The clock theorem for knotoids and linkoids

In this paper, we generalize the $\mathit{\text{Clock}}\mathit{\text{Theorem}}$ of Formal Knot Theory to knotoids in $S^2$. The clock theorem implies that clock states of a knotoid diagram form a lattice under transpositions. These states form the basis of many invariants of knotoids and linkoids including the Alexander polynomial, Mock Alexander polynomial and the Jones polynomial.