Route C: A Spectral Approach to Zero-Density Estimates, Conditional on Two Analytic Gaps

Abstract

Exploratory / conditional note. We outline a Route C architecture for the normalized GCD operator toward a spectral-limit conjecture, conditional on two named analytic gaps (local Möbius/parity evaluation and a uniform spectral-gap lower bound). We do not claim those gaps are closed, and we do not claim a proof of the Riemann Hypothesis.