Optimal local GHZ phase readout under weak leaf dephasing

We study discrimination of equally likely three-qubit GHZ signs by measuring only the central qubit after a controlled decoding evolution. Two commuting central-to-leaf interactions have nonnegative amplitudes subject to a shared instantaneous sum bound, while the leaves undergo equal independent Markovian dephasing. Among all measurable controls that decode perfectly without noise in the minimum duration, we determine the exact global optimum of the first-order loss in central trace distance. The optimal control activates the first coupling, then the second, and finally both equally. It is unique up to leaf exchange and changes on null sets. The switching parameter satisfies tan(a0) = 2a0 and gives an asymptotic error reduction of 5.76627% against either balanced or standard serial decoding. A control-independent remainder bound justifies optimization over noise-dependent schedules and certifies a strict advantage for 0 < kappa/Gamma < 0.01735394. We also prove existence of exact finite-noise optimizers within the same class and uniform convergence of their integrated profiles to the first-order solution, modulo leaf exchange, as the noise vanishes. An exact reduction to four real variables and numerical cross-checks support reproducibility. The result concerns the stated control class within standard quantum dynamics. This record contains the author preprint (version 1.0), supplementary materials, editable LaTeX sources, and numerical reproducibility files. It is not a peer-reviewed journal publication. The claim concerns the full theorem under the stated assumptions; historical priority is not certified by the literature comparison. The article, supplementary materials, LaTeX sources, figures, documentation and numerical data in this record are licensed under Creative Commons Attribution 4.0 International (CC BY 4.0; https://creativecommons.org/licenses/by/4.0/). The original Python scripts in the reproducibility archive are licensed under the MIT License (https://spdx.org/licenses/MIT.html). Third-party dependencies retain their respective licenses.