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  "slug": "epistemic-ineffability-in-finite-subsystems-an-information-theoretic-bound-on-co",
  "title": "Epistemic Ineffability in Finite Subsystems: An Information-Theoretic Bound on Coarse‑Grained Reconstructions",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Finite observers embedded in an information‑conserving whole cannot externalize their full epistemic state. Existing digital‑twin, multiscale, and uncertainty‑estimation studies illustrate this limitation but do not quantify the inevitable information loss. We formalize epistemic “handles’’ as finite‑resolution partitions of a system’s state space and derive an incommensurability bound that any such partition must satisfy under unitary or ultrametric dynamics. The bound states that the unrecoverable information Δ obeys Δ ≥ N - log₂ M, where N is the total bits describing the subsystem and M is the number of partition cells. Applying the bound to a brain‑scale subsystem (N=128 bits, M=2²0) yields Δ=108 bits (≈ 84 % loss). A second illustration with I_total=1000 bits, r=10 bits per partition, and five successive lenses gives a captured information of $50$ bits (5 % of the whole). The result explains why digital‑twin models of structural systems, epistemic‑uncertainty estimators in radiotherapy, and AI‑alignment interventions cannot achieve perfect fidelity when limited to finite parameterizations. We propose a minimal reversible‑dynamics simulation that could falsify the bound and discuss practical implications for structural‑health monitoring, neuroscience, and AI safety.",
  "abstract_markdown": "Finite observers embedded in an information‑conserving whole cannot externalize their full epistemic state. Existing digital‑twin, multiscale, and uncertainty‑estimation studies illustrate this limitation but do not quantify the inevitable information loss. We formalize epistemic “handles’’ as finite‑resolution partitions of a system’s state space and derive an incommensurability bound that any such partition must satisfy under unitary or ultrametric dynamics. The bound states that the unrecoverable information $\\Delta$ obeys $\\Delta \\ge N - \\log_2 M$, where $N$ is the total bits describing the subsystem and $M$ is the number of partition cells. Applying the bound to a brain‑scale subsystem ($N=128$ bits, $M=2^{20}$) yields $\\Delta=108$ bits ($\\approx$ 84 % loss). A second illustration with $I_{\\text{total}}=1000$ bits, $r=10$ bits per partition, and five successive lenses gives a captured information of $50$ bits (5 % of the whole). The result explains why digital‑twin models of structural systems, epistemic‑uncertainty estimators in radiotherapy, and AI‑alignment interventions cannot achieve perfect fidelity when limited to finite parameterizations. We propose a minimal reversible‑dynamics simulation that could falsify the bound and discuss practical implications for structural‑health monitoring, neuroscience, and AI safety.",
  "date": "2026-10-19",
  "first_published": "2026-10-19",
  "last_revised": "2026-10-19T00:00:00Z",
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  "url": "https://papers.qnfo.org/papers/epistemic-ineffability-in-finite-subsystems-an-information-theoretic-bound-on-co",
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    "titles": [
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        "title": "Epistemic Ineffability in Finite Subsystems: An Information-Theoretic Bound on Coarse‑Grained Reconstructions"
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