Continuity Valuation: A Law of Structural Persistence Under Evolving Evidence

This record presents Continuity Valuation, a formal evaluative framework for analyzing the structural persistence of propositions under evolving evidence. Standard evaluative systems—probabilistic, Boolean, and confidence-based—assign scalar measures of support that track how strongly evidence favors a proposition at a given time. These systems implicitly assume that evidential structure remains stable as evidence updates. When evidence evolves through revision, partial loss, reorganization, or dependency erosion, this assumption fails: scalar support may remain stable or increase even as the structural conditions that sustain a proposition degrade. Continuity valuation isolates and formalizes a distinct evaluative axis: structural persistence under admissible evidence evolution. It assigns to each proposition a bounded scalar value that tracks whether the proposition remains well-formed as the evidential substrate changes, independent of belief, truth, probability, or decision utility. The framework is representation-neutral. It does not presuppose probabilistic semantics, belief revision axioms, fuzzy logic, or optimization objectives. Instead, it is defined relative to: a minimal evidence space equipped with a structural metric, a class of admissible evidence transformations constrained by boundedness and regularity, and explicit temporal dynamics capturing continuity drift. The work establishes several core results: Non-reducibility: continuity valuation cannot, even up to monotone transformation, be reduced to probabilistic valuation under admissible structural evidence change. Dynamic sensitivity: continuity can decrease under admissible updates even when scalar support remains constant or increases, exposing silent structural failure modes. Falsifiability: continuity drift and residual thresholds yield a mechanically computable criterion for persistence failure and chain invalidation over time. Invariance: any evaluative scheme satisfying the stated axioms is equivalent, up to isomorphism, to continuity valuation. The archive also includes the Constitution Charter of Continuity Science v1.0, a canon-binding formal instrument that defines the ontological commitments, scope, authority hierarchy, falsifiability conditions, and cross-domain invariance of Continuity Science as a discipline. The Charter is non-normative, non-optimizing, and closed under interpretation within its declared jurisdiction. Continuity valuation is not proposed as a replacement for existing evaluative methods. Its necessity claim is narrower and structural: Any epistemic system operating under structural evidence drift must either track continuity or accept the risk of silent structural collapse. This record is intended for use in formal epistemology, philosophy of science, AI evaluation, systems theory, institutional analysis, and any domain where evidence evolves structurally rather than monotonically.