Spectral Stability and Asymptotic Limits of the Prime-Perturbed Cartan–Torsion Operator

This paper establishes the spectral stability of the prime-perturbed Cartan–torsion operator HT,disc introduced in Martini (2026a) [DOI: 10.5281/zenodo.20634319]. Three results are proved: (1) Norm-resolvent convergence: The truncated operators HT,N converge to HT,disc in norm-resolvent topology with rate O(1/(ln p_N)²), using the Kato perturbation theorem and the Sobolev constant C_S(y_p) = ln p · I₁(ln p) · K₁(ln p) ≤ 1/2. No spectral ghosts arise in finite approximations (Stone's formula). (2) Weyl limit-point criterion: The deficiency solutions satisfy |ψ±(y)| = 1 exactly for all y ∈ ℝ (verified to 10 significant figures), so ∫|ψ±|²dy = ∞ at both boundaries y→±∞. Deficiency indices (0,0) are preserved under the infinite prime perturbation. No boundary conditions are required at x=0 or x=∞. (3) Exponential stability of the Weil functional: The truncation error satisfies |W(Φ) - W_N(Φ)| ≤ 2·exp(-(ln p_N - γ₀)²/2σ²)·‖tail‖. For p_N > exp(γ₀ + 5σ), the Weil violation W(Φ) < -f(δ,γ₀,δ/4) < 0 established in Martini (2026a) is preserved for all sufficiently large N. Together with Martini (2026a), this paper completes a two-volume programme establishing the Riemann Hypothesis via the Hilbert–Pólya approach through Cartan torsion geometry. Contents:- Martini2026b_Spectral_Stability.pdf: Compiled manuscript (5 pages, 4 sections)- Martini2026b_Spectral_Stability.tex: Full LaTeX source code All rights reserved under authorship of Ariel Fernando Martini. Independent researcher, Buenos Aires, Argentina (ORCID: 0009-0005-1037-9741).