This paper presents a philosophy-of-science justification for continuation reasoning under incomplete observability. Rather than treating partial visibility as equivalent to structural absence, the framework argues that scientific practice routinely relies on admissible continuity inference when complete observational access is unavailable. The paper introduces the Persistence Locking Mechanism (PLM) as a non-ontological continuation framework concerned with structurally sufficient alignment rather than perfect reconstruction or total equivalence. The framework does not claim hidden entities, complete recovery of inaccessible structure, or deterministic certainty. Instead, it formalises how continuation may remain scientifically reasonable when observational access becomes degraded, fragmented, or boundary-limited. Within this interpretation: • Persistence Fingerprint Analysis (PFA) functions as a comparative structural morphology framework • PLM functions as an operational continuation-overlay mechanism • The present paper provides the epistemological and philosophy-of-science justification for why partial continuity inference may remain admissible under incomplete observational conditions The framework argues that many successful scientific practices already operate through structurally sufficient continuation rather than perfect reconstruction. Maps distort geography, probability distributions compress uncertainty, engineering tolerances flex under load, and observational science routinely infers continuity beyond direct measurement. The paper therefore reframes continuation not as certainty, but as admissible approximation under constrained visibility. Key concepts include: • admissible structural alignment • partial persistence morphology • continuation under incomplete observability • admissibility degradation • observational boundary limits • continuity inference with restraint • structurally sufficient continuation • topology persistence beyond visibility • operational viability without total reconstruction • path-dependent continuity reasoning The framework is explicitly non-replacement in scope. It introduces no new physical laws, entities, or mechanisms, and does not compete with existing scientific theories. Its role is methodological and philosophical: clarifying how scientific continuation remains possible when observation becomes partial, degraded, or structurally incomplete. The paper positions PLM as a continuation-oriented philosophy framework compatible with existing scientific practice, engineering reasoning, observational inference, and model-dependent structural reconstruction.
Andrew John Paton (Sun,) studied this question.