I will tell a story about a beautiful planar convex domain L, originating from the works of Vershik, Bárány, and Sinai, which in tropical number theory context is the only domain with C^1 smooth boundary for which we know a closed expression of its tropical zeta function: it turns out to be a minor decoration of the quotient of Witten SU(3) and Riemann zetas, reflecting a delicate balance of the free terms in primitive gradient equations of its rational slope support lines organized by caustic/Stern-Brocot tree. This phenomenon has practical consequences, with the one being a relative simplicity in the case of L of the novel layered cancelation scheme for extraction of the leading asymptotic in the Cesàro-regularized lattice point counting on the dilates of a planar convex domain.

The talk is based on sections 5 and 6, as well as appendix E of arXiv:2604.21709.