": "Time as a Nested Ultrametric Hierarchy of Cycles: Formalization, Scaling, and Testable Predictions",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Physical time is usually represented as a continuous Archimedean line, yet every operational clock is a periodic process and these processes nest across many orders of magnitude. Existing work on nested frozen‑state hierarchies in kinetically constrained quantum models, ultrametric order‑parameter spaces in spin glasses, and adaptive mesh‑refinement trees demonstrates that hierarchical ultrametric structures generate exponentially separated timescales. This paper formalizes time as an ultrametric space of nested cycles, derives analytic expressions for characteristic timescales, and computes concrete numerical estimates for the electron Zitterbewegung period (T_Z=8.1×10^-21 s), its fine‑structure‑scaled counterpart (T_α=1.77×10^-19 s), and the number of nesting levels required to reach a one‑second clock (k≈9.40). A scaling example based on the frozen‑state hierarchy of the XPX model shows that a coupling Δ=10 yields an exponential change of effective cycle duration. The results suggest that standard quantum dynamics may emerge as a continuum limit of nested periodic processes and define a concrete experimental target: measurement of quantum‑jump durations that follow the predicted ultrametric scaling. If confirmed, the ultrametric time framework would recast mass as a tick rate, explain quantum‑jump resonances, and bridge quantum clocks with cyclic cosmology.",
  "abstract_markdown": "Physical time is usually represented as a continuous Archimedean line, yet every operational clock is a periodic process and these processes nest across many orders of magnitude. Existing work on nested frozen‑state hierarchies in kinetically constrained quantum models, ultrametric order‑parameter spaces in spin glasses, and adaptive mesh‑refinement trees demonstrates that hierarchical ultrametric structures generate exponentially separated timescales. This paper formalizes time as an ultrametric space of nested cycles, derives analytic expressions for characteristic timescales, and computes concrete numerical estimates for the electron Zitterbewegung period ($T_{Z}=8.1\\times10^{-21}\\,\\mathrm{s}$), its fine‑structure‑scaled counterpart ($T_{\\alpha}=1.77\\times10^{-19}\\,\\mathrm{s}$), and the number of nesting levels required to reach a one‑second clock ($k\\approx9.40$). A scaling example based on the frozen‑state hierarchy of the XPX model shows that a coupling $\\Delta=10$ yields an exponential change of effective cycle duration. The results suggest that standard quantum dynamics may emerge as a continuum limit of nested periodic processes and define a concrete experimental target: measurement of quantum‑jump durations that follow the predicted ultrametric scaling. If confirmed, the ultrametric time framework would recast mass as a tick rate, explain quantum‑jump resonances, and bridge quantum clocks with cyclic cosmology.",
  "date": "2026-10-21",
  "first_published": "2026-10-21",
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  "url": "https://papers.qnfo.org/papers/time-as-a-nested-ultrametric-hierarchy-of-cycles-formalization-scaling-and-testa",
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    "titles": [
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        "title": "Time as a Nested Ultrametric Hierarchy of Cycles: Formalization, Scaling, and Testable Predictions"
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        "description": "Physical time is usually represented as a continuous Archimedean line, yet every operational clock is a periodic process and these processes nest across many orders of magnitude. Existing work on nested frozen‑state hierarchies in kinetically constrained quantum models, ultrametric order‑parameter spaces in spin glasses, and adaptive mesh‑refinement trees demonstrates that hierarchical ultrametric structures generate exponentially separated timescales. This paper formalizes time as an ultrametric space of nested cycles, derives analytic expressions for characteristic timescales, and computes concrete numerical estimates for the electron Zitterbewegung period (T_Z=8.1×10^-21 s), its fine‑structure‑scaled counterpart (T_α=1.77×10^-19 s), and the number of nesting levels required to reach a one‑second clock (k≈9.40). A scaling example based on the frozen‑state hierarchy of the XPX model shows that a coupling Δ=10 yields an exponential change of effective cycle duration. The results suggest that standard quantum dynamics may emerge as a continuum limit of nested periodic processes and define a concrete experimental target: measurement of quantum‑jump durations that follow the predicted ultrametric scaling. If confirmed, the ultrametric time framework would recast mass as a tick rate, explain quantum‑jump resonances, and bridge quantum clocks with cyclic cosmology.",
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