= Single-function spectral elimination for a rational-angle quadrant
{title2=$\Phi(k)=H_2(-k)-iJ_2(-k),\quad\operatorname{Im}k>0$}
Reality of the boundary derivatives gives $H_1(\bar k)=\overline{H_1(k)}$ and $H_2(-\bar k)=\overline{H_2(k)}$, and the same identities for $J_1,J_2$. The <global relation> and its conjugate express both <quarter-plane oblique boundary spectral functions> in terms of the known $H_1,H_2$ and the single bounded <holomorphic function> $\Phi$ in the upper half-plane. For $\gamma=\beta_1+\beta_2\in\{0,\pi/2,\pi\}$, its coefficients on the positive real and positive imaginary reconstruction rays are opposite, because $e^{4i\gamma}=1$. Closing the first-quadrant contour removes $\Phi$ by the <Cauchy integral theorem>.
// Target: analysis.bigb
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