The Local Uniform Gas, Priced: Thomas and Fermi's Imported Kinetic Energy, the Z^(7/3) Law It Returns, and the Shells It Cannot See

Census pricing (row CC-110, Scout Batch 7) of the founding step of Thomas's 'The Calculation of Atomic Fields,' Proc. Cambridge Phil. Soc. 23, 542-548 (1927) and Fermi's 'Un metodo statistico per la determinazione di alcune proprieta dell'atomo,' Rend. Lincei 6, 602-607 (1927), against a fixed bench (postulated / derived / numeric return / reach). The step is one local-density import: the uniform free-electron-gas kinetic-energy density C_F n^(5/3) spent point by point inside the atom. Verified in the notebook (8 checks, exit 0) from named constants plus one declared standard evaluation (the energy coefficient -0.768745 hartree, labelled declared, not re-solved): C_F = 2.8712 in atomic units; the energy law E = -0.768745 Z^(7/3) hartree verified as an exact scaling (E(2)/E(1) = 5.039684 = 2^(7/3)); the screening length b = 0.8853 Z^(-1/3) a_0 with its coefficient computed from pi alone. Remainders at full size: the uniformity premise fails inside its own solution -- the local Fermi wavelength over radius stands at 2.236 at r = 0.1 a_0 and 7.071 at r = 0.01 a_0 (Z = 1) and diverges as r^(-1/2) at the nucleus; shells are absent by construction (one smooth power law in Z), the density fades as r^(-6) with no atomic edge, and no molecule binds (Teller). 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.