The Opacity Fitted on One Star: Eddington's Mass–Luminosity Relation, Priced

In 1924 Arthur Stanley Eddington derived the first theoretical account of why a star's brightness is set chiefly by its mass: the mass–luminosity relation, built from hydrostatic equilibrium and an ideal-gas equation of state. I credit that paper at full strength: the scaling family's shape is a genuine derivation, the relation in its modern, composition-aware forms remains load-bearing in stellar astrophysics a century later, and nothing in this paper falsifies a result derived inside the relation. What I evaluate is the one material number the family is hung on. The opacity is evaluated from the single star Capella and then assumed the same for all stars — one star's fitted opacity, used universally, with no step in 1924 deriving the opacity from the theory of stellar matter or deriving its universality across stars of different composition. My bench evaluates that use on declared inputs only, on the scaling form L/L_a = (mu/mu_a)^4 (M/M_a)^3 (kappa_a/kappa) normalised to the Capella anchor. The imported opacity enters at elasticity −1.000000 exactly: at kappa/kappa_a = 10.000000 the relation returns L/L_a = 0.100000 at every mass. The composition input it must silently coexist with enters at elasticity +4.000000 exactly: mu = 0.500000 returns L/L_a = 0.062500 and mu = 2.000000 returns L/L_a = 16.000000, at fixed mass and opacity. At fixed luminosity and mass the two are locked together, kappa/kappa_a = mu^4 — 1 equation in 2 unknowns — so a star of different composition sits on the same relation only if its opacity differs by exactly the fourth power of its composition ratio. Counted plainly: 1 imported opacity against 0 derivations in 1924. Grade for this census entry, printed at full size: **REASON FOUND / STILL TURNING** — PREMISE-ONLY, explicitly not a kill and not a falsification. The program headline stands unmoved: **vacuum catastrophe NOT SOLVED / PARTIAL, producing-count 0.**