INSTANTANEOUS HAMILTONIAN DISPLACEABILITY AND ARBITRARY SYMPLECTIC SQUEEZABILITY FOR CRITICALLY NEGLIGIBLE SETS

The paper proves Theorem 6 and Theorem 14 rigorously via a product–measure lemma (Lemmas 22–23) and a careful Fubini-in-polar-coordinates argument (Lemma 21), yielding a linear Hamiltonian translation that disjoins A from B for almost every time; see the precise statement and proof sketch of Theorem 6 and Lemma 21 in the main text . The squeezing result (Theorem 14) is then obtained by an explicit folding construction formalized in Lemma 26 and iterated across factors, not by global capacity or packing arguments . By contrast, the candidate’s Phase (2) asserts key steps that are unproven or false as stated (e.g., covering by finitely many Lipschitz pieces with arbitrarily small n-content; asserting arbitrarily small Gromov width for thickened neighborhoods; and invoking Schlenk folding to push a polydisk containing the neighborhood into an arbitrarily small ball without quantitative conditions). Hence the model’s (2) is incomplete/incorrect, although its (1) aligns with the paper’s method.