Research Map: Multiplicative Concentration, Uniformity Barriers, and Pretentious Rigidity

Can we construct a modulus-stable, multi-scale concentration detector for completely multiplicative functions that does not factor through approximate characters?

This document maps out the precise dependency graph of this question. It traces how modern attempts to bypass spectral machinery invariably end up rebuilding it at the uniform threshold. It includes a step-by-step post-mortem of why localized, blockwise character patching fails under the weight of multiplicative convolution, and categorizes the rigid four-tiered proof structure that binds results like the Bombieri–Vinogradov theorem. No hype, no hand-waving "new routes to RH"—just a sober, mathematically dense layout of the current structural boundaries in multiplicative concentration and four concrete trajectories to push past them.