FSRE–CANLE: A Unified Framework for Orbital Sequence Analysis

We present FSRE–CANLE, a diagnostic and predictive framework for analyzing orbital period sequences in planetary systems. The framework operates in two complementary regimes, connected by the F5/J4 pivot where the Fibonacci and Jacobsthal sequences meet at value 5. For architecturally regular systems (low coefficient of variation in period ratios), FSRE–CANLE applies ratio-based extrapolation grounded in eigenvalue boundary theory, achieving 0.051% error for Neptune prediction. For irregular systems exhibiting high CV, the framework diagnoses departure from geometric progression and generates a ranked menu of candidate periods based on Jacobsthal-rational resonances. Applied to Pluto, the framework correctly refuses sequence extrapolation (CV = 0.53) and identifies the 3:2 resonance (J(3)/λ) as the highest-ranked candidate, achieving 0.30% error. We validate on 23 exoplanetary systems spanning diverse architectures, demonstrating that the framework’s diagnostic power and regime classification generalize beyond the Solar System. The framework’s resonance ranking—notably its prioritization of the 5:3 resonance over the 4:3—is vindicated by recent Kepler and TESS statistics showing 5:3 as the most prevalent second-order resonance. We distinguish clearly between established mathematical results, empirically validated methods, and physical hypotheses under continued testing.