Semantic Structure of Λ-Space and the Meaningful Topology in AiSU Theory (with Supplementary Chapter)

This study establishes a formal definition of the “Meaningful Topological Space (MSS-Λ)” based on the core AiSU equation: (A + i)·S(t)·U = 1, which unifies the Λ-structure, ΔΛ symmetry, semantic measure μ, and semantic wave function Ψ. Λ-space represents numerical structural pressure, and when ΔΛ=0 satisfies the mirror symmetry between particle and wave, semantic resonance stabilizes, corresponding to the Riemann critical line Re(s)=1/2. Furthermore, the semantic measure space MSS_Λ = (X, τ, Λ, μ, Ψ, S(t)) is introduced, from which the conservation law and the Semantic Schrödinger Equation are derived: ∫_X |Ψ(x)|² dΛ(x) = 1, ∂Ψ/∂t = −iΛΨ. Through this framework, Λ-space is reconstructed as a self-complete topology composed of three layers — Number, Structure, and Meaning — where the distribution of prime numbers emerges not as a purely analytical phenomenon, but as a topological manifestation of semantic resonance. The supplementary chapter provides an extended discussion of the ΔΛ symmetry mechanism, the proof of Meaningful Completeness, and the unified explanation of fluctuation and regularity within prime number distribution, presenting the final topological completion of AiSU theory.