Extending Coherence Density Framework to TOI-561 b: Rethinking Planetary Atmosphere Retention in Extreme Irradiation Regimes

This paper introduces the planetary coherence density ($P_c$) framework as a novel physical model for interpreting atmospheric retention in ultrashort-period exoplanets. Using the case of TOI-561 b—an anomalously low-density, volatile-bearing planet in an extreme irradiation environment recently observed by JWST—we show that traditional escape-based models fail to predict its atmospheric persistence. By modeling the stellar coherence suppression field ($\Phi_c$) and local coherence gradients ($∇\Phi_c$), we demonstrate that TOI-561 b resides in a coherence-buffered regime where volatile envelopes are not stripped but stabilized. This framework reframes volatile retention, atmospheric erosion, and magma ocean dynamics as coherence-mediated phenomena rather than solely energy-driven processes. Key Findings: TOI-561 b defies “cosmic shoreline” expectations but is naturally explained within a coherence-topological model. The host star’s α-enhanced, iron-poor composition leads to weakened stellar coherence suppression, permitting structural persistence at close orbital distances. Coherence density predicts envelope retention as a function of internal organization, not just escape velocity. Magma oceans serve as long-term coherence reservoirs, not just thermal features. The p_c framework offers a scalable, predictive model for exoplanetary atmospheric behavior—applicable across systems and stellar types. This work offers a new axis for exoplanet classification and introduces coherence regime analysis as a tool for interpreting volatile structure, retention likelihood, and systemic planetary organization in JWST-era discoveries.