Decomposition-Indexed Classicality and the Resolution of Nested-Observer Paradoxes

Standard accounts of the quantum-to-classical transition—decoherence, environmentinduced superselection, and Quantum Darwinism—explain how interference is suppressed and pointer bases emerge, but they do not specify when a quantum process delivers a classical fact for a given observer, nor how such facts relate across different observer-descriptions of the same experiment. Here we develop a decomposition-indexed framework in which classicality is not a global property of the universal quantum state, but a local, observerrelative feature defined with respect to a particular partition of the Hilbert space into system, detector, observer, and environment. To each decomposition we associate a trajectory ΓD(t) = (AD(t),RD(t), FD(t)), where A quantifies epistemic accessibility, R counts redundancy of environmental encoding, and F measures irreversible detector flux. Classicality obtains when ΓD(t) enters a threshold region B in this space and remains there for at least a minimal dwell time. The resulting classical propositions are valid only within the local classical domain associated with that decomposition. We show that multi-observer paradoxes—Wigner’s friend, Brukner-type multi-agent arguments, and in particular the Frauchiger–Renner (FR) protocol—arise when one combines classical propositions drawn from incompatible decomposition-and-time contexts as if they belonged to a single global Boolean algebra. Within the present framework, the FR contradiction is reclassified as a type error: an illegitimate attempt to form a joint classical description from statements that are not simultaneously well-typed with respect to any common decomposition and time. The framework thus functions as a “syntax checker” for classical reasoning in unitary quantum mechanics. We do not postulate a new ontology or collapse mechanism; instead, we constrain when classical discourse is licensed by detector physics, decoherence, and redundancy. A simple qubit–detector–environment toy model illustrates how A(t), R(t), and F(t) can be computed and how decomposition-dependent classicalization times arise. We situate the proposal relative to relational, QBist, and consistent-histories approaches to the FR problem. The present article is self-contained; three companion papers provide extended developments but are not required for the definitions used here.