RTLI Eigenvalue-Based Variance Geometry as a Diagnostic for Exoplanet Transit Vetting: An Empirical Analysis of TESS Objects of Interest

This paper introduces eigenvalue-based variance geometry as an empirical diagnostic for vetting exoplanet transit candidates. Using a sample of 7,192 TESS Objects of Interest (TOIs) from the NASA Exoplanet Archive, we quantify the internal coherence of transit and stellar parameters via the eigenvalue ratio \lambda_e = \sigma_1^2 / \sigma_2^2, which measures the dominance of a primary variance mode relative to competing modes in parameter space. We find that confirmation probability exhibits a non-monotonic dependence on \lambda_e. Planet types with intermediate coherence (\lambda_e \approx 1.4–1.65) show the highest confirmation rates (20–40%), while both sub-critical (\lambda_e < 1.4) and strongly super-critical (\lambda_e > 1.75) regimes correspond to reduced confirmation efficiency. Confirmed and known planets cluster at high \lambda_e, whereas unvetted candidates and false positives occupy lower values, with ambiguous candidates concentrated near the boundary region. Statistical tests demonstrate that confirmed planets exhibit significantly tighter internal parameter consistency than false positives (Mann–Whitney p < 10^{-30}), validating \lambda_e as a meaningful structural diagnostic. These patterns are robust across stellar host types and planet size regimes. We emphasize that the identified “corridor” is empirical rather than fundamental, reflecting detection and vetting dynamics within the TESS dataset. The eigenvalue ratio provides an orthogonal diagnostic axis to traditional metrics such as SNR and MES, capturing global parameter coherence rather than individual failure modes. This approach is computationally inexpensive and well-suited for automated candidate ranking in current and future transit surveys, including Kepler archival reanalysis and PLATO pre-vetting.