An Upper Bound on Atomic-Structure Corrections to the Germanium X-Ray Bound on CSL

The strongest experimental bound on white, mass-proportional continuous spontaneous localization (CSL) at the canonical correlation length rC = 10-7 m is the Majorana Demonstrator's 2022 search for collapse-induced X-ray emission from germanium (Phys Rev Lett 129, 080401). That bound was derived assuming the emission rate scales as 1/E with the coherent-nucleus-plus-electron amplitude S = Np2 + Ne. In 2024, Piscicchia and colleagues showed the true atomic-system emission spectrum departs from 1/E in exactly the band the Majorana search used, and called for the Majorana analysis to be reconsidered. This paper bounds that departure two ways. First, an assumption-free bound: the two k-dependent terms of the emission strength are bounded separately by the true extrema of sinc(x) (minimum -0.2172, not -1), giving 0 ≤ S(k) ≤ Np2+Ne2+2|sincmin|NpNe for every photon momentum and every atomic configuration. For germanium (Np = Ne = 32) this caps any atomic-structure correction at a factor 2.361 (not the looser 3.879 obtained from the naive triangle inequality, which is not attainable): the tightest conceivable corrected ceiling is 2.09 × 10-15 s-1, and the GRW parameter point survives it by a further factor 20.9. Second, a Hartree-Fock argument, given hypotheses stated explicitly in the paper, that within that structure the correction can only weaken the bound, not tighten it. Under the best currently published spectrum (Manti, Bortolotti, Diósi, Piscicchia and Curceanu 2026, arXiv:2608.07205), GRW survives by 79-87 times, against a published margin of 49.4 times. All arithmetic is executed in VERIFY.py and reproduced in VERIFY-OUTPUT.txt. Combined with a scoped 34-source census of the field's other constraint classes, the result is that the white-CSL window at rC = 10-7 m remains open and is bounded against future spectrum corrections by a proved ceiling, strengthened by a hypothesis-bearing argument for its sign.