A Connected Positive Model with a Nonsemialgebraic Likelihood Cell

We give a connected compact rational polygonal model on four outcomes, all of whose probabilities are at least 1/32, with a nonsemialgebraic logarithmic Voronoi cell at a smooth rational point. Near a positive data vector, the cell is the epigraph of an explicit binary entropy expression in rational coordinates. A uniform likelihood gap shows that the connecting segment does not alter this boundary. An elementary proof establishes nonsemialgebraicity over the real numbers. Four outcomes are minimal at a positive-dimensional smooth interior model point, by log-normal containment and convexity. This five-page note complements the earlier work of Alexandr and Heaton and Alexandr's 2026 nonalgebraicity results. It provides a complete explicit theorem relevant to AIM-COMPUTATION-0040, not a full closure of the open-ended AIM Question 26. AI-assisted, self-audited and unrefereed; no formal verification, independent peer review, or absolute priority is claimed.