The contraction threshold, 31 August 2026: the 4.4-radian optimum is a property of the chord solver

This note gives the mechanism behind the 4.4-radian optimum reported in this deposit on 30 August 2026 and adds two citations. The five passages that report the optimum are listed in §1 and carry a pointer to this note, so a reader can read them with the mechanism beside them. raising a sharp cut-off of the Selberg prime sum makes the placement of the next zero worse while making the reconstruction of better; that the sharp cut-off has an optimum at log(cut) mean gap radians, the same at , and ; and that the mechanism is that the counting equation "acquires spurious roots" once the fastest tone turns most of a cycle within one zero spacing. This record holds one paper on its own and is refreshed every couple of months. The complete deposit, 10.5281/zenodo.21788037, holds every paper with its code and data and is updated first; for the newest version of this paper, go there.