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| Format: | Recurso digital |
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Zenodo
2026
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| Accès en ligne: | https://doi.org/10.5281/zenodo.19104750 |
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Table des matières:
- <div> <div>The contextual character of quantum observables—formalized by the Kochen--Specker theorem</div> <div>and Bohr's complementarity—represents a fundamental rupture in classical binary logic.</div> <div>In interference regimes, such as the double-slit experiment, polar questions</div> <div>(e.g., ``Which path did the particle take?'') are operationally unaskable, yet standard</div> <div>logical frameworks fail to formalize this unaskability without collapsing into truth-value</div> <div>gaps or triviality. We resolve this by introducing a context-indexed formal logic that</div> <div>adjoins an explicit \emph{applicability predicate} to the valuation space.</div> <br> <div>Drawing structural inspiration from the ancient \emph{catuṣkoṭi} (tetralemma), we map</div> <div>quantum operational states onto four distinct logical sectors: \emph{Thesis/Antithesis}</div> <div>(strong measurement and decoherence), \emph{Synthesis} (paraconsistent gluts realized</div> <div>via weak measurement), and \emph{Holothesis} (paracomplete gaps representing typed</div> <div>inapplicability). From this logical foundation, we generate a $*$-algebra equipped with</div> <div>a positive warrant functional. Through the Gelfand--Naimark--Segal (GNS) construction,</div> <div>we demonstrate that Hilbert-space structure—and the \emph{physical complex phase structure}—emerges</div> <div>canonically from an order-$4$ logical symmetry rather than being presupposed.</div> <div>Contextuality is quantified via incompatibility graphs, with chromatic number bounding</div> <div>minimal classical embeddings.</div> <br> <div>We establish a \emph{locus symmetry-breaking} correspondence wherein physical symmetry</div> <div>breaking dictates logical polarity, while symmetry preservation dictates logical</div> <div>transcendence (self-duality). This \emph{logic-first reconstruction} unifies Relational</div> <div>Quantum Mechanics (Rovelli) and Consistent Histories (Griffiths, Omnès, Gell-Mann, Hartle)</div> <div>as regime-relative logical stances within a pre-geometric ontology of \emph{interdependent</div> <div>origination} (contextual co-arising of observer and observable), where the observer's</div> <div>contextual frame and the system's observable reality are co-arising and non-separable.</div> <div>The framework yields testable deviations in many-body or higher-dimensional interference</div> <div>regimes ($I_3 \neq 0$), providing an empirical pathway for detection.</div> </div>