Pre-Chemical Closure: Physical Persistence Thresholds Enabling Chemical Complexity

Chemical complexity requires environments in which molecularinteractions can persist long enough to form stable reactionnetworks. This work defines pre-chemical closure as a set ofphysical persistence thresholds spanning cosmic dust formation,planetary stabilization, and environmental shielding. Thesethresholds enable molecular stability, collision-driven reactions,and the accumulation of chemical complexity without invokingspecific biochemical pathways. The framework integrates established results from astrophysics,planetary science, and chemistry into a cross-scale persistencemodel linking astrophysical structure formation to chemicalclosure conditions. A closure functional and transition operatorare introduced as formal devices representing threshold-gatedadmissibility between closure layers, enabling domain-specificmodels to be integrated within a unified framework while remainingfully compatible with established physical laws. This work does not propose new chemical pathways or origin-of-lifemechanisms. Instead, it formalizes the environmental conditionsrequired for chemical persistence, providing a structural bridgebetween astrophysical processes and chemical complexity.