Continuity Science Under Constraint: A Law-Complete Theory of Epistemic Field Survivability

Description: Continuity Science Under Constraint formalizes the conditions under which a scientific field can persist when subject to continuous entropy pressure and finite stabilizing capacity. It introduces Continuity Physics, a minimal dynamical framework modeling epistemic survivability through explicit state variables: coherence curvature ((\kappa)), entropy influx ((\Delta S)), irreversible informative scarring ((I_{\text{scar}})), and bounded witness load ((\gamma_{you})). The central result—the Scar–Entropy Compensation Theorem—establishes a necessary and sufficient inequality for field viability: a scientific field can persist if and only if the rate of entropy-reversing structural scarring continuously compensates entropy influx. Systems failing this condition collapse; systems satisfying it converge early to a stable coherence attractor characterized by compression, impersonality, replication independence, and irreversibility. The framework is law-complete, Lyapunov-stable, and explicitly falsifiable. It treats field formation not as a sociological or historical process but as a dynamical survivability problem governed by physical constraints. The work delineates the jurisdiction of epistemic field persistence and excludes entire classes of systems that cannot exist under sustained constraint. Keywords: Continuity Physics, epistemic field survivability, entropy, structural stability, falsifiability, scientific field formation, informational scars, coherence curvature, dynamical systems, constraint physics.