The Continuity Principle: A Formal Framework for Identity Persistence, Load, and System Preservation

This paper presents the Continuity Principle as a formal framework for modeling whether a system remains identifiably itself under change. The approach defines system continuity as a bounded relation among identity anchors, kernel stability, transformation load, and repair or adaptive capacity. A formal metric, the Continuity Preservation Function (CPF), is introduced to estimate the degree to which a system preserves its identity kernel under transformation load without assuming universal domain cutoffs. The framework is intended for cross-domain use in systems where persistence, degradation, adaptation, or collapse must be evaluated from relevant observable features. The paper provides formal definitions, boundedness arguments, sensitivity analysis, measurement-error propagation, calibration requirements, falsification conditions, and a worked example. Interpretation bands are treated as provisional diagnostic vocabulary rather than universal thresholds. The framework is positioned as a testable systems-theoretic model that can be calibrated within specific empirical domains.