One incorporation clock, one dilution factor, eight deficient species: a fit-free test of the extinct-radionuclide inventory of the early solar

The inventory of short-lived radionuclides in the early solar system is normally interpreted by fitting supernova or Wolf-Rayet yields to measured initial abundances. We show that a structural test is available that needs no fitting. If one nucleosynthetic channel supplied every species, one dilution factor D set their level, and one delay Δ elapsed before incorporation, then the ratio of measured abundance to production ratio, \(D_{i}\) , must obey ln \(D_{i}=\) In \(D-\Delta(1 / \tau_{i})\) ). This is affine in inverse mean life: the yield model fixes the intercept only, and the slope is the delay. For the thirteen species that carry both a measured initial abundance and a quoted production ratio, the values of \(D_{i}\) span 3.76 dex, so a single channel fails at once. Fixing the two parameters on the shortest- and longest-lived species alone ( \((^{41} Ca,^{146} Sm)\) gives \(\Delta=1.22\) Myr and \(D=0.88\) pereent. That law then predicts \(^{36} Cl\) \(^{26} Al\) and \(^{244} Pu\) to within 21 percent, across a factor of \(10^{3}\) in decay rate, while the remaining eight species fall short by factors of 3 to 700 and none is in excess. The inventory therefore consists of one dominant channel with a short incorporation delay, plus at least one further channel responsible for the deficiencies. An independent channel filter reduces 63 candidate channel subsets to four minimal ones without using any yield table, and three falsifiable consequences are stated.