Enumerating tame friezes over $\mathbb{Z}/n\mathbb{Z}$
Sammy Benzaira, Ian Short, Matty van Son, Andrei Zabolotskii · arXiv (Cornell University) · 2024
Enumeration of regular and tame frieze patterns over finite commutative rings. The tame count is rigid: T(m,R) = T(m,F_q)|m|^(m-1) for every finite local ring in every residue characteristic, extending Theorem A of Benzaira-Short-van Son-Zabolotskii from Z/nZ to every finite commutative ring. The regular count is not rigid, and what it detects is the singular locus of the monodromy variety, an ordinary double point at the widths m = 2 mod 4. Includes a Lean 4 / Mathlib formalization, sorry-free and axiom-clean, in which the tame rigidity theorem is verified in full.