The Saturation Density — one r₀, five jobs, and a circularity warning first

Every equation of state and every nuclear force fit takes one number as input before anything else: the saturation density of nuclear matter, . The packed sphere ties it to the deposit's radius parameter in one line: . The circularity warning comes before the number, so it can never be unsaid. fm is not something this framework derived — it is the standard empirical radius parameter, chosen long ago by the field from radius and density data. So and are the same fact wearing two units, and this paper may never be quoted as a prediction of the saturation density. It is a consistency check, and it is deposited because the deposit now uses one single across five different observables — a framework quietly drifting its radius per observable would score better everywhere and be worth less. 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.