Minimum Perimeter of Central Hyperplane Sections of the Cube

For every integer n >= 3, we prove that a central hyperplane section of the side-one real cube has perimeter at least 2(n-1), where perimeter is the (n-2)-dimensional measure of its relative boundary. Equality holds exactly for coordinate sections. The proof is analytic in dimensions three and four and in every dimension at least seven; dimensions five and six use complete finite certificates checked with exact arithmetic. Ordered facet densities transfer a cubic negative-moment estimate for section volume to perimeter, while a quantitative comparison of nearby graph sections validates all cells of the finite certificates. This answers item 2 of Problem 1 in the 2013 AIM list on sections of convex bodies, not the other functionals, codimensions or measures in that bundled record. This AI-assisted, self-audited preprint is unrefereed; absolute priority and proof-assistant formalization are not claimed.