LAVAURS ALGORITHM FOR CUBIC SYMMETRIC POLYNOMIALS

The paper’s Theorem 5.15 is proved by a careful dynamical separation argument: choose a preperiodic point, build a dendritic q-lamination with critical sets ±Δ (via Lemma 4.9), locate the first iterate where Δ or −Δ separates the minors m=σ3(c) and m′=σ3(c′), and then apply Lemmas 5.7 and 5.13 to produce a periodic leaf y of period < n that separates m and m′; the short pullback of y yields the desired co-periodic comajor d with smaller block period (and the type B case is handled analogously), see Theorem 5.15 and its proof . By contrast, the model’s proof assumes, without justification, that: (i) σ3 preserves the under-order for comajors because their holes have length < 1/3; (ii) the convex hull of Fix(σ3^n) inside a chosen arc has edges that are leaves in the given lamination; and (iii) any short σ3-preimage of the found periodic leaf is a comajor. These are precisely the nontrivial points that the paper addresses through Lemmas 4.9, 5.7, 5.8, and 5.13; the model omits these hypotheses and tools, so its argument is incomplete and not currently valid in this setting .