The Cavity Surface Price — the quantum wall charge computed, and the surface term's two halves on the table

Paper 85 ended with a debt: "deriving the discount from the Bessel modes is the remaining work." The computable part of that work is done here, exactly. A nucleons fill the modes of a hard spherical cavity of radius fm — the ledger's own size constant, nothing fitted — each mode costing its exact Bessel-zero kinetic energy. Summed for every A from 8 to 300 and separated into volume, surface and curvature: volume (kinetic): 20.06 MeV per ball — validating the method to four figures against the Thomas–Fermi value 20.05; surface (kinetic): +37.2 MeV — the quantum wall charge, the Weyl correction made concrete; curvature: +45.0 MeV. [computed — the wall charge and the overcharge; open — the soft wall; nothing entered in the ledger] 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.