ANALYTIC PSEUDO-ROTATIONS II: A PRINCIPLE FOR SPHERES, DISKS AND ANNULI

The paper’s principle works by allowing a controlled deformation of the complex/symplectic structure and proves realizations via J-holomorphic extensions on a complexification, then invokes uniqueness of real-analytic symplectic structures. The candidate solution attempts to run AbC entirely within the canonical real-analytic symplectic category by asserting a density of analytic maps in the centralizer of rational rotations with uniform holomorphic extension to a fixed complex neighborhood. This density claim contradicts the paper’s highlighted rigidity (analytic entire extensions on the cylinder must be shears) and is not justified for large complexifications. Key analytic/complex-domain control and exact centralizer constraints are missing, so the model’s proof does not go through, whereas the paper’s argument is coherent and complete.