A σ-SELECTIVITY FRAMEWORK VIA SECH2-WEIGHTED CURVATURE: REDUCTION TO THE ANALYST'S PROBLEM

"A σ-Selectivity Framework via sech²-Weighted Curvature: Reduction to the Analyst’s Problem" presents a conditional, structural reduction of the Riemann Hypothesis (RH) to a single real-variable positivity inequality. The paper introduces a three-tier epistemic architecture: T1 (Unconditional): Establishes finite-dimensional algebraic results, notably the σ-selector QN(σ) T2 (Conditional on Standard Inputs): Bridges the algebraic framework to analytic number theory using the Parseval identity, the Riemann–Siegel formula, the Weil explicit formula, and Ingham–Huxley zero-density estimates. It shows that any hypothetical off-critical zero would inject a negative term into the Weil decomposition that asymptotically dominates the prime-side and tail contributions, forcing the functional negative. T3 (Open): Isolates the sole remaining gap as The Analyst's Problem: proving uniform non-negativity of the sech⁴-weighted curvature functional No proof of RH is claimed; the work instead delivers a precise conditional equivalence and maps the exact analytic hurdle required to complete the reduction.