Minimality and unique ergodicity of Veech 1969 type interval exchange transformations

The paper proves that for prime N the Veech N-example Tf over an irrational rotation is not minimal exactly when β = mα + n with m,n multiples of N, and likewise for T_{1−f} with β = mα + n + 1 (Lemma 2 + Theorem 3 imply Theorem 1) . The candidate’s solution claims non-minimality already for β ∈ Zα + Z (independent of N), via a two-jump coboundary lemma that omits the necessary N-divisibility constraints. This contradicts Theorem 1 and also the explicit one-jump criteria (Theorem 11) that recover N | m in the case β = mα, and more generally show the arithmetic dependence on N . The model further assumes without justification that non-minimality yields a nonconstant continuous invariant function, a step that is not generally valid and is unnecessary for the (correct) minimality criteria established in the paper.