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This paper systematically elaborates on a constructive mathematical framework named "Jiuzhang Constructive Mathematics (JCM)", which aims to reconcile the tension between infinite cardinals in set theory (such as Woodin cardinals) and finite observable quantities in the physical world. JCM transforms infinite objects in classical ZFC set theory into finite objects that can be manipulated and measured in physical experiments through three core principles: Domain Confinement Principle, Operational Finitization Principle, and Dual Isomorphism Principle. We provide rigorous mathematical definitions of JCM, prove its consistency with existing constructive mathematics (such as Bishop’s constructive analysis) and classical mathematics, and demonstrate its application value through the physical realization of Woodin cardinals. This paper also discusses in detail the relationship between JCM and existing mathematical systems, and provides multiple rigorous mathematical proofs and illustrative examples.