SKEW-INVARIANCE AND MAHLER FUNCTIONS

The uploaded paper proves the precise statement the model labeled as likely open: if p and q are multiplicatively independent and f, g are p- and q-Mahler of non-exceptional polynomial type, then f and g are algebraically independent over C(t). This is stated in the abstract and developed via a refined classification of skew-invariant curves (Theorem 1.3) and a difference-field argument culminating in Theorems 3.3 and 3.4; the key multiplicative-independence step is handled directly without invoking a general nonlinear Cobham theorem (see the explicit valuation argument excluding nontrivial solutions to τ(σ(1+ε)/(1+ε)) = (σ(1+ε)/(1+ε))^M when p and q are multiplicatively independent). Thus, the paper closes precisely the gap the model flagged as open, and by a different method than the model anticipated .