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Abstract

We construct complete signed-frequency certificates for odd Weil forms and prove q_H[h] ≥ −5.289 × 10⁻¹⁹ ‖h‖₂² on the original polar-constrained minimal domain in the reciprocal-theta norm. At arithmetic cutoff sixteen, an exact eleven-null reduction and 206 disjoint positive-frequency allocations pay all 286 negative observations. The 614-direction head retains every mixed covariance with the positive sources and all twelve physical constraint rows. Exact dyadic receiving maps, a full congruence and directed matrix signs certify the complete infinite-dimensional return. A common Schur row bounds the omitted arithmetic shifts; continuous approximation, complete theta kernels, quadrature, root strips and infinite tails are paid in their stated metrics. We also prove degree-independent Fourier locality, quantitative growing-cutoff constraint costs and exact-coordinate precision bounds. The accompanying reader reconstructs the complete source Grams and signed tests from compact source moments.