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  "id": "oai:papers.qnfo.org:p-adic-spacetime-and-the-evading-of-lorentz-invariance-no-go-theorems",
  "slug": "p-adic-spacetime-and-the-evading-of-lorentz-invariance-no-go-theorems",
  "title": "p‑adic Spacetime and the Evading of Lorentz‑Invariance No‑Go Theorems",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "The incompatibility between a discrete quantum substrate and the continuous Lorentz‑invariant manifolds of general relativity has motivated a series of no‑go theorems that forbid locally finite, Poincaré‑invariant networks on Archimedean Minkowski space. These theorems block the construction of fundamentally discrete spacetime models that retain the observed absence of a preferred inertial frame. Existing proofs rely on Archimedean geometry, ultrametric norms, and compactness properties that do not hold in a p‑adic setting. We define a p‑adic analogue of local finiteness and invariance under the p‑adic orthogonal group preserving a quadratic form, then derive combinatorial properties of the Bruhat–Tits tree that serve as a concrete p‑adic spacetime scaffold. The principal result is an explicit construction of an invariant locally finite graph on Q_p^n for any prime p, together with exact counts of vertices, comparable ordered pairs, and a vanishing comparability fraction in the large‑depth limit. Quantitatively, for p=2 and depth D=10 we obtain V₁0=3070 events, C₁0=27645 unordered comparable pairs, and a comparability fraction f₁0≈5.87×10^-3. This demonstrates that the Archimedean no‑go arguments do not extend to non‑Archimedean geometry, opening a pathway for discrete fundamental physics without observable preferred frames.",
  "abstract_markdown": "The incompatibility between a discrete quantum substrate and the continuous Lorentz‑invariant manifolds of general relativity has motivated a series of no‑go theorems that forbid locally finite, Poincaré‑invariant networks on Archimedean Minkowski space. These theorems block the construction of fundamentally discrete spacetime models that retain the observed absence of a preferred inertial frame. Existing proofs rely on Archimedean geometry, ultrametric norms, and compactness properties that do not hold in a $p$‑adic setting. We define a $p$‑adic analogue of local finiteness and invariance under the $p$‑adic orthogonal group preserving a quadratic form, then derive combinatorial properties of the Bruhat–Tits tree that serve as a concrete $p$‑adic spacetime scaffold. The principal result is an explicit construction of an invariant locally finite graph on $\\mathbb{Q}_p^n$ for any prime $p$, together with exact counts of vertices, comparable ordered pairs, and a vanishing comparability fraction in the large‑depth limit. Quantitatively, for $p=2$ and depth $D=10$ we obtain $V_{10}=3070$ events, $C_{10}=27645$ unordered comparable pairs, and a comparability fraction $f_{10}\\approx5.87\\times10^{-3}$. This demonstrates that the Archimedean no‑go arguments do not extend to non‑Archimedean geometry, opening a pathway for discrete fundamental physics without observable preferred frames.",
  "date": "2026-10-21",
  "first_published": "2026-10-21",
  "last_revised": "2026-10-21T00:00:00Z",
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  "url": "https://papers.qnfo.org/papers/p-adic-spacetime-and-the-evading-of-lorentz-invariance-no-go-theorems",
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    "titles": [
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        "title": "p‑adic Spacetime and the Evading of Lorentz‑Invariance No‑Go Theorems"
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    "publicationYear": "2026",
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