Half-line NLS Riemann-Hilbert reconstruction ($d=a{A}^{♯}-b{B}^{♯},q=2i{\lim }_{k\to \infty }k{M}_{12}$)

Combine columns of the three normalized Lax pair eigenfunctions in their common Volterra analyticity sectors for a half-line NLS Lax pair, dividing by the relevant determinants $a,d,d^{♯},a^{♯}$. The resulting matrix is normalized to the identity at infinity and has jumps on the real and imaginary axes. Connection matrices determine each jump explicitly. Zeros of those determinants require residue conditions or local contour deformations.