A three-zero sign pattern with different real and rational minimum ranks

A known ten-line arrangement yields an explicit 10 by 12 sign pattern with exactly three zeros in every column, real minimum rank three and rational minimum rank four. The note gives the oriented pattern, a complete product table, an elementary support-only rational obstruction and an integer rank-four witness. Rational rank three would force a rational root of t^3 - t^2 + t + 1. This supplies proposed counterexamples to Conjectures 5.1 and 5.2 of Fang and collaborators (2018) and historical formulations. The configuration and cubic obstruction are prior work; explicit matrix priority is not claimed. The conclusions are provisional candidate results.