Orientation sign in quadrant harmonic spectral inversion ($q_z=-\frac{1}{2\pi }\left({\int }_0^{\infty }{e}^{ikz}{\hat{q}}_{2}dk+{\int }_0^{i\infty }{e}^{ikz}{\hat{q}}_{1}dk\right)$)

The clockwise definitions in quarter-plane oblique boundary spectral functions require the minus sign in this reconstruction. Indeed integrating first in $k$ gives $i/(z-w)$, and clockwise boundary traversal has Cauchy integral $-2\pi i{q}_z(z)$. Reversing both boundary spectra or both reconstruction-ray orientations reverses this sign; mixing the two conventions gives the negative of the desired holomorphic function.

// Target: analysis.bigb