Discrete Curvature, Interval Coverage, and the Entropy–Determinism Transition in Prime Gap Prediction

We study prime gaps using an exact discrete curvature operator and a forward interval coverage framework derived from modular exclusion constraints. We prove that curvature is an information complete representation of the prime gap sequence up to linear drift. Empirically, we demonstrate a smooth transition from structured uncertainty to exact prediction as residue exclusion depth increases. Below square root constraint depth, prime gaps exhibit constrained uncertainty. When exclusion depth reaches the square root scale of the candidate region, prediction becomes exact because the method becomes equivalent to primality certification. We formalize this transition and clarify the structural boundary between predictive constraint and deterministic certification.