A singular continuous stationary law for the binary logistic Elo chain

We give a computer-assisted counterexample to the universal absolute-continuity assertion in AIM Problem 637. The admissible parameters are two equally skilled players, logistic scale $c=1/2$, and update size $K=9/10$. The stationary law is singular continuous, has full support on the zero-sum line, and has measure Hausdorff dimension at most $10\log 2/7<1$. The central finite certificate verifies an explicit drift inequality at 5,001 rational points using integer interval arithmetic. Analytic curvature and tail estimates turn this into a global inequality. A self-contained martingale and covering argument then proves the dimension bound; no histogram, numerical Lyapunov exponent, differential-entropy assumption, or compact-support hypothesis is used. Review status. This is a complete proposed computer-assisted disproof, not an independently audited or proof-assistant-verified resolution. The source code and exact results are part of the proof package.