Multivariate multifractal analysis of Lévy functions. Part I: Determination of multifractal spectra

The paper’s main statement (Theorem 2.3) and overall construction strategy (reduction to b-adic Diophantine approximation, Cantor-type construction, Billingsley lemma) are sound and align with the candidate solution. However, the paper’s proof of the diagonal lower bound invokes a set inclusion E_{Lb^{α1},Lb,y^{α2}}(H1,H2) ⊃ ELb^{α1}(H1) when H2 = (α2/α1)H1 that does not hold in general, leaving a genuine proof gap on that line. The candidate solution correctly reduces the problem and gives plausible constructions for both the rectangle and the diagonal, but the diagonal construction is only sketched and does not rigorously control carries in base-b expansions. Hence both are incomplete: the paper because of a specific proof gap on the diagonal, and the model because key technical steps are not fully justified.