A Complete Computational Survey of Solution-Space Geometry in Circuit-SAT for 4-Input Boolean Functions

We carry out a complete computational survey of the solution-space geometry of circuit-SAT instances for all 222 NPN-equivalence classes of 4-input Boolean functions over the basis B₂. For every class f, we enumerate structurally distinct circuits at and near the minimum size, compute pairwise Hamming distances, extract H₀ persistence via Vietoris–Rips filtrations, and explore the reconfiguration graph by breadth-first search. The dataset comprises 665 instance–size pairs across three slack levels. A column-shuffled null model confirms that approximately 85% of the raw diameter–complexity correlation is attributable to dimensional scaling; a statistically significant but modest residual persists after normalisation.