Abstract
<jats:p>A filtered self-reconstruction framework is developed in which finite descriptions are retained through protected interfaces fixed before reduction. Presentation data whose removal preserves the interface and all downstream maps are eliminated, while induced normal and Schur penalties remain in the reduced operator. Finite-core minimality, witness descent, and no-phantom reduction are thereby placed in one ordered residual system. At the state level, the trace-preserving conditional expectation defines a completely positive reconstruction semigroup with monotone subalgebra entropy. For a codimension-three timelike Codazzi defect, atomicity fixes the positive line $\mathcal O(1)$ over the projective link $\mathbb{CP}^1_\Gamma$. Under exact degree fidelity, the order-one current moment and order-two trace-free Codazzi moment occupy distinct Borel-Weil levels and select the multiplicity-free carrier $E_3\oplus E_2$. Selection-witness descent leaves the split grading and determinant line, whose unitary automorphism group is $S(U(3)\times U(2))$; the centered grading determines the hypercharge direction and the even exterior package. The finite cocharacter shadow is $\mathbb Z_6$, and parity reduction gives a three-dimensional induced module with a torsor Hodge complex. An Alena-Codazzi collar provides a conditional realization of the graded charges and their boundary transport. Exact covariance and a Callias-Schur gap are required for attachment to an isolated low bundle. Mass, mixing, Majorana, scalar, and contact data are assigned by the $B-L$-filtered Schur completion, with masses encoded as spectral penalties of the reconstructed defect. Numerical values are reported only for a specified completed branch.</jats:p>