Odd Weil-form bounds by positive exterior elimination

Overview

Abstract

We give a complete lower certificate for the odd part of the original minimal theta-weighted Weil form. A positive infinite-rank exterior is absorbed through its directional covariance with the signed low-frequency features. An endpoint chord for the receiving resolvent reduces the required information to two finite matrices, without assuming a positive lower bound for the true feature Gram. At arithmetic cutoff eight this yields q_H[h] ≥ −1.88 × 10⁻⁹ ‖h‖₂² for every odd h in the original form domain V. The proof retains the original polar constraint, four odd exact derivative-null rows, the complete arithmetic remainder and all low/exterior mixed terms. Directed ball arithmetic verifies the resulting matrix of order 4085. The method also has a concrete boundary: at arithmetic cutoff eleven, with the same frequency band and multiplication parameter, the actual positive exterior has odd ambient norm greater than 1.7. We prove the first-moment receiver’s optimality in its finite information class and a convergent higher-moment refinement.

Keywords Weil form · theta function · operator lower bounds · Schur complement · directed ball arithmetic · spectral certificates