Three-Colourability of Random Lifts of K_5

Let L_n be the random n-lift of K_5 obtained by independent uniform perfect matchings over its ten edges. We prove that P(chi(L_n)=3) tends to one. The main ingredient is an exact-marginal edge entropy inequality for pairs of fibrewise balanced three-colourings. A sharp three-coordinate fractional-power inequality yields the edge bound through a spectral absolute-value estimate. This gives the unique global maximum in the degree-four second-moment calculation. We derive the Gaussian constants and integer-lattice factors, treat every lift size by bounded affine-lattice shifts, and apply classical small subgraph conditioning. An odd-cycle argument gives the matching lower bound. The exact K_5 question in OPG-37656 is answered; the corresponding question for arbitrary complete bases is not addressed. Prior random-lift moment machinery is credited to Nir and Perez-Gimenez. This is an unrefereed, AI-assisted preprint with reproducible exact checks, not independent or formal verification, and makes no absolute priority claim.