We prove a universal carrier theorem for connection data and completion-locked analytic–spectral realization. Analytic, determinant, and spectral structures are not treated here as separately chosen operators, normalization schemes, or independent spectral inputs. Rather, once the completion, normalization, regularization, geometric, representation, domain, and regularity data are fixed, these structures descend from the tautological carrier over the affine bundle of principal-bundle connections. The universal carrier is realized through the tautological connection D₀ on the pullback bundle over the affine bundle of connections. We prove its structural properties, including gauge equivariance, base-change functoriality, affine curvature translation, and the canonical symplectic geometry of the rank-one abelian U(1) sector. From the same carrier, after fixing a section and twist direction, one obtains analytic holonomy/twist families, Kato-analytic Laplace-type operator families, zeta-regularized generating functionals, and the corresponding locked spectral data, including kernel stability, zeta regularity, joint meromorphy, parameter analyticity, and zeta-variation formulas. The tautological connection D₀ therefore serves as a universal carrier for connection data together with their locked analytic realization. The analytic realization requires the fixed geometric, representation, domain, and completion data used to construct the Laplace-type family, but no independently specified Laplacian, Hamiltonian, spectral operator, or post hoc normalization scheme is introduced as a primitive input. The same locked datum determines the primitive holonomy/twist and spectral channels, through which branch projections and invariant quantities factor once the corresponding fixed data are specified. License note: Distributed under CC BY-NC-ND 4.0.
Salimah Meghani (Thu,) studied this question.