Pruning as Rendering: A Decoherent-Histories Reformulation of the Observer-Rendering Criterion in Simulation-Theoretic Quantum Mechanics

Abstract

This paper develops a formal reconstruction, within the Gell-Mann–Hartle decoherent-histories framework, of the Campbell–Owhadi observer-rendering criterion familiar from simulation-theoretic quantum mechanics. Under an explicit records-theoretic reading of "information available to an observer," the rendering criterion corresponds to a decoherence-functional condition weighted by algorithmic-information distance on observer records. The construction is metaphysically neutral: the parameter K may equally be read as a literal simulator budget or as a resource bound on observer-internal record consolidation. The author defines a pruning admissibility functional A(α | O, K) and establishes a correspondence in which Campbell–Owhadi rendering events coincide with transitions across the pruning-admissibility boundary. The framework recovers standard decoherent-histories statistics (Born rule, medium decoherence) in the limit K → ∞. For finite K, a heuristic derivation yields a complementary-error-function form, saturating at the contextuality/Bell margin, for the predicted sub-Tsirelson and sub-Klyachko–Can–Binicioğlu–Shumovsky deviations and for the threshold structure in delayed-choice eraser visibility. Two photonic protocols on existing single-photon platforms are proposed, at estimated costs of approximately $180k each in an existing facility or $200–400k from scratch.

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