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  "slug": "non-archimedean-statistical-foundations-for-a-fully-connected-reality",
  "title": "Non‑Archimedean Statistical Foundations for a Fully Connected Reality",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Standard parametric statistics assume independent, identically distributed (i.i.d.) observations, an assumption that fails when all events share a common causal ancestry encoded by an ultrametric (p‑adic) structure. This paper addresses the gap between classical significance testing and a fully connected reality in which dependence follows a Bruhat–Tits tree. We formalize a p‑adic probability measure on such a tree, derive ultrametric analogues of the central limit theorem and hypothesis‑testing formulas, and compute the variance inflation for a binary hierarchical dataset of depth three. The analytical result shows that the variance of the sample mean under ultrametric dependence is $0.3625$, compared with the i.i.d. variance $0.125$, a factor of $2.9$ increase that dramatically deflates classical p‑values. Consequently, classical tests can misstate significance by orders of magnitude when the underlying reality is fully connected. The work provides a concrete mathematical foundation for re‑evaluating statistical inference in domains where hierarchical causal sharing is plausible.",
  "abstract_markdown": "Standard parametric statistics assume independent, identically distributed (i.i.d.) observations, an assumption that fails when all events share a common causal ancestry encoded by an ultrametric (p‑adic) structure. This paper addresses the gap between classical significance testing and a fully connected reality in which dependence follows a Bruhat–Tits tree. We formalize a p‑adic probability measure on such a tree, derive ultrametric analogues of the central limit theorem and hypothesis‑testing formulas, and compute the variance inflation for a binary hierarchical dataset of depth three. The analytical result shows that the variance of the sample mean under ultrametric dependence is $0.3625$, compared with the i.i.d. variance $0.125$, a factor of $2.9$ increase that dramatically deflates classical $p$‑values. Consequently, classical tests can misstate significance by orders of magnitude when the underlying reality is fully connected. The work provides a concrete mathematical foundation for re‑evaluating statistical inference in domains where hierarchical causal sharing is plausible.",
  "date": "2026-10-20",
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    "titles": [
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