= Finite-horizon Robin spectral elimination
{title2=$\Gamma-\widetilde\Gamma=\frac{h(k)e^{-4ik^2T}c_T^\sharp(-k)}{d(k)\Delta(k)}$}
Here $\Gamma=B^\sharp/(ad)$ and $\Delta=\mathcal D/(2k+ic)$. The difference follows algebraically from the <half-line NLS global relation> and the Robin symmetry. Multiplication by the spatial-temporal jump factor gives $e^{2ikx-4ik^2(T-t)}$, decaying in the second quadrant for $t<T$. A triangular analytic change of the <Riemann-Hilbert problem> removes this finite-horizon defect while retaining the reconstruction and transferring all genuine pole information to the known determinant. No unproved large-time decay of the boundary values is needed.
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