Sharp Induced-Norm Paving for Symmetric Weighing Matrices

For real symmetric zero-diagonal weighing matrices W with W^2=dI, we deduce induced-l_p epsilon-paving into at most ceil(36 epsilon^(-q)) parts, where q=min(p,p′) and q=1 at the endpoints. The exponent q is optimal uniformly over symmetric conference matrices. The elementary compression estimate ||W[S]||_p <= ||W[S]||_2^(2/q) transfers the published Ravichandran--Srivastava Hilbert multi-paving theorem; a single spectral paving also gives quantitative bounds for every p simultaneously. The matching lower order follows from classical Paley conference matrices. This four-page, theorem-dependent note proves a precise special case of AIM-ANALYSIS-0089, not the general arbitrary-matrix induced-norm paving question. It is self-audited and unrefereed; the observation may be folklore and no absolute priority is asserted. No independent peer review or formal verification is claimed. The accompanying source and verification report preserve the accepted proof and 15,701 finite exact-arithmetic regression checks. These finite checks do not replace the general proof. Author: Alper Ferudun, Mercury Software GmbH.