On the Topology of Subjective Self-State Space

On the Topology of Subjective Self-State Space (PCP — Paper 3) is a theoretical preprint within the Physics of Conscious Persistence (PCP) initiative.The paper formalizes subjective persistence as a continuous owned trajectory γ(t) in a subjective self-state space Σ, and introduces the Minimal Structural Basis (MSB) for ownership and continuity. Persistence is treated as a topological and reachability problem rather than a question of content similarity or reconstruction.A central focus is the post-brain-decay case: whether fundamental physics forbids, in principle, any lawful return to the same owned corridor, or whether current science merely lacks a continuity-preserving bridge. The work separates empirically supported carrier failure from stronger claims of universe-level impossibility, and specifies the kinds of invariants or theorems that would be required to close the question.No protocol, technique, feasibility claim, or promise is made. The contribution is strictly conceptual: clarifying definitions, constraints, and failure modes (copy, replay, fork) to prevent common misreadings and to frame the open problem precisely.