Self-Reconstructing Codazzi Defects, CP<sup>1</sup> Quantization, and the Minimal Standard-Model Carrier

<jats:p>Filtered minimal reconstruction is applied to a codimension-three timelike Codazzi defect with primitive $\mathbb{CP}^1$ link and nonzero first- and second-order normal source grades. Marked Borel-Weil descent selects the multiplicity-free carrier $E_3\oplus E_2$, whose determinant-preserving automorphisms have faithful global form \((\mathrm{SU}(3)_c \times \mathrm{SU}(2)_L \times \mathrm{U}(1)_Y) / \mathbb{Z}_6 \). Clifford completion gives the even exterior package of one chiral generation with a neutral singlet, on which the local anomaly and mod-two parity coefficients vanish as consequences rather than conditions. The same centered integral degree fixes hypercharge and generates a $\mu_6$ finite shadow whose parity-selected corner is three-dimensional. Under the Alena-Codazzi realization hypotheses, the isolated low sector is obtained through a microscopic Gram-Riesz splitting and carries the gauge connection as projected transport, not as added structure. One determinant-tangent normalization fixes both the neutral cell and the central mixing seed, giving $\lambda_{\rm cen}=0.22501$ and the parameter-eliminated relation $15m_h^2=266m_Z^2-306m_W^2$. The first Hodge incidence step gives the Eisenstein packet $(1,4,5;7)$; the Hodge-Eisenstein jet completion fixes the CKM magnitudes, while the commensurate torsor branch gives $\delta_{\rm CKM}=65.360^\circ$ and $\sin2\beta=0.71030$. A normalized neutral completion gives the three PMNS angles within $0.1\sigma$ of the NuFIT 6.1 central values, $\delta_{\rm PMNS}=207.13^\circ$, and $\sum m_\nu=0.0599\,{\rm eV}$. Independently, parity-paired adjoint thresholds select $M_H^{\rm RG}\simeq6.32\times10^{14}\,{\rm GeV}$, coincident at the quoted accuracy with the neutral half-flux scale $M_R$. Structural, conditional, and normalized results are kept distinct throughout.</jats:p>