Peer review The Simons Observatory-Quantifying the impact of beam chromaticity on large-scale B-mode science DACHLYTHRA KONSTANTINA

In this technical note we provide a variational consistency assessment of the recent CMB B-mode analysis frameworks adopted by the Simons Observatory and related collaborations. Using the Universal Ψ Equation as a closed-generative formulation, we show that the recovery of the tensor-to-scalar ratio rrr is not physically well-posed within current pipelines based on component-separation heuristics, parametric dust models, and instrument-derived beam chromaticity corrections. We identify four fundamental obstructions: (1) foreground fields are not solutions of any physical variational functional; (2) instrument response is not coherently coupled to sky polarization; (3) likelihood approximations artificially suppress physical correlations; (4) degeneracy among nuisance parameters prevents unique inference. Appendices provide the explicit Ψ-based variational closure, the emergent neutrino mass, a formal proof of why experiments cannot measure rrr in the present framework, and a compact comparison table between Ψ and the Standard Model cosmological pipeline. The result is a model-independent conclusion: without a closed variational generator, no CMB experiment can claim a physical measurement of primordial tensors.