= Half-line mKdV spectral global relation
{title2=$S^{-1}s=e^{4ik^3T\widehat\sigma_3}\mu_3(0,T,k)$}
For the three corner-normalized <Lax pair> eigenfunctions, let $s=\mu_3(0,0,k)$ and $S=e^{4ik^3T\widehat\sigma_3}\mu_2(0,T,k)^{-1}$. Their constant connection matrices give the displayed <global relation>. If their second columns are $(b,a)^T$ and $(B,A)^T$, its upper-right entry is $Ab-Ba=e^{8ik^3T}\mu_{3,12}(0,T,k)$. The right side is analytic in the lower half-plane. In the linear limit this is the <backward-sign Airy half-line global relation> at Fourier parameter $2k$, coupling all three boundary traces rather than allowing three independent boundary conditions.
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