Structural Instability of King–Plot Linearity A Model–Independent Proof and Geometric Interpretation

This article demonstrates that exact King-plot linearity is not a generic property of isotope shifts but a structurally unstable special case. It proves, in a model-independent way, that whenever isotope shifts arise from more than one internal contribution projecting onto an observable transition frequency, nonlinear curvature is mathematically unavoidable. King-plot nonlinearity therefore does not, by itself, signal new interactions or particles, but reflects the presence of multiple internal projection channels. The work reframes the interpretation of high-precision isotope-shift measurements by identifying the minimal geometric structure responsible for nonlinearity: the projection of a multidimensional internal deformation space onto a one-dimensional observable axis. This geometric insight is general and applies independently of any specific microscopic model. As an explicit example, the article shows that the Methane Metauniverse provides one possible physical realization of this required geometry, leading to universal, parameter-free King-plot nonlinearities. The central result, however, transcends the MMU and establishes a general structural origin of King-plot nonlinearity that is relevant for precision spectroscopy, metrology, and searches for physics beyond the Standard Model.