Profinite geometric iterated monodromy groups of postcritically finite polynomials in degree 3

The paper proves Theorem 1.5 rigorously via (Y)-restricted model groups, establishing (i) finite invariable generation with the standard set S (including g_∞) and (ii) classification up to Aut(T)-conjugacy by the ramification portrait, with clear references to Corollary 3.7 (g_∞ is an odometer) and Corollary 4.1 (structure of standard generators), and executes the argument through Theorems 5.1, 5.5, and Section 5.3 . The candidate solution reaches the same conclusions but via a different route: a levelwise π1 argument for invariable generation and an inductive conjugacy construction using the ramification portrait. While the candidate’s approach is plausible, it omits some technical details and contains a minor inaccuracy (sections “g_q^2” should be just g_q per the paper’s classification), yet these do not affect the final conclusions. Hence both are correct, but proofs differ and the model’s write-up needs minor tightening.