On the Topology of Subjective Self-State Space

On the Topology of Subjective Self-State Space develops a formal structural framework for subjective identity by modeling the self as a continuous causal trajectory within a subjective self-state space. Using topological and dynamical constraints, the paper analyzes the conditions under which ownership, continuity, and identity are preserved, as well as the conditions under which they are irreversibly broken. The work introduces the Structural Track, emphasizing structural impossibility rather than physical feasibility. It shows that once a specific self-trajectory γ(t) undergoes a qualifying structural cut, the original identity cannot be resumed as the same trajectory, even if informational reconstruction or functional similarity is achieved. Any post-cut realization necessarily constitutes a distinct trajectory with a different identity under the defined constraints. The paper does not address whether physical laws permit or forbid existential erasure. Instead, it provides a precise classification of what counts as the same self under strict topological, ownership, and continuity requirements. The results establish necessary conditions for identity preservation and delineate the limits of continuity independently of technological, biological, or physical implementation details. AI-assisted editing was used for language refinement and clarity only. All concepts, structure, and claims are the author’s own.