Fans, phans and pans

The paper proves that in a 1‑dimensional hereditarily unicoherent continuum X which is the union of arcs whose pairwise intersections are exactly {v}, the only ramification point is v (Lemma 3.2), and then asserts X is a fan (Theorem 3.3) . While the paper does not explicitly spell out why X is arcwise connected, this follows immediately from the union‑of‑legs structure. The candidate solution supplies this missing step and also shows v is indeed a ramification point when |L|≥3. The candidate’s proof of uniqueness of ramification points is sound in idea but contains a minor slip (“removing x from an arc leaves exactly two components,” which fails when x is an endpoint); this is easily patched. Hence both are substantively correct, with different proof details.