The Packing Key — the arrangement inside, asked to predict the power laws, and the answer

The author's idea, in his own words: go off the shape of the balls inside — the way it's packed — maybe the packing is the key to it all; look at similar numbers of balls packed in on each atom group. This paper makes that sentence exact and runs it. "How packed" has a parameter-free, credited counting: the number of balls sitting outside the nearest closed arrangement — valence protons times valence neutrons , Casten's scheme, the standard forty-year-old predictor of where deformation lives. The prediction stated before the run: if the arrangement is the key, the organised chains of Papers 91/96 should sit at packing extremes — far from any closed pack, or exactly at one — with the packing-ordinary middle unorganised. Confirmed at . Organised chains carry a mean valence product of 218 against 79 for the rest, and the split is the predicted U: 20 of the 21 organised chains sit at a packing extreme. 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.