A Minimal Relational Sketch for the Emergence of the Golden Ratio in PDL

This note proposes a minimal relational sketch for the emergence of the golden ratio φ\varphiφ within the Projective Dynamic Logo (PDL) framework. Starting from the hierarchical proton architecture (valence cores, relational sea, and active surface) it shows how a self-similar partition of the total relational content between core and surface naturally leads to \varphi -like proportions. The aim is not to present a definitive derivation, but to identify the simplest combinatorial conditions under which the golden ratio appears as an optimal redistribution of coherence on a closed relational structure.