Martin Kernels without Green-Line Contact on an Annulus

Arsove and Johnson asked whether every normalized Martin kernel on a multiply connected Green domain agrees with the Harnack envelope along a Green line issuing from the normalization point. We give a negative answer on the circular annulus exp(-pi/2)<|z|<exp(pi/2), based at1. For every outer boundary point whose argument differs from pi by at most1/40, its minimal Martin kernel lies strictly below the envelope throughout one common punctured neighborhood of1, with gap at least |log z|/25. Periodizing the elementary strip Poisson kernel gives explicit formulas. Four competing normalized kernel gradients form a rectangle containing all target gradients strictly in its interior; elementary series inequalities and uniform Taylor estimates give the gap. A Green-function quotient and boundary-measure argument verify the Martin interpretation and minimality. This is a complete negative answer to Hayman-Lingham Problem7.42 (UnsolvedMath AMR-022-7042). The five-page manuscript includes reproducible symbolic and independent Fourier checks. Classical kernel and Harnack methods are credited. AI-assisted preprint with a detailed originating-system self-audit; no independent peer review, formal verification or exhaustive priority certification is claimed.