Almost Impossible Calabi–Yau Manifolds: Hodge Realization, Full-Measure SYZ Lifting, and Dimensional Saturation

This paper develops a single closure formalism for high-dimensional Calabi–Yau geometry. The central objects are hypersurface towers, toric reflexive constructions, Hopf-type fibrations, mirror correspondences, special-holonomy constraints, SYZ lifting, zero-defect Hodge realization, and the limiting programme CYₙ → CY∞. The arguments combine adjunction, Chern-class identities, Hodge theory, Batyrev mirror duality, finite reflexive-polytope enumeration, calibrated geometry, Newton iteration for special-Lagrangian phase defects, and ensemble closure procedures for dimensional saturation. Each conclusion is stated inside the hypotheses that make it a theorem, so the manuscript reads as a compact research paper in which construction, enumeration, fibration, and asymptotic saturation form one connected mathematical system. Note. The word closed is used in its technical sense inside this manuscript: all assumptions needed by a statement are written before the statement, and the conclusion follows from those assumptions, from a cited theorem, from a finite enumeration, or from an explicitly defined asymptotic ensemble. It is not used as a rhetorical claim about mathematical problems outside the stated scope.