This work proposes a cyclic‑stability extension to exoplanet habitability scoring that addresses a central omission in standard indices such as the Earth Similarity Index and habitable‑zone overlap scores: they measure instantaneous Earth‑likeness, not whether a system can sustain a stable climate over geological time. As the manuscript states, “habitability is a property of trajectories, not of snapshots,” and the framework therefore augments a baseline score with four dynamical factors: long‑term orbital stability, obliquity stabilisation, bounded Milanković‑type climate forcing, and a new multi‑cycle recurrence metric. The core innovation is RSaros, a generalised Saros‑like measure of how closely a system’s orbital, nodal, and apsidal periods nearly synchronise. It is defined through an integer‑relation search that quantifies “how closely a system’s several orbital clocks nearly synchronise,” calibrated to the Earth‑Moon‑Sun Saros. The framework embeds RSaros within a falsifiable model‑comparison pipeline (M0–M3), preregistered hypotheses (H0–H5), and explicit failure conditions to ensure that any claimed predictive value is out‑of‑sample and not an artefact of overfitting. A major extension treats natural satellites as possessing two habitability channels—surface and subsurface—where recurrence acquires direct causal meaning via resonance‑maintained eccentricity and tidal heating. The result is a transparent, testable methodology for assessing long‑term habitability across planetary and satellite systems. This project was developed by Marco Gericke, with structured assistance from a large language model. All scientific concepts and conclusions were generated, verified, and interpreted by the author. Dedicated to Peter Plichta, who envisioned the code before it could be computed.