The Separation, Priced: Born and Oppenheimer's Adiabatic Truncation, the Parameter of a Seventh That Justifies It, and the Couplings It Deletes

Census pricing (row CC-121) of the founding step of Born and Oppenheimer's 'Zur Quantentheorie der Molekeln,' Ann. Phys. 389, 457-484 (1927), against a fixed bench (what is postulated, what is derived, what the postulates return numerically, what they cannot reach). The step is a truncation: the molecular wavefunction expanded in kappa = (m_e/M)^(1/4), the electronic problem solved at fixed nuclei, the electronic energy spent as the nuclear potential surface, and the derivative (nonadiabatic) couplings dropped -- with no error bound on the deleted terms proved in the paper. Verified in the notebook (8 checks, exit 0) from named constants (proton-electron mass ratio 1836.15267343; atomic mass unit 1822.888486209 electron masses) and declared bench inputs: kappa = 0.152765 for hydrogen (1/kappa = 6.546 -- a parameter of a seventh), kappa^2 = 0.023337, kappa^4 = 5.446170e-4 returning the mass ratio identically; the ladder 1 : kappa^2 : kappa^4 spends the declared Rydberg input (13.605693 eV) down to a vibrational rung of 0.317516 eV = 2560.94 cm^-1 and a rotational rung of 0.007410 eV = 59.76 cm^-1, printed as order exhibits only. Remainders at full size: adjacent rungs are separated by only 1/kappa^2 = 42.850, so kappa^2-order terms are 2.33% effects at the lightest nucleus and the deleted couplings are a whole class of them; across the declared nuclear grid kappa falls from 0.152743 (H-1) to 0.055961 (Fe-56), so the truncation is weakest at its motivating nucleus; and where electronic surfaces approach within the vibrational rung (0.3175 eV at bench) the deleted couplings become the leading physics -- a fence the 1927 paper contains no term to price. Scout-grade verification disclosed on the manuscript's face: no verbatim quotation, no page-specific claim. EXTENSION. Vacuum catastrophe NOT SOLVED; quantum gravity NOT SOLVED.