Structural Analysis of the Riemann Hypothesis: A Multi-Scale Diagnostic for Directing Research Effort

We apply structural analysis tools — failure-prime decomposition, multi-scale gap detection, and cross-domain isomorphism transfer — to the research landscape of the Riemann Hypothesis. The goal is not to prove RH but to identify where research effort is wasted and where it should concentrate. We find the landscape has failure signature F3·F6·F7·F10, structurally analogous to Fermat's Last Theorem before 1985. Connes' 2025-2026 results reduce RH to a convergence statement whose structure matches intrinsically contractive dynamics. Numerical experiments on the Redheffer operator show monotone growth of a Perelman-type W-functional, consistent with the needed convergence.