CAT-12 Resonant Architecture of the TRAPPIST-1 System: A CDCL Analysis of Orbital Ratios and Resonance Tolerance Bands

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 presents a comprehensive CAT-12 analysis of the TRAPPIST-1 planetary system, focusing on orbital resonance ratios and their alignment with the Law of Dynamic Precision. Using published orbital data (Gillon et al. 2017; Agol et al. 2021), we calculate adjacent orbital period ratios and demonstrate that all six fall within ±2% of ideal commensurabilities, fully satisfying CAT-12’s resonance tolerance bands. The study introduces the Cross-Domain Coherence Ladder (CDCL) as a framework for embedding orbital resonance into a broader schema of thermal and phase coherence. Results show a resonance plateau near 3:2 ratios, a structured decay ladder analogous to CMB acoustic peaks (Planck Collaboration 2018), and strong phase-lock and thermal-lag coherence indices. Together, these findings establish TRAPPIST-1 as a natural laboratory for resonance universality across planetary, cosmological, and thermodynamic domains. This work situates TRAPPIST-1 within the CAT-12 resonance framework, connecting planetary system dynamics to universal resonance laws. It builds on prior CAT-12 studies of cosmology, black holes, and exoplanets, demonstrating that resonance invariants transcend scale and system type. Keywords: TRAPPIST-1, exoplanets, orbital resonance, CAT-12, Law of Dynamic Precision, Cross-Domain Coherence Ladder, resonance universality, cosmology