Exact Strip-to-Disk Transport: Weight-Jacobian Cancellation and Local Kernel Bounds

We develop a local, scale-adaptive method for windowed boundary flux on vertical strips that resolves two obstacles to localization: endpoint weights in Dirichlet-to-Neumann (DtN) traces and the diagonal singularity of the associated bilinear form. A canonical strip-to-disk reparametrization yields an exact weight-Jacobian cancellation, turning weighted strip flux into an unweighted circle pairing. The resulting circle form induces a one-dimensional kernel calculus with two explicit kernels: a principal hyperbolic-cosecant-squared kernel and an integrable hyperbolic-secant-squared mirror. Working with the completed zeta function xi simplifies the analysis, as its linear Hadamard factor contributes only a constant that is annihilated by the DtN map. On the lower-bound side, a midpoint Taylor expansion of the DtN pair profile against an even window-plus-smoothing probe cancels the linear term and yields a coercive gain of order one over a, where a denotes the proximity to an off-line zero. On the upper-bound side, the kernel’s singularity is neutralized by the bilinear form’s two-sided difference structure, and the remaining data reduce to local small-values averages on a fixed buffer, producing at most logarithmic growth like log(1/a).