Emergence from Finite Arithmetic Obstruction: Bounded Novelty, Stabilization, and Non-Liftability Pressure in Distinct Coverings

We establish a structural bridge between finite arithmetic obstructions and infinite covering dynamics in the Odd Distinct Covering System (ODCS) problem. Using a certified finite obstruction in a fixed Chinese Remainder quotient, we prove the Bounded Emergence Theorem: any ODCS supported on a fixed finite radical cannot stabilize into a low-novelty refinement regime. Consequently, any such system must generate infinite novelty. We then analyze the only remaining escape route—indefinite lifting along prime-power towers—and identify a fundamental scaling tension between obstruction demand and the supply of distinct moduli. This motivates a precise Non-Liftability Conjecture, under which any ODCS must involve infinitely many prime factors. The results isolate the exact arithmetic frontier at which time-asymmetric refinement becomes unavoidable, clarifying the structural necessity of emergence in distinct covering systems.