Failure of Deep Fall for Finite Laurent Matrices and Contractible Covers

For the usual group-first order on two copies of Z, we prove that the finite Laurent row [1,c+t] is deep-fall exactly when |c|<=1. For |c|>1, the distance from an essential column image to the closed span of earlier inessential images is sqrt(1-|c|^(-2)). Thus [1,2+t] is an integral counterexample with separation sqrt(3)/2. The construction extends to every nontrivial left-ordered group after choosing a positive element. We realize the integral row as the third cellular differential of a finite K(Z,1), whose contractible universal cover has a free cocompact ordered action without third deep fall. This answers the explicit nonexample clause of AIM Problem 44.1; the remaining multi-part research program stays open. Reversing the order restores deep fall. Global closed range, generation by all inessential columns and equality in the associated von Neumann dimension bound do not imply the local condition. Two column orbits are minimal over C[Z]. The inherited von Neumann algebra spectral-projection example is credited. This six-page English preprint was developed with AI assistance and self-audited; 5,173 exact supplementary checks support the written proof. It is unrefereed, with no formal verification or certified absolute priority.