Log-Ratio Propagation on the Simplex: A Theory of Cellwise Contamination for Compositional Data

ArXi:2605.31345v1 Announce Type: cross Compositional data must be analysed through log-ratios: scale invariance, the defining axiom of the field, leaves no alternative. The centred log-ratio divides by the geometric mean of every part, so a single contaminated component shifts every centred-log-ratio coordinate at once, displacing the log-ratio vector by a fixed amount that no choice of coordinates can reduce. We develop a theory of cellwise contamination on the simplex around this observation.