Uniform polynomial negative values for trigonometric sums with near-unit coefficients

For arbitrary distinct positive integer frequencies, we prove a uniform n^(1/12) lower bound for the magnitude of the negative minimum of the real part of a trigonometric sum whose complex coefficients satisfy |c_j-1| <= 0.021. A standard correlation argument gives a uniform n^(1/24) bound for coefficients of modulus in [0.99,1.01], with arbitrary independent phases. The contribution concerns continuous coefficient perturbations, combining Shankar's asymmetric-boundary count with Bedert's cubic Fourier framework and a directional low-leakage multiplier. This does not settle the full square-root Chowla conjecture. Exact unit-modulus arbitrary-phase bounds already follow from known unweighted results. Status: project-internal independent proof and manuscript audits passed; external review and global priority confirmation are pending. An announced 26 October 2026 Bedert-Sahasrabudhe graph analogue has no precise weighted statement available in the checked sources; its coverage remains unknown and is disclosed in the manuscript.