Fourth Edition of the Reader's Map for the "Geometry of the Critical Line" programme (March 2026). This is the navigation guide to a 46-paper, 32-research-note open-access programme that investigates the spectral geometry of the Riemann critical line through the SCT 5-manifold, the chiral spectral obstruction, the connection matrix, and the asymptotic Evans zero law. The programme proves five independent characterisations of the critical line σ = 1/2, isolates a chiral spectral obstruction in the Friedrichs domain, derives an asymptotic Evans zero law for the connection-matrix entry M₂₁, and reduces the Riemann Hypothesis conditionally to a single remaining assumption: the SCT–Connes dictionary. No claim is made that the Riemann Hypothesis is proved. 73 falsified hypotheses are catalogued. This edition substantially expands the Third Edition (March 18, 2026, which covered 34 papers and 6 research notes) with: • A complete critical arithmetic endgame (Papers 38–40, RN7–12): critical sector isolation, flat parametrix, carrier/extractor split, chiral spectral exclusion, conditional critical-line theorem. • A complete connection matrix theory (Papers 41–45, RN13–25): involution theorem, transport ratio, Bessel reduction, Wronskian cancellation, λ-blindness hierarchy. • A complete Evans spectral theory (Paper 46, RN26–28): η-stable Evans function M₂₁, asymptotic zero law with sinh structure, depth formula, multi-sector universality in resolved windows. • A perturbative refinement arc and structural closure (RN29–32): Whittaker cancellation, all-orders Olver protection, non-canonicity of the subleading depth drift. • A Weil prime-side triad (RN20–22): formal assembly of the prime side of the Weil explicit formula from the SCT geometric carrier. New front matter includes an executive summary, current doctrinal state, core mathematical objects, and a section documenting how the programme changed under falsification. The programme lies at the intersection of spectral geometry, analytic number theory, non-self-adjoint ODE theory, complex dynamics, and operator-algebraic models inspired by the Connes/Bost–Connes framework. Part of a 46-paper open-access programme on the geometry of the Riemann zeta function's critical line, anchored by the SCT 5-Manifold and the cover equation Φ + e^iπ − 1/Φ = 0.
Pavel Kramarenko-Byrd (Mon,) studied this question.