Empty bigon and rectangle counts in Heegaard Floer homology

An embedded positive domain which is a bigon or rectangle, has convex alternating alpha and beta corners, and contains no other selected coordinate in its interior, has Maslov index one. A bigon has Euler measure $1/2$ and two corner averages $1/4$; a rectangle has Euler measure zero and four corner averages $1/4$. For the usual regular complex structure, its holomorphic disk count modulo translation is $\pm 1$. For a bigon the Riemann map to the strip is unique up to translation. For a rectangle, the tautological correspondence represents the disk in the symmetric product by a branched double cover of the strip onto the rectangular domain: its conformal modulus fixes the branch parameter, and the only remaining freedom is translation. The resulting isolated regular disk gives one point in the oriented moduli space. The differential coefficient is $\pm U^{n_z}$, so a basepoint-free domain contributes a unit.