The Light-End Residual: Lopsidedness, Shape, and the Limit of the Drop

The TDF mass ledger reproduces the atomic mass evaluation to a mean 0.0062% across 2,938 measured nuclides (QFT), with a known weak spot on the lightest dozen at ~0.164%. This paper characterises that weak spot and finds It is a function of compositional imbalance: the residual is 95.6% one-sided and correlates at +0.76 with . A single fitted term in that variable, determined on the 45 nuclides with and applied unchanged to the 2,893 it never saw, reduces the light residual from 0.1587% to 0.0588% while improving rather than degrading the mid-mass set. A second, independent result is reported alongside it and carries no fitted parameter: across all 186 mirror pairs in the measured table, the proton-rich member is under-bound relative to its partner in 185 cases, a sign asymmetry with . The mirror result is identified as the Nolen–Schiffer anomaly (1969), unresolved for fifty-seven years, and is offered as independent confirmation rather than discovery. After a joint refit the residual is not distributed but concentrated in four identifiable classes — species with no bound-state mass, shell-closed nuclei, halo nuclei, and ordinary light nuclides — leaving 0.0027% across the 2,875 remaining on this paper's five-coefficient scoring (the deposit's four-knob ledger gives 0.0032%, and RULES D14 makes 0.0032% the quotable figure). Thirteen further readings were tested and failed, and each is recorded with the figure that killed it. The paper closes by establishing that the residual cannot be attributed to measurement: the helium-4 discrepancy exceeds its published uncertainty by a factor of , and carbon-12 — exact by definition of the mass unit — is missed by 5.89 MeV. The light-end failure is a limitation of the liquid-drop form at low mass number, and the open question is whether the nested-ball construction can replace that form where it fails. 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.