RTLI Diagnostic Tool for JWST Exoplanet Transmission Spectra: A Fast Corridor-Based Triage Metric with Null Tests

This technical note presents RTLI–PCA, a fast and reproducible diagnostic tool for triaging James Webb Space Telescope (JWST) exoplanet transmission spectra prior to computationally expensive atmospheric retrievals. The method applies Principal Component Analysis (PCA) to sliding spectral windows to quantify organized structure using three complementary metrics: a structure index (λₑff) derived from eigenvalue ratios, a quadratic coupling cost (Cq) measuring deviation from an operational reference marker, and an Intrinsic Variance Ratio (IVR) quantifying signal above measurement noise. Spectra are categorized into operational bands (sub-critical, near, in-corridor, super-critical) to enable rapid, reproducible prioritization of retrieval targets. Application to 12 publicly available JWST transmission spectra demonstrates that most rocky exoplanet spectra are noise-dominated, while a small subset exhibit organized, wavelength-dependent structure. In particular, LHS 1140b shows a strong transition from sub-critical behavior in NIRISS to super-critical structure in NIRSpec, consistent with molecular features emerging at longer wavelengths. We emphasize that corridor boundaries are operational reference markers, not claims of fundamental constants. The diagnostic is validated through explicit null tests, injection–recovery experiments, binning stability checks, and cross-instrument consistency criteria. RTLI–PCA is intended as a triage and ranking tool, not a replacement for Bayesian atmospheric retrievals, and is designed to improve observational efficiency in the JWST era. This tool utilizes the mathematical fixed point $\sqrt{e} \approx 1.649$ as a universal phase-boundary anchor to resolve the 'Fulton Gap' in exoplanetary data. By mapping planetary radii to this threshold, the framework distinguishes between 'Tier 1' (Terrestrial/Linear) and 'Tier 2+' (Gas-rich/Quadratic) relational states with high precision." "Furthermore, the tool identifies the 'Hardness Ratio' attractor ($H = 1/\sqrt{e} \approx 0.6065$) as the governing density ratio between Super-Earth and Sub-Neptune populations. By applying a Power-Mean Hierarchy ($M_{3,3} \approx M_3$), it diagnoses hierarchical closure and relational stability, allowing for the classification of planetary composition based on their proximity to the $8\%$ ($\delta \approx 0.08$) structural variance cap.