Accounting for the factor of seven in the 1975 cold-neutron Stern–Gerlach experiment

Version 2 is superseded by version 3 (https://doi.org/10.5281/zenodo.22387870). The supplementary material in this version printed "??" in place of its cross-references to the main text; the main paper is unchanged. Please use version 3. The cold-neutron Stern–Gerlach measurement of Hamelin, Xiromeritis and Liaud (1975) was recently modelled with a constant gradient of 300 T/m and found to over-predict the published 6 mm splitting by a factor of about seven. From the primary sources, that factor divides into three. A factor 2.09 is a misattribution: the 1975 article quotes its maximum gradient as a range, 1 to 3 x 10^4 G/cm, and assigns its Fig. 6 to a tapered dihedral of 5 mm entrance and 8 mm exit gap, whereas 3 x 10^4 G/cm belongs to a 4 mm parallel gap whose own splitting is 12.6 mm. Integrating the thesis's measured field instead of a uniform one removes a factor 1.41. A factor 2.40 remains between our best forward calculation and the observation, unsubdivided; it contains the beam's wavelength distribution, 1-45 A against a single 10 A. We derive the D^-2 gradient scaling from a magnetomotive force constant to 4.2 % over a factor 3.75 in gap; a forward calculation with nothing fitted returns 0.92, 1.23 and 0.77 of the observed splitting in the three stable configurations. The 1974 thesis had already identified the non-uniformity and measured lambda^1.83 over six velocity settings; that measurement cannot discriminate uniform from non-uniform gradients, and its exponent lies 4.7 sigma below either prediction, which we leave unresolved. Classical mechanics with the unreduced neutron moment describes both datasets to about 25 %; neither requires a modified deflection law, nor can exclude one at that level.