Minimal Stationary Closures in the Projective Dynamic Logo Framework: Necessity of the (4,6) Block

This paper strengthens the foundational status of the (4,6) block within the Projective Dynamic Logo (PDL) framework. PDL models physical reality as a network of finite signed graphs selected by relational axioms and a coherence-oriented optimisation principle. While previous work identified the complete signed graph on four vertices and six edges as the prototype of an electron at rest, its minimality and necessity had remained only partially formalised.In this work, the four core PDL axioms (binary pulsation, triangular coherence, minimal completeness, and logical optimisation) are reformulated directly in graph-theoretic terms, and a precise notion of \emph{minimal stationary closure} is introduced. The paper then analyses small signed graphs and proves two key results: (i) no elementary stationary closure can exist for graphs with at most three vertices; (ii) the complete signed graph on four vertices admits sign assignments and a binary pulsation that realise an elementary stationary closure in the sense of the axioms. In this sense, the (4,6) structure appears as the first admissible minimal stationary closure compatible with PDL.Beyond existence, the paper discusses minimality with respect to vertex and edge number, introduces an optimisation functional on signed graphs, and shows that the (4,6) block is a natural candidate for the first local maximiser of this functional among small configurations. It further argues, up to graph automorphisms and global sign inversion, for a quasi-uniqueness of the (4,6) stationary closure within the considered class. Together, these results justify treating the (4,6) block not as a convenient modelling choice but as a structurally selected elementary building block of stationary existence in PDL, providing a rigorous basis for its rôle as an electron prototype in the broader programme.