<ul><li>Over 5,000 labeled CNF formulas were generated and analyzed for SAT solvability using spectral features and UMAP projection.</li><li>Satisfiable and unsatisfiable instances across different clause lengths were found to be separable in spectral space, indicating a general phenomenon.</li><li>The dynamic match rule, utilizing μ ± σ thresholding, identifies the 'spectral core' of solvable problems across various clause types.</li><li>The complexity landscape of SAT was visualized as a topological structure in a UMAP projection, suggesting new perspectives on P vs NP complexity classes.</li></ul>

Clause-Arity and the Spectral Manifold of Complexity: Mapping the Geometry of SAT Solvability

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