Observer Persistence as a Code Subspace: Quantum Information Constraints on Identity Branching

This paper develops an operational framework for analyzing persistence and branching of observer states using concepts from quantum information theory and quantum error correction. Observer states are modeled as encoded informational structures within code subspaces, and persistence is defined in terms of constrained recoverability under a specified class of allowed operations. The framework introduces persistence neighborhoods and recoverability-based continuity measures using fidelity and information geometry. Branching processes are analyzed operationally through reduced-state structure and local recoverability rather than metaphysical identity claims. Connections to decoherence, Everettian branching, and quantum information constraints such as no-cloning and no-deleting are discussed. The paper does not propose a theory of consciousness or derive metaphysical identity conditions from physics. Instead, it provides a formal structure for studying operational persistence under branching dynamics within a quantum-information-theoretic setting.