Translation generated by two square-root monodromy reflections
= Translation generated by two square-root monodromy reflections
If continuation around two square-root branch points acts on a primitive as $R_A(W)=2A-W$ and $R_B(W)=2B-W$, then
$$
R_B\circ R_A(W)=W+2(B-A).
$$
Thus pairs of branch-point loops generate additive periods of an inverse function.