Expanded Algebraicity Targets for Hodge Classes

For a smooth projective complex variety X, we introduce typed Hodge sectors, single-sector algebraicity targets, and expanded targets in which several typed mechanisms admit to a common receiving structure while retaining their separate hypotheses and Chow-level certification. We prove that every certified span \( V^p(\mathcal T) \) lies in \( \operatorname{cl}_X(CH^p(X)_{\mathbf Q}) \), and develop direct-sum aggregation, fiber-product comparison, and certificate-preserving receiver widening. We distinguish structural widening from certification-strict widening, show that shared reception need not enlarge the certified span, and characterize strict gain by a shared-gain quotient \( \Delta_{\mathrm{sh}}^p \). Under maximal rational certification this quotient vanishes, revealing the construction-relative nature of rational gain. We also introduce integral constructional defect quotients \( D_{\tau,\mathcal T}^p(X)\ \)and exhibit a receiver widening that strictly reduces integral defect while leaving the rationalized span unchanged. Coverage remains a separate condition throughout.