Abstract
We construct the general four-sector minimal two-spin extension of the fermionic elliptic eight-vertex operator and determine its admissible regular branch through exact residual projection. On an explicit nondegenerate meromorphic projection chart, we show that Yang–Baxter consistency eliminates all decorated coefficients on the branch connected to the ordinary sector and selects the factorized ordinary eight-vertex solution. We then identify the two commuting anisotropic transverse-field XY Hamiltonians and the corresponding factorized lattice Lax pair associated with the selected branch.