Logarithmic Density, Metric Correction, and the Chiral Spectral Obstruction

Paper 40 and capstone of the "Geometry of the Critical Line" programme (40 papers, 11 research notes, 70 falsified hypotheses). This paper proves three culminating results of the SCT programme: Density theorems: the raw winding-sector eigenvalue counting function satisfies N_raw(E) ~ E² log E / (4ω), with a conditional post-quotient match to the Riemann counting N(T) ~ T log T / (2π) that uniquely determines the metric constant k = π/8. The chiral spectral obstruction (Theorem 6.5): the corrected Frobenius boundary analysis gives indicial roots with Re(r₁) ≈ 3/2 and Re(r₂) ≈ −1/2. The Friedrichs form-domain condition (finite kinetic and potential energy, inherited from the global Laplace–Beltrami operator)…