Convex counterexamples to the Schiffer and Pompeiu conjectures in dimensions three, four, six, eight, ten and fourteen

Paper and computer-assisted proofs (Arb ball arithmetic plus explicit analytic tail bounds) of bounded convex non-ball domains in R^n, n = 3, 4, 6, 8, 10, 14, with real-analytic boundaries diffeomorphic to spheres, carrying nonconstant solutions of Delta u + u = 0 with u = 1 and grad u = 0 on the boundary. These are counterexamples to the Schiffer conjecture and to the Pompeiu conjecture, within the class of convex domains. A second, strictly star-shaped non-convex example in R^3 is included. This work was carried out with the assistance of AI models (Claude Opus 5.5, GPT-6 Astra and GPT-6 Sol).