Discrete Scale Invariance and the Hamiltonian Structure of Prime Gap Dynamics

Boundary and Scope Notice (CRL-0): This document is observer-only and non-authoritative. Any method-like descriptions, contrasts, figures, or illustrations are interpretive and non-normative; they are not offered as deployment guidance, certification criteria, or operational decision rules. No recommended calibration, thresholds, protocols, or implementation guidance are provided. Any evaluable instantiation belongs to downstream evaluation artifacts. Structural claims and results are unchanged. This paper introduces the generative structure underlying the Constraint Program. It presents a minimal Hamiltonian framework from which admissibility, constraint geometry, finite resolution, and irreversibility are treated as structural consequences rather than imposed rules. The formulation does not propose a mechanism, control policy, or optimization procedure. Instead, it distinguishes the roles of geometry, resolution, and enforcement, and frames admissibility as the condition under which continuation remains well-defined within the model. Within this framing, admissibility is not presented as a policy choice but as a structural selection. The Hamiltonian is used here as a generative object for organizing symmetry, boundedness, and operator consistency, not as an operational prescription. This paper closes the foundational sequence while opening the next phase: using admissibility as a criterion for interrogating hard systems without attempting to solve them. Version 1.1: scope tightened; implementation-dependent fitted values removed; results unchanged