On normal numbers and self-similar measures

The uploaded paper proves exactly the theorem the model labels as likely open: for any equicontractive IFS {ϕ_i(x)=λx+t_i} and any integer b≥2 with log b / log|λ| irrational, every non-atomic self-similar measure gives almost-everywhere normality in base b. This is Theorem 1.2 in the paper, with a complete proof leveraging a disintegration into random measures and Hochman’s dynamical argument, not the uniform Fourier decay along lacunary sets that the model seeks. The abstract and Theorem 1.2 state the result unambiguously, and the proof is fully developed in Section 2 (disintegration: Proposition 2.1; equidistribution and the key L^2 bound: Theorem 2.3 and Lemma 2.4). The model also incorrectly claims that even the Cantor-measure/base-2 case is unresolved; this was already covered by Cassels–Schmidt for b not a power of three and is explicitly discussed in the paper’s background. Thus the paper resolves the stated problem; the model’s status assessment and necessity of Step (B) are incorrect.