Particle Mass on Three Dials: The Packed-Ball Ledger, the Electron Term, and the Mass of Every Measured Nuclide to 0.0062%

We predict the mass of an atom from its proton and neutron counts through a single geometric picture — a nested, flipping resonance whose pieces pack together and ring in common — and test it against all 2,938 measured nuclides. Counting the packed pieces and subtracting one binding term of about 8 MeV per ball reaches a mean deviation of 0.043% (one_binding_number.py; PROBLEMS P31 records the earlier 0.082%, which had no runner behind it). Shaping the binding per atom (the standard liquid-drop terms) and then, crucially, folding in the electron rest energy so the prediction is compared like-for-like against the measured atomic mass, brings the mean to 0.0062%, and for the roughly two thousand medium and heavy atoms to 0.0012% — tighter than the five-parameter textbook formula. The electron term is the single largest correction on heavy atoms (47 MeV for uranium) and was the dominant residual before this pass. The lightest nuclei remain the honest weak spot at ~0.164%, a few-body effect where the liquid-drop approximation has no bulk to average over. All results are reproducible from the included code. 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.