NP-hardness of Gaussian c-separation
A Lean 4 proof development of reduction idea toward NP-hardness of feature selection for relative Gaussian c-separation in the formulation of Borozan et al. The argument starts from NP-completeness of equal-cardinality partition of positive squares, giving integral Gaussian data via integer roots and an even paired total. Three Gaussians enforce partition balance, and a schedule of d+1 Gaussians enforces binary selectors. Explicit separation of the two blocks makes cross-block hinge penalties vanish. The fixed threshold is (dot s 1 / 2)*d*(d+1)/2 - 3*d/4, an integer multiple of 1/4 for…
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