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This paper systematically constructs the axiom system and theoret ical framework of Jiuzhang Constructive Mathematics (JCM), aiming to resolve the essential contradiction between infinite cardinals (such as Woodin cardinals) in set theory and finite observable quantities in the physical world. JCM is based on three pillars: the Domain Constraint Axiom, the Operational Finitization Axiom, and the Dual Isomorphism Axiom, transforming infinite objects in classical ZFC set theory into math ematical structures that can be approximated through finite operations and measured by physical experiments. The core contributions of this work include: 1) Formal definition of the constructive universe and con structibility concepts in JCM; 2) Rigorous proof of the consistency and progressive relationship between JCM, Bishop’s constructive analysis, and ZFC set theory; 3) Establishment of JCM’s mathematical toolchain (finite embedding sequences, three-state blocking mechanism, etc.); 4) Exten sion of JCM applications in number theory, topology, quantum gravity, and quantum computing. Research shows that JCM is not a new founda tion independent of existing mathematics, but rather a ”bridge system” connecting abstract mathematics with physical reality, providing a new paradigm for interdisciplinary research in constructive mathematics and theoretical physics.