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  "slug": "conditional-state-distances-pw-clocks",
  "title": "Conditional State Distances in Page-Wootters Quantum Clocks: When Does Ultrametricity Emerge?",
  "authors": [
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  "abstract": "The Page-Wootters formalism resolves the problem of time in quantum gravity by conditioning a globally static Wheeler-DeWitt state on clock readings, producing an emergent notion of evolution. We investigate the mathematical structure of distances between these conditional states and ask: under what conditions do they organize into an ultrametric hierarchy.",
  "abstract_markdown": "The Page-Wootters formalism resolves the problem of time in quantum gravity by conditioning a globally static Wheeler-DeWitt state on clock readings, producing an emergent notion of evolution. We investigate the mathematical structure of distances between these conditional states and ask: under what conditions do they organize into an ultrametric hierarchy.",
  "date": "2026-07-01",
  "first_published": "2026-07-01",
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        "title": "Conditional State Distances in Page-Wootters Quantum Clocks: When Does Ultrametricity Emerge?"
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