Operational Tests for the Emergence Ladder: From Cosmic Dust to DNA via Threshold-Gated Admissibility

Chemical complexity requires environments in which molecular interactions can persist long enough to form stable reaction networks. This work defines pre-chemical closure as a set of physical persistence thresholds spanning cosmic dust formation, planetary stabilization, and environmental shielding. Together, these thresholds enable molecular stability, collision-driven reactions, and the accumulation of chemical complexity without invoking specific biochemical pathways. The proposed framework integrates established results from astrophysics, planetary science, and chemistry into a cross-scale persistence model linking large-scale structure formation to chemical closure conditions. Within this model, a closure functional and a transition operator are introduced as formal devices representing threshold-gated admissibility between closure layers. These devices allow domain-specific models to be unified within a common structure while remaining fully compatible with established physical laws. This work does not propose new chemical pathways or origin-of-life mechanisms. Instead, it formalizes the environmental conditions required for chemical persistence, providing a structural bridge between astrophysical processes and chemical complexity. By expressing persistence thresholds in a unified framework, the model supports quantitative testing across observational and laboratory domain