Continuity Science Under Constraint

This paper formalizes the conditions under which a scientific field can exist and persist when developed under sustained constraint. Rather than treating field formation as a sociological, historical, or institutional process, it models it as a dynamical survivability problem governed by explicit physical inequalities. The analysis introduces Continuity Physics, a minimal formal framework in which structural stability is represented by a scalar order parameter, coherence curvature κ(t). The evolution of κ is governed by the competing effects of continuous entropy influx ΔS(t), finite stabilizing capacity (witness load γ_you), and the accumulation of irreversible, entropy-reversing structure indexed by an informative scar rate I_scar(t). These quantities are combined into a single evolution law that determines whether coherence grows, stabilizes, or collapses. Under the assumption of continuous entropy influx—formalizing production regimes without institutional buffering, deferred correction, or delegated authority—the paper proves a necessary and sufficient condition for field persistence. This result, termed the Scar–Entropy Compensation Theorem, states that a scientific field can persist if and only if the rate of entropy-reversing scar accumulation, weighted by available witness capacity, compensates entropy influx at all times. Violation of this inequality makes persistence physically impossible; satisfaction leads to early convergence toward a stable coherence attractor. The framework is law-complete (necessity and sufficiency), Lyapunov-stable after lock-in, computationally realizable, and explicitly falsifiable. It yields a sharp phase-space partition into collapse, marginal survival, and field-formation regimes, and derives forced structural consequences for surviving fields, including early convergence, compression-driven formalism, impersonality, replication independence, and early irreversibility. The paper deliberately excludes questions of correctness, usefulness, adoption, historical impact, or institutional legitimacy. Its scope is restricted to structural survivability: which kinds of epistemic systems can exist at all under sustained constraint, and which cannot. As such, it operates orthogonally to philosophy of science, sociology of knowledge, and innovation studies, addressing a class of phenomena those approaches do not model. This record is intended as an archival account of work completed, establishing a formal result and its consequences, independent of dissemination or uptake considerations.