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The study aims to formally establish the necessity and minimality of the (4,6) block within the Projective Dynamic Logo framework.

March 4, 2026Open Access

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

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The study aims to formally establish the necessity and minimality of the (4,6) block within the Projective Dynamic Logo framework.
Reformulated four core axioms in graph-theoretic terms.
Introduced a concept of minimal stationary closure.
Analyzed small signed graphs and proved key results regarding stationary closures.
No elementary stationary closure exists for graphs with three vertices or fewer.
The complete signed graph on four vertices can realize an elementary stationary closure under certain conditions.
The (4,6) block is shown to be a candidate for a local maximizer of an optimisation functional.

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Demonstrates the necessity of the (4,6) block in the Projective Dynamic Logo framework, indicating its foundational importance.

Cédric Laubscher (2026) studied this question.

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