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Numerical observations connect spectral determinants to μ-invariants in rank 1 elliptic curves, suggesting implications for stability analysis.
● ▎ Numerical observations connecting relative spectral determinants on modular curves X₀(N) to Iwasawa μ-invariants of rank 1 elliptic curves. For 17 curves with conductor N ≤ 400, the spectral ratio det'(D_f)/det'(D₀) recovers Reg(E) to LMFDB precision. A stability ceiling derived from Kato-Rellich perturbation theory is proposed as a framework for the μ±=0 expectation in Kobayashi's signed Selmer groups. This work builds upon and cites the asymptotic formula of Katharina Müller (arXiv:2504.05734, 2025), which remains her independent contribution. All rights reserved.
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