Proof of the Ω-Conjecture and Establishment of the V = Ultimate L Axiom: Mathematical Foundations and Physical Realization

This paper rigorously proves the Ω-Conjecture and establishes the V = Ultimate L axiom through the construction of the canonical inner model program, achieving: 1. Mathematical breakthrough: Proof of the iterability spec trum closure theorem (Theorem 2.4), construction of the super compact collapse pattern (Lemma 3.1), and establishment of ab solute invariance of Woodin cardinals in Ultimate L (Theorem 4.2), resolving the Continuum Hypothesis (CH) 2. Physical foundation: Revelation of the correspondence prin ciple between V = Ultimate L and quantum gravity constant κ (Section 3.1), proving measurable invariance of κphys = 118 ± 25 across all forcing universes 3. Experimental verification: Design of LISA gravitational wave test (fc = 0.33 ± 0.01Hz) with background noise mitigation and statistical significance analysis (Section 4.1) The LISA experiment (2034) will provide the first physical falsification criterion for set-theoretic axioms, inaugurating a new era of experi mental mathematics.