The Assumed Attraction: BCS Superconductivity, Priced

Two electrons in a metal repel each other, and in 1957 Bardeen, Cooper and Schrieffer built the first microscopic theory of superconductivity by starting from the opposite sign. I credit what that move bought at full strength: given its interaction, the theory is complete — the gap equation, the condensate ground state, the temperature dependence of the gap, the form of the transition temperature, and a universal ratio confirmed across the conventional superconductors, with Cooper's instability, the theorem that an arbitrarily weak attraction binds a pair at the Fermi surface, as its engine. What I price is the object every one of those derivations starts from: a reduced interaction whose net attractive sign, sharp Debye cutoff, and single fitted strength are all spent as inputs, computed by no step in the 1957 paper from the electron–phonon and Coulomb problem it replaces. My bench prices what that intake carries, returning the gap and the transition temperature together in absolute units from declared inputs. On a declared bench cutoff of Θ_D = 350 K, the transition temperature runs from 0.505049 K at the fitted coupling λ = 0.15 to 53.708223 K at λ = 0.50 — the whole absolute scale is the imported cutoff times the fitted exponential, and no 1957 step fixes either factor. The theory's most famous number turns out to be an exact identity of its inputs: Δ₀/(k_B T_c) = πe^(−γ) = 1.763876988862046, and 2Δ₀/(k_B T_c) = 3.527753977724091, exact at every grid point because the same fitted exponential sits in both quantities and cancels. And the isotope exponent, α = 0.500000 at every grid point, is carried entirely by the imported cutoff's mass scaling — the fitted strength contributes nothing to it. Grade for this census entry, printed at full size: **REASON FOUND / STILL TURNING** — a PREMISE-ONLY pricing grade, explicitly not a kill and not a falsification. The program headline stands unmoved: **vacuum catastrophe NOT SOLVED / PARTIAL, producing-count 0.**