A local reconstruction scheme for Codazzi defects in 4D Lorentzian branches uses a lexicographic residual and CP1 Toeplitz visibility to select the S(U(3)×U(2))/Z6 form and standard one-generation SM exterior package.
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Einstein warped products in 4D are classified algebraically via curvature matrix blocks into Petrov types (3+1 generically type I, 2+2 type D, 1+3 type O), with closed Riemannian half-conformally flat cases required to be flat.
citing papers explorer
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Self-Reconstructing Codazzi Defects, $\mathbb{CP}^1$ Quantization, and the Minimal Standard-Model Carrier
A local reconstruction scheme for Codazzi defects in 4D Lorentzian branches uses a lexicographic residual and CP1 Toeplitz visibility to select the S(U(3)×U(2))/Z6 form and standard one-generation SM exterior package.
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Warped Product Einstein Manifolds in Four Dimensions
Einstein warped products in 4D are classified algebraically via curvature matrix blocks into Petrov types (3+1 generically type I, 2+2 type D, 1+3 type O), with closed Riemannian half-conformally flat cases required to be flat.