EQUIVALENCE OF NEIGHBORHOODS OF EMBEDDED COMPACT COMPLEX MANIFOLDS AND HIGHER CODIMENSION FOLIATIONS

The candidate solution reproduces the paper’s Newton–dyadic scheme for full linearization almost verbatim: it sets adapted splitting-preserving coordinates (matching (2.11)–(2.12)), invokes the linear cohomological solvers with the K(·), D(·) bounds from Proposition 1.1, performs the m → 2m step by solving the horizontal and vertical homological equations (cf. (5.17)–(5.23)), packages the tame losses into D*(2m) as in (5.27), and closes the iteration under the Bruno-type summability Σ_k log D*(2^{k+1})/2^k < ∞, which is exactly Theorem 1.5’s small-divisor condition. Minor issues: the solution states that, under m-flatness, all vertical degree-ℓ components for m<ℓ≤2m are cocycles; in general the vertical part is a cocycle at ℓ=m+1, and for m+1<ℓ≤2m only when NC is flat (Lemma 2.10), while in the general (non-flat) case the vertical equation includes the Dtkj term and must be solved using the coupled system. Aside from this nuance, the scheme, estimates, and convergence criterion align with the paper’s proof of Theorem 1.5. See Theorem 1.5 and the construction in §5, esp. (5.17)–(5.27) and (5.35) . The cohomology bounds used by the model are those in Proposition 1.1 (1.1)–(1.2) , and the ‘cocycle at degree m+1/flat case for higher degrees’ point is Lemma 2.10 .