{
  "id": "oai:papers.qnfo.org:global-coherence-constraints-in-a-web-of-measurement-contexts-a-categorical-mode",
  "slug": "global-coherence-constraints-in-a-web-of-measurement-contexts-a-categorical-mode",
  "title": "Global Coherence Constraints in a Web of Measurement Contexts: A Categorical Model, Trilemma, and Empirical Illustration",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Contemporary quantum‑foundational research and immersive augmented/virtual reality (AR/VR) systems both require the reconciliation of measurement data obtained in heterogeneous contexts. Existing practice either assumes a hidden, context‑independent state or tolerates incoherent cross‑context data, leading to costly redesigns and ambiguous interpretations. The specific gap is the absence of a formal calculus that determines when a global coherence condition forces a unique, context‑consistent assignment of observable values and when a context‑independent invariant cannot exist. We construct a categorical framework in which measurement contexts are objects, translation rules are morphisms, and a global coherence condition is imposed as a commutative diagram constraint. Within this framework we (i) prove that coherence forces a unique family of observable assignments and excludes any terminal object representing a context‑independent value, (ii) establish a trilemma linking global consistency, absence of invariant values, and aperiodicity of translation loops, and (iii) compute exact counts for three illustrative webs: a three‑node cycle over Z/7 (0 consistent sections), a modified cycle (7 sections), a commuting diamond example (details omitted), and a two‑step majority‑rule coarse‑graining chain (2 fixed points among 512 configurations, fraction 1/256≈0.00390625). Numerical illustrations use the spatial volume of the Reality Distortion Room (4.5m × 5.5m × 2.5m) and the file size of a fitted‑avatar PDF (3 263 KB). The result changes practice by providing a mathematically grounded method for synchronizing measurements across heterogeneous AR/VR platforms and relational quantum experiments without invoking hidden states, thereby reducing engineering overhead and clarifying ontological commitments.",
  "abstract_markdown": "Contemporary quantum‑foundational research and immersive augmented/virtual reality (AR/VR) systems both require the reconciliation of measurement data obtained in heterogeneous contexts. Existing practice either assumes a hidden, context‑independent state or tolerates incoherent cross‑context data, leading to costly redesigns and ambiguous interpretations. The specific gap is the absence of a formal calculus that determines when a global coherence condition forces a unique, context‑consistent assignment of observable values and when a context‑independent invariant cannot exist. We construct a categorical framework in which measurement contexts are objects, translation rules are morphisms, and a global coherence condition is imposed as a commutative diagram constraint. Within this framework we (i) prove that coherence forces a unique family of observable assignments and excludes any terminal object representing a context‑independent value, (ii) establish a trilemma linking global consistency, absence of invariant values, and aperiodicity of translation loops, and (iii) compute exact counts for three illustrative webs: a three‑node cycle over $\\mathbb{Z}/7$ (0 consistent sections), a modified cycle (7 sections), a commuting diamond example (details omitted), and a two‑step majority‑rule coarse‑graining chain (2 fixed points among 512 configurations, fraction $1/256\\approx0.00390625$). Numerical illustrations use the spatial volume of the Reality Distortion Room ($4.5\\,$m × $5.5\\,$m × $2.5\\,$m) and the file size of a fitted‑avatar PDF (3 263 KB). The result changes practice by providing a mathematically grounded method for synchronizing measurements across heterogeneous AR/VR platforms and relational quantum experiments without invoking hidden states, thereby reducing engineering overhead and clarifying ontological commitments.",
  "date": "2026-10-19",
  "first_published": "2026-10-19",
  "last_revised": "2026-10-19T00:00:00Z",
  "modified": "2026-10-19T00:00:00Z",
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  "url": "https://papers.qnfo.org/papers/global-coherence-constraints-in-a-web-of-measurement-contexts-a-categorical-mode",
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
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        "title": "Global Coherence Constraints in a Web of Measurement Contexts: A Categorical Model, Trilemma, and Empirical Illustration"
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