Hölder curves with exotic tangent spaces

The uploaded paper (Shaw–Vellis) proves exactly the target statement (Theorem 1.2) using a two-model planar construction for discrete exponents α_n = log(5n−6)/log n, a measure-theoretic choice-function argument to ensure “randomness,” explicit control of tangents at typical points (with precise cut-point counts), and then a snowflaking + Assouad embedding step to reach every s>1; see the statement of Theorem 1.2 and the proof outline in Sections 1.2, 5–9 . Tangents are defined via Attouch–Wets convergence (following [BL15]) , and the bi-Hölder invariance of tangents needed for the snowflake/embedding step is provided in Section 9 (Lemma 9.1) . The candidate solution adopts the same two-step strategy and is substantively correct; it differs only in a minor quantitative detail: it incorrectly states the exact count of local cut points in the discrete-stage tangents as (n^k−1)/(n−1), whereas the paper proves 1/(5n−7)((5n−6)^k−1) (Proposition 8.1, used in the proof of Theorem 1.2) . This discrepancy does not affect the main conclusion (infinitely many pairwise non-homeomorphic tangents), so the model’s approach aligns with the paper’s proof.