Moving Quotient Persistence for Law-Level Concept-Objects: Future-Viability Quotients, Stable Carriers, and Non-Identical Regeneration

The program announces no discovered law; its claim is a method, not a noun. This paper is the technical carrier of the cut-quotient first-law program. The linguistic base defines a law as a stable concept-object with generative consequence closure. Persistence is then treated as a law-level property only when a quotient-placed object remains stable under admissible re-description and continues to generate survival consequences. In non-stationary environments, the bearer of such persistence is generally not a fixed entity but a moving quotient class. We define Q_t = S/≡_t, where s ≡_t s' means equality of future-survival profiles over admissible horizons and environments. Its central proved result is the necessity of non-identical regeneration: in a drifting (escaping-and-bounded) environment, under entity obsolescence, every infinitely-surviving viable path must change its entity-form infinitely often — no fixed entity can bear infinite survival — the rigorous, proved form of the no-terminus generative first law inside a specified regime. Around it the paper proves the supporting machinery: measurable quotient representation under countable determination, universal factorization through the quotient, and liftability under quotient congruence.