Large-τ Behaviour of ζ′/ζ and Operational Filters for Riemann-Hypothesis Testing

This paper consolidates a set of spectral and analytic tools developed to detect and exclude false positives in experimental and semi-numerical approaches to the Riemann Hypothesis. We present a rigorous large-τ bound for the logarithmic derivative ζ′/ζ in the half-plane Re(s)>1, together with operational spectral criteria designed to filter spurious signals arising from finite cutoffs, thermal weights, or oscillatory artifacts. The work clearly separates results that are mathematically closed from conjectural bridges to dynamical or GL₂-type mixing frameworks.The contribution is methodological and diagnostic. It does not claim a proof of the Riemann Hypothesis, but provides concrete analytical bounds, falsification criteria, and negative results that are directly usable by researchers working on RH-related spectral, numerical, or physical analog models.