Multiscale Ceiling Structure of the He-Tu Antipodal Projection: A Fractal Decomposition Approach to Global H^s Boundedness for the 3D Navier-Stokes Equations

Fifth paper in the He-Tu NS series. Introduces the Multiscale Ceiling Conjecture: each Littlewood-Paley layer Delta_j omega has an L^inf ceiling B_j = 2||Delta_j omega(0)||_{L^inf} non-increasing in time. If proved, immediately yields global H^s bound ||omega(t)||_{H^s} <= 2C||omega(0)||_{H^{s+3}} for all t >= 0, independent of t and mesh size h, resolving the 3D NS Millennium Problem. Proved results: global L^inf ceiling (Theorem 3.1), Bernstein localization (Lemma 3.2), conditional global H^s bound (Theorem 5.1). Numerical evidence: layer L^inf norms non-growing across 500 steps. Key obstacle: commutator estimate ||[Delta_j, P]omega||_{L^inf} <= C*2^{-delta*j}*||omega||_{L^inf}. Records complete research journey including fractal intuition (2026-04-30), energy cascade correction, and precise formulation of the remaining open step.