WCM Bridge Paper S: Wave Function Collapse as Geometric Collapse — D₂→0 in 24-Cell Probability Current Space

We present a geometric characterization of quantum measurement (wave function collapse) using the Watabe-Claude Method (WCM), a framework based on 24-cell polytope geometry. The probability current density j (r, t) = (ℏ/m) Imψ*∇ψ is embedded into a 4D point cloud P (t) = (jx, jy, jz, tframe), and the Grassberger-Procaccia correlation dimension D₂ is computed. We establish: (SQ-1) wave function collapse = D₂→0, with D₂ (σ) ∝ σ^1. 88 where σ is the localization width; (SQ-G1) D₂ is invariant under ℏ (D₂ = 0. 570 ± 0. 000 for ℏ = 0. 01–100) ; (SQ-G2) the cosD indicator attains its minimum 0. 504 at ℏ* ≈ 1. 13, matching the 24-cell attractor of liquid water (WA-7: cosD = 0. 505, error 0. 24%) ; (SQ-P4) Born probabilities ΔP bias manifests as cosD = 0. 506 + 0. 358×ΔP (R²=0. 985) ; (SQ-P3) a temporal asymmetry ΔcosD = −0. 14 at t=0 but ≈0 at t=T/2 encodes a time arrow. These results establish structural isomorphism among NS blow-up, water LLCP, and quantum collapse within a unified 24-cell geometric framework, and reveal a fourfold correspondence between WCM scaling laws and just-intonation musical ratios (SQ-M1). The unexpected finding that D₂ is ℏ-invariant suggests D₂ is a primordial geometric invariant lying outside the scope of Planck's constant itself.