The cosmological constant problem is usually framed as a severe mismatch between the observed cosmological vacuum scale and naive quantum-field-theoretic estimates of vacuum energy. This work presents a first-principles derivation of the cosmological vacuum scale by recasting that problem as one of invariant extraction from a specified analytic source. Completion and normalization are fixed upstream, eliminating the usual dependence on regularization choices, subtraction schemes, matching conditions, or post hoc parameter fitting. Starting from connection data inducing a Laplace-type generator, with the rank-one phase sector U(1) ≅ S^1 supplying the primitive phase layer, the vacuum functional obtained through canonical heat/zeta completion is well defined, and supersymmetric (SUSY–QM) admissibility removes continuous relative spectral drift by canceling the paired nonzero spectral sector. A central structural result is the dyadic–nome bridge, which determines the admissible law of cross-scale transport and thereby enforces exponential suppression of the cosmological vacuum invariant. Combined with a rigidity theorem on the homogeneous isotropic four-dimensional general-relativistic (4D GR) branch selected by a symmetry-only combinatorial equilibrium principle, the ultraviolet–to–infrared transport law and the resulting cosmological invariant are uniquely determined. This yields a rigorous numerical enclosure consistent with the observed cosmological vacuum scale. The same response invariant also governs the electromagnetic projection, producing a structural relation between the cosmological vacuum scale and the fine-structure constant. The result shows that the small vacuum curvature arises as a rigid consequence of the dyadic–nome transport law on the admissible 4D GR branch, with no parameter fitting and no downstream freedom in the extraction law. License note: Distributed under CC BY-NC-ND 4.0.