Objects That Must Exist: Kohn–Sham's Missing Functional and EPR's Criterion, Priced Jointly

Two of my census papers price, thirty years apart, the same logical move: an exact theory resting on an object that is asserted to exist, or a property asserted to be certified, without the object being given or the certification being derived. CC-128 priced Kohn and Sham's 1965 equations: the interacting system mapped onto a fictitious non-interacting one under an assumed representability, and everything the mapping does not compute swept into one object, the exchange–correlation functional E_xc[n] — named, not given, with no explicit form for arbitrary density in 1965 or derived since, and the open face sized by a declared later parametrisation at 0.164462 of the local exchange–correlation energy per electron at r_s = 2, rising to 0.334172 at r_s = 20. CC-126 priced Einstein, Podolsky and Rosen's 1935 argument: a criterion of reality that certifies an element of reality wherever a value can be predicted with certainty without disturbance, riding on a separation premise — two premises, both spent as definitions, whose conjunction an exhaustive enumeration prices exactly, forcing |S| ≤ 2 against the singlet's returned 2.828427, an excess of 0.828427, or 41.421356 per cent of the bound. This paper states the joint claim the two parents make together and prices it with their own exhibits: across the two addresses, four load-bearing postulated objects — one representability, one functional, one criterion, one separation — stand against zero derivations, and in each case the theory built on the object is exact or valid exactly where the object is granted, so that the object's standing, not the machinery downstream of it, is the whole question. My bench reproduces both parents' exhibits digit for digit — the sixteen-assignment enumeration returning 8 assignments at S = +2 and 8 at S = −2, the singlet sweep returning 2.449490 at 15 and 75 degrees, 2.732051 at 30 and 60, and 2.828427 at 45, and the exchange–correlation table returning the open-face fractions 0.115165 at r_s = 1 through 0.334172 at r_s = 20, growing by a factor of 2.031910 across the declared grid — and then counts, jointly: 4 postulated objects, 0 derivations, 2 exact theories, and 1 shared structure, the existence claim spent where a construction was needed. Grade for this joint entry, printed at full size: REASON FOUND / STILL TURNING — PREMISE-ONLY, explicitly not a kill and not a falsification of either parent paper. The program headline stands unmoved: vacuum catastrophe NOT SOLVED / PARTIAL, producing-count 0.