On the Non-Existence of Z'-Bosons: A Fossil Refutation of Gaul, Cong & Budker

The study by Gaul, Cong and Budker (2026) interprets parity violation measurements on barium monofluoride molecules (BaF) as evidence for a new vector-boson-mediated interaction between electrons and atomic nuclei beyond the Standard Model, carried by hypothetical Z'-bosons of a new gauge group U(1)'. This supplement demonstrates on two independent grounds that Z'-bosons cannot exist. First, theory-independent objections apply: anomaly consistency conditions require unnamed new fermions, electroweak precision tests are incompatible with the implied Z-Z' mixing, and cosmological bounds exclude a new light U(1)' interaction. Second, fossil gravity theory shows structurally: the 12 degrees of freedom of the four-dimensional causal structure are fully exhausted by U(1) x SU(2) x SU(3). No degree of freedom for an additional gauge group exists - algebraically, not approximately. What Gaul et al. observe has a fossil explanation without new entities: the Z_S term of the fossil unification equation describes the sought interaction as a geometric effect of causal condensation. The fossil theory explains more with less.