We consider the max-type equation $$x_{n+4}=\max\{x_{n+3},x_{n+2},x_{n+1},0\}-x_n,$$ with arbitrary real initial conditions. describe completely its set of periods $\mathrm{Per}(F_4)$, as well associate periodic orbits. also prove that there exists a natural number $N\notin\mathrm{Per}(F_4)$ for which $$\left\{N+m:m\geq 1,m\in\mathbb N\right\}\subset\mathrm{Per}(F_4).$$

A bstract We study the symmetric square of Picard-Fuchs operators genus one curves and thereby induced generalized Clausen identities. This allows computation analytic expressions for periods all one-parameter K3 manifolds in terms elliptic integrals. The resulting are globally valid throughout moduli space allow explicit inversion mirror map exact distances, useful checks Swampland Distance Co...