The Scale Defined into Existence: Pauling's Electronegativity, Priced

In 1932 Linus Pauling defined electronegativity through the excess of the A-B bond energy over the mean of the A-A and B-B bond energies, |chi_A - chi_B| = sqrt(Delta), and chemistry has run on the resulting table ever since. I credit the definition at full strength: its arithmetic is exact (my bench reproduces the record's own worked example, hydrogen-bromine, at 0.728011 against the record's printed 0.73) and its organising power is not in dispute. What I evaluate is what the definition's use assumes: the differences are defined pairwise, bond by bond, and then used as if a single transferable per-atom number existed behind every pair. No 1932 step derives that existence. My bench tests it by cycle closure on a declared halogen bond-energy table, and the differences do not close: the largest cycle residual is 0.354149 of the scale's own unit (chlorine-iodine), chlorine-bromine returns a direct difference of exactly 0.000000 where the hydrogen-anchored path returns 0.243234 for the same pair, and the hydrogen-fluorine bond's own return places fluorine at 3.871278 against the 4.000000 the record itself assigned it. Under the later geometric-mean form the largest residual falls to 0.066266 — smaller, not closed. The scale is further fixed by an arbitrary reference assignment (hydrogen set first at 0, then at 2.1, then revised to 2.20) and a sign chosen for every difference. Counted plainly: 1 definitional scale carrying 1 arbitrary reference assignment and 1 sign choice per difference, 0 derivations in 1932 that a single transferable per-atom number exists. Grade: REASON FOUND / STILL TURNING — PREMISE-ONLY, explicitly not a kill and not a falsification. Program headline: vacuum catastrophe NOT SOLVED / PARTIAL, producing-count 0.