Continuity as the Operator of Identity: Beloskrasis and the Resolution of the Ship of Theseus

Continuity as the Operator of Identity develops a substrate‑neutral model of identity grounded in the persistence of collapse orientation rather than the endurance of matter, form, memory, or function. Through the operator beloskrasis—which stabilizes relational waves into coherent, directed configurations—the paper reframes continuity as an active mechanism rather than a passive property. Identity emerges as the invariant pattern generated by this continuity. This operator‑level account dissolves the Ship of Theseus paradox, generalizes across physical, biological, cognitive, artificial, and social systems, and establishes identity as the structural consequence of directed collapse rather than substrate persistence.