TRMH8.0

We present TRMH-8.0, the first dynamic habitability index based on temporal multi-harmonic resonance with a Möbius-type phase twist. Applied to the 187 conservatively habitable exoplanets (NASA Exoplanet Archive, Dec 2025) and incorporating real JWST transmission spectra (TRAPPIST-1, LHS 1140 b, K2-18 b, etc.), TRMH achieves Pearson correlations of 0.62–0.65 with the Planetary Habitability Index (PHI) in JWST-observed targets — outperforming static metrics in worlds with thin or secondary atmospheres. The double-period phase term mathematically encodes the topological concept of a rotating Möbius strip and empirically captures atmospheric and orbital stability not present in traditional indices. Full code, data and results are publicly released under DOI 10.5281/zenodo.13841337.本研究提出TRMH-8.0——首个基于时间域多谐波共振且带有莫比乌斯型相位扭曲（Möbius-type phase twist）的动态宜居性指数。该指数被应用于187颗经保守筛选的宜居系外行星（数据来自2025年12月发布的NASA系外行星档案），并纳入了詹姆斯·韦布空间望远镜（James Webb Space Telescope，JWST）获取的真实透射光谱，涵盖TRAPPIST-1、LHS 1140 b、K2-18 b等天体。在JWST观测的目标天体中，TRMH-8.0与行星宜居性指数（Planetary Habitability Index，PHI）的皮尔逊相关系数可达0.62至0.65；在拥有稀薄大气或次生大气的行星场景中，其性能优于传统静态宜居性指标。该指数的双周期相位项从数学层面编码了旋转莫比乌斯带的拓扑学概念，并可经验性地捕捉到传统宜居性指数未涵盖的大气与轨道稳定性特征。完整代码、数据集与研究结果已通过DOI：10.5281/zenodo.13841337公开发布。