Hilbert-Pólya Programme via Cartan Torsion: State of the Art, June 2026

Research programme document summarising the complete state of a Hilbert-Pólya approach to the Riemann Hypothesis via Cartan torsion geometry, as of June 2026. Contents:- 12 verified results across Papers I-III (DOIs: 10.5281/zenodo.20634319, 10.5281/zenodo.20634902, 10.5281/zenodo.20644683)- Analysis of three avenues toward closing the central gap- Identification of the open functional obstruction: connecting local Cauchy negativity T_ρ₀(Φ)<0 (Formulation B, Li-Bombieri-Lagarias) to global Weil form negativity W(Φ★Φ̃)<0 (Formulation A, Weil 1952)- Connection to the frontier literature: Burnol (2002), X.-J. Li (2019), Connes-Consani (2019) This document is not a preprint of new results but a working programme record fixing the state of the research at this date.