TRAPPIST-1e as a Resonant Filter for Habitability: A CAT-12 Framework Application

Versioned Update (CAT-12 Standard v1.0; PTR v1.2) as of 10/7/2025 This paper now follows the CAT-12 reporting standard: SNHS/HP in ratio space, with rn (scale-normalized coordinate), Rx (reporting unit), and Tu (corridor width as a posterior, not a fixed ±%). Peaks are scored with Q and Ch against pre-declared families in the Periodic Table of Resonance (PTR v1.2); any “URSL” mention is retired in favor of standard GR mass–frequency scaling used only as a prior (where applicable). Measurements and conclusions are unchanged; presentation and uncertainty are stricter. For definitions, governance (negative ledger, prereg, hold-out), and rationale, see Arthur & Muon (2025), CAT-12: The Cross-Domain Ratio Lattice of Ratio Theory—Standardized Terminology, PTR v1.2, and Governance. Did conclusions change? No—only reporting/uncertainty language. Where’s the new standard? See the Cross-Domain Ratio Lattice paper. Will you update the PDF? A minor v1.1 with a 1-page front note (and Tu where needed) is planned. This paper applies the Cosmic Algorithm Theory–12 (CAT-12) framework to TRAPPIST-1e, one of the most promising Earth-sized exoplanets in the TRAPPIST-1 resonant chain. Rather than attempting full climate reconstructions, the study uses resonance-based indices as filters to reduce false positives in habitability assessments. We calculate and apply five core CAT-12 metrics: Resonant Precision Index (RPI): evaluates orbital placement within ±2% tolerance corridors. Thermal–Lag Coherence (TLC): measures phase-locking between thermal and orbital cycles. Synergy–Entropy Balance (SEB): distinguishes coherence-dominated from entropy-dominated zones. Cross-Domain Coherence Ladder (CDCL): integrates orbital, thermal, and hydrological stability. Anchored Harmonic Ladder (AHL-12): situates TRAPPIST-1e between Earth’s biospheric and Neptune’s gaseous anchors. Findings indicate TRAPPIST-1e maintains long-term resonance stability (RPI ≤ 2%), a composite CDCL score of ~0.86 (surpassing the 0.8 stability threshold), and structural surface partitions of ~56% ocean, ~8% brackish coasts, <1% freshwater basins, and ~35% land. Only ~4.6% of the surface exceeds a high-habitability index (≥0.6), concentrated in a substellar corridor where TLC ≈ 1 and SEB > 0.6 favor stability. The study concludes that TRAPPIST-1e functions as a resonant filter for habitability, narrowing the search space for biosignature persistence and guiding observational strategies with JWST and future direct-imaging missions. By demonstrating resonance-governed stability, this work positions TRAPPIST-1e as a hybrid anchor and a proof-of-concept testbed for resonance-based habitability filtering across planetary systems . Keywords: TRAPPIST-1e, habitability filtering, exoplanet resonance, Law of Dynamic Precision, CAT-12, synergy–entropy balance, cross-domain coherence