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Classify all C1-admissible dynamical pulsation laws within the Projective Dynamic Logo framework and assess whether frustration-based criteria can uniquely select a relational dynamic.

August 20, 2026Open Access

The Pulsation as a Bipartition: Complete Classification of C1-Admissible Dynamical Laws, and a Singleton Obstruction Theorem for Frustration-Based Selection (Projective Dynamic Logo Framework — Document D68)

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Classify all C1-admissible dynamical pulsation laws within the Projective Dynamic Logo framework and assess whether frustration-based criteria can uniquely select a relational dynamic.
Derived unconditional mathematical theorems from axioms C1–C4 applying signed graph theory, vertex switching involutions, and two-graph parity conditions.
Carried out explicit manual proofs configuration-by-configuration on complete graph K4 and executed exhaustive algorithmic verification scripts up to n = 7.
Proved that C2-admissible sign configurations are exact vertex bipartitions, classifying exactly 2(2^n − 2) admissible laws across two families that generate 2^(n−1) − 1 distinct relational dynamics on n entities.
Showed that frustrated triangles are pointwise invariant under vertex switching, establishing that frustration counts are identical across all candidate bipartitions.
Demonstrated a singleton obstruction theorem proving that boundary frustration minimization strictly selects a cut of size one, ruling out frustration-based selection functionals in relational systems.

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Implication

Theoretical analysis classifies C1-admissible dynamical laws as complete graph bipartitions, revealing that frustration minimization inherently fails to select relational dynamics.

Cite This Study

Cédric Laubscher (2026) studied this question.

synapsesocial.com/papers/6a86b5b08a91293e6a1cd1be https://doi.org/10.5281/zenodo.21997432

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Implication

Theoretical analysis classifies C1-admissible dynamical laws as complete graph bipartitions, revealing that frustration minimization inherently fails to select relational dynamics.

The Pulsation as a Bipartition: Complete Classification of C1-Admissible Dynamical Laws, and a Singleton Obstruction Theorem for Frustration-Based Selection (Projective Dynamic Logo Framework — Document D68)

Key Points

Discussion

Implication

Cite This Study

The Pulsation as a Bipartition: Complete Classification of C1-Admissible Dynamical Laws, and a Singleton Obstruction Theorem for Frustration-Based Selection (Projective Dynamic Logo Framework — Document D68)

Key Points

Discussion

Implication

Cite This Study

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