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  "id": "oai:papers.qnfo.org:hierarchical-suppression-of-vacuum-energy-in-p-adic-ultrametric-geometry",
  "slug": "hierarchical-suppression-of-vacuum-energy-in-p-adic-ultrametric-geometry",
  "title": "Hierarchical Suppression of Vacuum Energy in p‑Adic Ultrametric Geometry",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "The observed dark‑energy density is smaller than the naïve Planck‑scale vacuum energy by a factor of order 10^-120, a discrepancy that challenges the predictive power of quantum field theory and hinders the design of a unified quantum‑gravity framework. Existing approaches have not demonstrated a mechanism that naturally yields such a suppression without fine‑tuning. We adopt a non‑Archimedean spacetime model in which the underlying geometry is an ultrametric tree associated with a prime p. By replacing the standard Archimedean propagator with the Vladimirov‑type p‑adic propagator, loop‑momentum contributions are truncated by the strong triangle inequality, and we postulate that the zero‑point energy acquires an additional factor p^-1 per hierarchical level of the tree. Using the phase‑transition condition p=3 from the p‑adic Potts model [4] and the observed suppression factor 10^-120, we solve 3^-N=10^-120 to obtain a hierarchical depth N=252. The resulting suppression factor 3^-252≈10^-120 reproduces the observed dark‑energy scale without adjustable continuous parameters. This analytical result suggests that a discrete prime‑indexed ultrametric substrate can resolve the cosmological‑constant problem and points to concrete computational pathways for testing p‑adic vacuum‑energy predictions.",
  "abstract_markdown": "The observed dark‑energy density is smaller than the naïve Planck‑scale vacuum energy by a factor of order $10^{-120}$, a discrepancy that challenges the predictive power of quantum field theory and hinders the design of a unified quantum‑gravity framework. Existing approaches have not demonstrated a mechanism that naturally yields such a suppression without fine‑tuning. We adopt a non‑Archimedean spacetime model in which the underlying geometry is an ultrametric tree associated with a prime $p$. By replacing the standard Archimedean propagator with the Vladimirov‑type $p$‑adic propagator, loop‑momentum contributions are truncated by the strong triangle inequality, and we postulate that the zero‑point energy acquires an additional factor $p^{-1}$ per hierarchical level of the tree. Using the phase‑transition condition $p=3$ from the $p$‑adic Potts model [4] and the observed suppression factor $10^{-120}$, we solve $3^{-N}=10^{-120}$ to obtain a hierarchical depth $N=252$. The resulting suppression factor $3^{-252}\\approx10^{-120}$ reproduces the observed dark‑energy scale without adjustable continuous parameters. This analytical result suggests that a discrete prime‑indexed ultrametric substrate can resolve the cosmological‑constant problem and points to concrete computational pathways for testing $p$‑adic vacuum‑energy predictions.",
  "date": "2026-10-20",
  "first_published": "2026-10-20",
  "last_revised": "2026-10-20T00:00:00Z",
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  "url": "https://papers.qnfo.org/papers/hierarchical-suppression-of-vacuum-energy-in-p-adic-ultrametric-geometry",
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    "titles": [
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        "title": "Hierarchical Suppression of Vacuum Energy in p‑Adic Ultrametric Geometry"
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        "description": "The observed dark‑energy density is smaller than the naïve Planck‑scale vacuum energy by a factor of order 10^-120, a discrepancy that challenges the predictive power of quantum field theory and hinders the design of a unified quantum‑gravity framework. Existing approaches have not demonstrated a mechanism that naturally yields such a suppression without fine‑tuning. We adopt a non‑Archimedean spacetime model in which the underlying geometry is an ultrametric tree associated with a prime p. By replacing the standard Archimedean propagator with the Vladimirov‑type p‑adic propagator, loop‑momentum contributions are truncated by the strong triangle inequality, and we postulate that the zero‑point energy acquires an additional factor p^-1 per hierarchical level of the tree. Using the phase‑transition condition p=3 from the p‑adic Potts model [4] and the observed suppression factor 10^-120, we solve 3^-N=10^-120 to obtain a hierarchical depth N=252. The resulting suppression factor 3^-252≈10^-120 reproduces the observed dark‑energy scale without adjustable continuous parameters. This analytical result suggests that a discrete prime‑indexed ultrametric substrate can resolve the cosmological‑constant problem and points to concrete computational pathways for testing p‑adic vacuum‑energy predictions.",
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