NUMERICAL EVIDENCE OF DYNAMICAL SPECTRAL RIGIDITY OF ELLIPSES AMONG SMOOTH Z2-SYMMETRIC DOMAINS

The uploaded paper (Ayub–De Simoi, 2020) presents numerical evidence and explicitly states a conjecture that ellipses with eccentricity e in (0, 0.3) are dynamically spectrally rigid among Z2-symmetric smooth convex domains, rather than proving it; the text emphasizes the 0.3 threshold is an artifact of the numerics and not a natural bound . The paper relies on the De Simoi–Kaloshin–Wei framework, which proves rigidity near the circle without an explicit quantitative eccentricity threshold, a point summarized in the paper’s introduction and methodological discussion . Thus, the specific quantitative claim with e ≤ 0.3 remained unproved as of 2020-06-10, matching the model’s assessment.