Missing faces and topological embeddings of sphere skeleta

Let S be a finite simplicial triangulation of the topological sphere S^(2d), and let T be a missing d-face. We prove that adjoining T to the d-skeleton of S prevents a topological embedding in S^(2d). For d >= 3, a graded Koszul calculation combines with established ambient-completion, anisotropy and metastable embedding theorems. For d = 2, we apply the Nevo-Wagner bistellar transfer theorem in the PL class supplied by the given triangulation: a contractible complementary manifold supplies the required disk map, and a flag subdivision supplies the base. This proves the statement of their Conjecture 1.3 without a standard PL structure assumption on the source. No claim of first priority or a new general method is made. Unrefereed preprint. No independent human peer review has been obtained. AI tools were used extensively in solving, drafting, independently auditing, checking finite computations, and preparing the materials. AI-assisted review is not formal verification or independent human peer review. The accompanying verification programs supply bounded finite consistency evidence only; the universal conclusion is supported by the mathematical proof and its cited theorems.