Redundancy-Induced Nonlocality of Frame Information in Branching Decoherence Dynamics Exact Leakage Curves, a Universal Record-to-Frame Exclusion Theorem, and a Secret-Sharing Interpretation

This paper quantifies a structural exclusion principle in quantum decoherence dynamics: when environment fragments carry redundant classical records of a pointer observable, information about any conjugate observable (the frame variable) is forced into nonlocal, high-order correlations. The analysis provides an exact complementarity law across every bipartition, demonstrating that pointer accessibility in the unobserved complement is precisely the resource that suppresses frame accessibility to a verifier. Key results include a quantitative redundancy-leakage tradeoff with explicit constants , a universal record-to-conjugate exclusion theorem valid for general Stinespring isometries without product-branching assumptions , and a formal cross-domain equivalence establishing that physical branching dynamics induce a ramp secret-sharing and data-hiding access structure for the frame bit. The work formalizes the transition from quantum coherence to classical objectivity by elevating complementary information bounds to exact, model-independent structural identities.