A Filtered Link-Cycle Reconstruction of a Minimal Standard-Model Representation Carrier from Primitive Optical Codazzi Defects

A local finite-carrier theorem is proved for primitive optical Codazzi defects. After real blow-up of a codimension-three core, the resolved optical link is $\mathbb{CP}^1$, and the primitive transverse class gives $L_\Gamma\simeq\mathcal O(1)$. The positive equivariant Dirac index is then the Borel-Weil tower. For any natural scalar-sector transverse source of order $\leq2$, after the scalar singlet is separated, the non-scalar associated-graded source has only the $V_1$ and $V_2$ types. When both non-scalar channels are present and separated at principal order, Toeplitz visibility gives their first separated supports as $E_2$ and $E_3$, hence the minimal separated carrier $E_3\oplus E_2$. After the link-equivariant selection has fixed the blocks, the selected blocks are read as Hermitian carrier spaces. With the unimodular top-form constraint this gives the compact basis group $S(U(3)\times U(2))$ and the standard one-generation exterior package. The same primitive class has a mod-three projective-color shadow, giving a central $\mathbb Z_3$ family-response torsor. An Alena-type current-residual collar is used as a sufficient realization of the source hypotheses. In the gauge-branch reading, the same collar gives a conditional self-description mechanism in which the gauge-side stress supplies the separated current and stress-response channels. Flavor, thresholds, and running remain closed spectral data.