# Memory zeta

- 2026-09-21 [Proved] The no-zero factor `1/det(I - base^(-s) A)` of the memory zeta is the Artin-Mazur zeta of the width-`k` subshift the rule accepts at `z = base^(-s)`, the product over its primitive periodic orbits, and on a design it is the zeta `1/(1 - fill base^(-s))` of the full shift on `fill` symbols, the Lyndon product of the zeta page. Witness: Bowen and Lanford 1970, zeta.md Lyndon product bullet, beneath.md THE MEMORY ZETA.