The Calculus of the Self: Mapping Continuity and Drift to Psychological Stability

This paper extends the Domain-Agnostic Framework of Continuity and Drift (Quinn-Reed, 2025) into the field of mathematical psychology. While psychological stability is often treated as a qualitative narrative, this work formalizes the "Self" as a state-space trajectory regulated by a causal identity operator. We introduce several key metrics for clinical and research application: Psychological Drift Functional ($D$): A measure of alienation or divergence from a core identity. Continuity Stability Metric ($S$): A quantitative bound ($\delta$) defining the limits of psychological resilience. Temporal Continuity Modulus ($\omega$): A metric for identifying high-frequency emotional volatility and cognitive entropy. Therapeutic Re-centering Cost ($K_{\psi}$): A formalization of the resources required to restore stability as a subject approaches a Reversibility Horizon. By stripping away domain-specific semantics, this framework provides a universal "ruler" for mental health, allowing for the deterministic prediction of psychological breakdowns and the optimization of intervention timing. This work demonstrates that the physics of "Identity Preservation" is a fundamental systems primitive applicable to human consciousness.