Analytic Classification of Generic Unfoldings of Antiholomorphic Parabolic Fixed Points of Codimension 1

The paper’s Strong Classification Theorem (Theorem 7.4.1) states that, for generic unfoldings of antiholomorphic parabolic germs of codimension 1, strong equivalence, equality of weak modulus, and equality of strong modulus are equivalent, and gives a detailed proof using Fatou coordinates, transition maps commuting with T1, and a careful complex-parameter extension on a sector Ωδ (including a special argument in the trivial-modulus case) . The candidate solution mirrors this structure: it (i) shows strong conjugacy preserves the canonical parameter ε and formal invariant b (as in Theorem 3.3.2) and aligns transition functions up to translations, hence strong moduli coincide ; (ii) constructs a conjugacy from equality of strong moduli via translations in Fatou coordinates, matching the paper’s construction using holomorphically varying normalized Fatou coordinates on Ωδ ; and (iii) sketches the upgrade from weak to strong by extending the translation constant C(ε) holomorphically, aligning with the paper’s Section 7 (though the model omits the paper’s explicit treatment of the trivial case and compatibility on overlaps). Overall, the model’s proof sketch follows the paper’s method closely and arrives at the same equivalence, but it is less rigorous in the weak→strong upgrade step.