{
  "id": "oai:papers.qnfo.org:time-as-epistemic-emergence-on-a-p-adic-bruhat-tits-tree-static-constraint-count",
  "slug": "time-as-epistemic-emergence-on-a-p-adic-bruhat-tits-tree-static-constraint-count",
  "title": "Time as Epistemic Emergence on a p-Adic Bruhat–Tits Tree: Static Constraint, Counting Laws, and the Observer-Generated Arrow",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "The problem of time in quantum gravity blocks any straightforward union of general relativity, in which the time coordinate is dynamical, with quantum mechanics, in which evolution requires an external background parameter; until it is resolved, a non-perturbative quantum theory of gravity cannot specify what its observables are. Existing timeless proposals keep a continuum configuration space and leave the emergence of an experienced arrow unquantified. We formulate a conjectural but internally precise alternative: the fundamental ontology is a static, rooted (p+1)-regular Bruhat–Tits tree carrying a quantum state Ψ satisfying a Wheeler–DeWitt-type constraint HΨ=0 with H=A-(p+1)I built from the adjacency operator A; experienced time is a subsystem-relative ordering of node traversals, not an ontology-level parameter. With all arithmetic shown, we derive for p=2: the depth-$10$ ball contains V₁0=3070 events, of which only C₁0=27651 ordered pairs out of binom30702=4710915 are temporally comparable, a fraction f₁0≈ 5.8696× 10^-3 with asymptotics f_D∼ 2(p-1)D/((p+1)p^D)→ 0; the future cone of a depth-$5$ vertex holds $62$ events against $5$ ancestors at horizon $10$, growing to $65534$ against $5$ at horizon $20$; and a single observer path costs $10$ bits against $3070$ bits for the full depth-$10$ state, a compression factor of $307$. Linear narrative ordering thereby becomes an optimal predictive compression of branching structure rather than a fundamental fact, and any competing model of emergent time on a discrete geometry must reproduce these numbers.",
  "abstract_markdown": "The problem of time in quantum gravity blocks any straightforward union of general relativity, in which the time coordinate is dynamical, with quantum mechanics, in which evolution requires an external background parameter; until it is resolved, a non-perturbative quantum theory of gravity cannot specify what its observables are. Existing timeless proposals keep a continuum configuration space and leave the emergence of an experienced arrow unquantified. We formulate a conjectural but internally precise alternative: the fundamental ontology is a static, rooted $(p+1)$-regular Bruhat–Tits tree carrying a quantum state $\\Psi$ satisfying a Wheeler–DeWitt-type constraint $\\hat{H}\\Psi=0$ with $\\hat{H}=\\hat{A}-(p+1)\\hat{I}$ built from the adjacency operator $\\hat{A}$; experienced time is a subsystem-relative ordering of node traversals, not an ontology-level parameter. With all arithmetic shown, we derive for $p=2$: the depth-$10$ ball contains $V_{10}=3070$ events, of which only $C_{10}=27651$ ordered pairs out of $\\binom{3070}{2}=4710915$ are temporally comparable, a fraction $f_{10}\\approx 5.8696\\times 10^{-3}$ with asymptotics $f_D\\sim 2(p-1)D/((p+1)p^{D})\\to 0$; the future cone of a depth-$5$ vertex holds $62$ events against $5$ ancestors at horizon $10$, growing to $65534$ against $5$ at horizon $20$; and a single observer path costs $10$ bits against $3070$ bits for the full depth-$10$ state, a compression factor of $307$. Linear narrative ordering thereby becomes an optimal predictive compression of branching structure rather than a fundamental fact, and any competing model of emergent time on a discrete geometry must reproduce these numbers.",
  "date": "2026-10-15",
  "first_published": "2026-10-15",
  "last_revised": "2026-10-15T00:00:00Z",
  "modified": "2026-10-15T00:00:00Z",
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  "doi": null,
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  "url": "https://papers.qnfo.org/papers/time-as-epistemic-emergence-on-a-p-adic-bruhat-tits-tree-static-constraint-count",
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  "sha256": "9d35da1b2357ca0eaafd28e87f96c86a222e28cfc28a2c1fb8080ebc65e6b3d8",
  "version_url": "https://papers.qnfo.org/papers/time-as-epistemic-emergence-on-a-p-adic-bruhat-tits-tree-static-constraint-count/v/1.0.1",
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    "creators": [
      {
        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "Time as Epistemic Emergence on a p-Adic Bruhat–Tits Tree: Static Constraint, Counting Laws, and the Observer-Generated Arrow"
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    ],
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    "publicationYear": "2026",
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        "description": "The problem of time in quantum gravity blocks any straightforward union of general relativity, in which the time coordinate is dynamical, with quantum mechanics, in which evolution requires an external background parameter; until it is resolved, a non-perturbative quantum theory of gravity cannot specify what its observables are. Existing timeless proposals keep a continuum configuration space and leave the emergence of an experienced arrow unquantified. We formulate a conjectural but internally precise alternative: the fundamental ontology is a static, rooted (p+1)-regular Bruhat–Tits tree carrying a quantum state Ψ satisfying a Wheeler–DeWitt-type constraint HΨ=0 with H=A-(p+1)I built from the adjacency operator A; experienced time is a subsystem-relative ordering of node traversals, not an ontology-level parameter. With all arithmetic shown, we derive for p=2: the depth-$10$ ball contains V₁0=3070 events, of which only C₁0=27651 ordered pairs out of binom30702=4710915 are temporally comparable, a fraction f₁0≈ 5.8696× 10^-3 with asymptotics f_D∼ 2(p-1)D/((p+1)p^D)→ 0; the future cone of a depth-$5$ vertex holds $62$ events against $5$ ancestors at horizon $10$, growing to $65534$ against $5$ at horizon $20$; and a single observer path costs $10$ bits against $3070$ bits for the full depth-$10$ state, a compression factor of $307$. Linear narrative ordering thereby becomes an optimal predictive compression of branching structure rather than a fundamental fact, and any competing model of emergent time on a discrete geometry must reproduce these numbers.",
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