Unified Framework of Woodin Cardinal as a Holographic Renormalization Group Invariant

This paper establishes a unified framework for Woodin cardinal κ as a fundamental physical in- variant in quantum gravity unification. We synthesize three breakthrough perspectives: (1) κ as a renormalization group invariant derived from AdS/CFT correspondence, (2) rigorous error control via enhanced TOENS framework with tensor norm constraints, and (3) experimental signatures in- cluding gravitational wave spectral dips, quantum error correction thresholds, and CMB polarization modifications. The unified expression κ = K IR(U)V dg/ √β(g) resolves critical controversies in quan-tum gravity. Verification pathways span LISA (2034), quantum processors (2027), and LiteBIRD (2027), establishing quantum gravity as an experimental discipline.Key enhancement: Weresolve the apparent tension between Woodin cardinal’sinfinitary nature and physical constant’s finiteness through Jiuzhang Constructive Mathematics, implementing domain confinement, operational finitization, and dual isomorphism.