Coherence Leakage, Hierarchical Filtering, and the Exponent 18 in the Projective Dynamic Logo Framework

This paper refines the treatment of coherence leakage and hierarchical filtering in the Projective Dynamic Logo (PDL) framework. PDL models physical reality as a network of minimal logical closures on finite signed graphs, with elementary (4, 6) blocks and a combinatorially selected proton architecture providing the main building blocks. Beyond these static structures, previous PDL work introduced the idea that even optimised proton closures exhibit a small but irreducible leakage of coherence, and suggested that a strongly filtered remnant of this leakage might underlie an effective gravitational coupling, encoded through an empirical exponent 18. The present work gives this proposal a more precise structural basis. First, it defines a class of admissible proton graphs, built on the PDL proton integer architecture and associated constraints, and introduces a minimal closure defect as the infimum of the triangle-violation fraction over this class. This defect is interpreted as a combinatorial invariant measuring intrinsic coherence leakage at the proton level, distinct from ordinary dissipative effects. Second, the paper organises the exponent 18 as the total number of independent coherence filters in a three-level hierarchy: from elementary (4, 6) bricks to protons, from protons to nuclei, and from nuclei to ordinary matter and an effective gravitational regime (three blocks of six filters). On this basis, the paper sketches an effective gravitational ansatz G₄₅₅^PDL = C\, ^n, with n interpreted as the number of hierarchical filters (typically n=18), and formulates qualitative constraints that any such effective coupling must satisfy: monotonicity in, approximate universality for ordinary matter, compatibility with the observed order of magnitude of Newton’s constant, and emergence of a Newtonian 1/r^2 regime in appropriate limits. While a full quantitative derivation of gravitation from PDL is not claimed, the work clarifies the logical status of coherence leakage and of the exponent 18, identifies which aspects are structurally enforced and which remain conjectural, and outlines a concrete research programme for assessing the robustness and physical relevance of the PDL gravitation proposal.