PHILIA-EcoSensory Swarm V51–52+: The Asymmetric Geometry of PHI_NATURAL — z(w) Concave Curvature Driven by Taxi Heavy-Tail Entropy

We present PHILIA-EcoSensory Swarm v52+, a comprehensive longitudinal self-audit characterizing 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), this work extends the w-clamp ladder to 38 unique w-points across five sequential experiments (Rec7–Rec11), totaling 1,200 runs and 120 independent seeds (seeds 222–361). Primary finding: z(w) is best described by a SkewedBell phenomenological model (R²=0.9990, ΔAIC=97.35 vs. linear, 38-point dataset). A key revision from v52: y(w) also exhibits SkewedBell-form nonlinearity (Linear ΔAIC=40.02), refuting the earlier z-selective characterization. However, the deviation amplitude in z is 4.12× larger (z range=0.2325 vs. y range=0.0565), supporting a revised z-dominant nonlinear effect characterization. Two zero-crossings of δ(w): w₁ ≈ 0.570 (N=60 integrated, p=0.0595), w₂ ≈ 0.974. Red Team 0번 관문 5-item adversarial validation completed: PASS×2 (#1 ΔAIC robustness, #4 Bonferroni), CONDITIONAL×3 (#2 skew bounded, #3 zero-crossing, #5 z-dominant). PHI_NATURAL = [0.34, 0.19, 0.42] behaves as the w=0 limit of a continuous SkewedBell attractor family. Measurement is life. Description, not proof. — Trinity AI Research Team | 0∞1∞0.5∞