One Hundred and Thirty-Seven, Claimed A Priori: Eddington's Fundamental Theory, Priced

Arthur Eddington claimed that the constants of physics could be deduced by logical reasoning from qualitative assertions, without any use of quantitative data from observation — and his flagship deduction was the inverse fine-structure constant: first exactly 136, then, when measurement moved, exactly 137. I credit the ambition at full strength, and I credit the parts of Eddington that need no defence from me: the radiative model of stellar structure, the mass–luminosity relation, and the 1919 eclipse work stand on their own addresses and are not evaluated here. This paper evaluates only the a priori claim for 1/alpha, and it evaluates it against the measured number. My bench uses one declared input — the CODATA 2022 value 1/alpha = 137.035999177(21), stated — and returns the defects exactly: the 136 claim misses by -1.035999, which is -7560.051251 parts per million, which is -4.933329e+07 times the stated uncertainty; the revised 137 claim misses by -0.035999, which is -262.698687 parts per million, which is -1.714247e+06 times the stated uncertainty. The count that produced 136 is evaluated for stiffness: it is the triangular number of a chosen frame dimension, n(n+1)/2 at n = 16, and the neighbouring choices return 120 at n = 15 and 153 at n = 17, so every digit of the answer is supplied by a dimension that no step of the theory derives. The same machinery's Eddington number, 136 x 2^256, is printed by my bench as the exact 80-digit integer it claims to be, and its claimed proton–electron mass ratio of 1847.6 is evaluated against the stated measured 1836.15267343: a defect of 11.447327, or 6234.408901 parts per million. This paper is distinct from my census's Eddington 1924 entry (CC-131), which evaluates the mass–luminosity relation's single-anchor opacity use; no exhibit of that entry is re-used here. Grade for this census entry, printed at full size: REASON FOUND / STILL TURNING — explicitly not a kill and not a falsification of Eddington's observational work, which is not this paper's target. The program headline stands unmoved: vacuum catastrophe NOT SOLVED / PARTIAL, producing-count 0.