PHILIA-EcoSensory Swarm v51~52: The Asymmetric Geometry of PHI_NATURAL — z(w) Concave Curvature Driven by Taxi Heavy-Tail Entropy

PHILIA-EcoSensory Swarm v52 presents a comprehensive longitudinal self-audit establishing the complete nonlinear geometry of the PHI_NATURAL z-coordinate under Taxi input mixing. Building on v50's linear approximation z(w) = 0.4234 − 0.2159·w (R²=0.991, 3-point), v51–v52 extend the w-clamp ladder to 27 unique w-points across four sequential experiments (Rec7–Rec10), totaling 540 runs and 100 independent seeds (seeds 222–321). Primary findings:- z(w) is best described by a SkewedBell phenomenological model (R²=0.9981, ΔAIC=65.5 vs. linear)- Two zero-crossings: w₁ ≈ 0.570 (dynamical memory → Taxi nonlinearity), w₂ ≈ 0.974 (endpoint recovery)- δ_min = −0.0239 at w = 0.775 (trough)- y(w) remains nearly linear — z-selective nonlinear effect confirmed- L075 cross-validation PASS: |Δz|=0.0056, Cohen's d=0.51, p=0.141- z_std(w) decreases monotonically (slope=−0.0158, p<0.001) — deterministic attractor confirmed- PHI_NATURAL = [0.34, 0.19, 0.42] behaves as the w=0 limit of a continuous SkewedBell attractor family Hardware: AMD Ryzen 9 9800X3D + RTX 4080 SUPER 16GB, DDR5 32GB, Windows 11All results executed locally by GritMan_D.S. No AI-generated or proxy values used. Trinity AI Research Team | 실측이 생명. 증명이 아닌 기술. | PHILIA OS — 0∞1∞0.5∞