The Linearised Atmosphere, Priced: Debye and Hückel's Point Ions in a Continuum, the Limiting Law It Returns, and the Boundary Where Its Own Approximation Fails

Census pricing (row CC-112, Scout Batch 7) of the founding step of Debye & Hueckel's 'Zur Theorie der Elektrolyte,' Phys. Z. 24, 185-206 (1923), against a fixed bench (postulated / derived / numeric return / reach). The step is a bundle sold as one theory -- point charges in a structureless dielectric continuum, complete dissociation, Boltzmann distribution -- plus the linearisation of the Poisson-Boltzmann equation (valid only where ze psi << kT) that produces the closed form. Verified in the notebook (7 checks, exit 0) from named constants plus the permittivity of water as a named input (eps_r = 78.4 at 298.15 K) and two NaCl activity coefficients as named measured inputs (comparison only): Bjerrum length 0.7149 nm; Debye length 9.614 / 3.040 / 0.961 / 0.304 nm at I = 0.001 / 0.01 / 0.1 / 1 mol/L; limiting-law constant A = 0.5106 computed from the constants (no fitted number), returning gamma = 0.8891 at I = 0.01 against the measured input 0.905. Remainders at full size: the linearisation's own condition, priced generously at one Debye length, reaches e psi = 0.25 kT at I = 0.0835 mol/L and kT at I = 1.336 mol/L; and the extended law's fitted ion-size parameter (a = 4 angstrom, labelled fitted) buys back the return at I = 0.1 (0.6895 -> 0.7691 against the measured 0.778). Scout-grade verification disclosed on the manuscript's face (CC-91 form): no verbatim quotation, no page-specific claim. EXTENSION. Vacuum catastrophe NOT SOLVED; quantum gravity NOT SOLVED.