What question did this study set out to answer?

This research aims to characterize the nonlinear geometry of the PHI_NATURAL z-coordinate under various conditions, specifically focusing on the impact of Taxi input mixing.

May 3, 2026Open Access

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

Key Points

This research aims to characterize the nonlinear geometry of the PHI_NATURAL z-coordinate under various conditions, specifically focusing on the impact of Taxi input mixing.
Conducted five sequential experiments totaling 1,200 runs across 120 independent seeds.
Analyzed data using the SkewedBell phenomenological model to describe z(w) and y(w) behavior.
Evaluated model performance using statistical metrics such as R² and ΔAIC.
The skewedbell model provided a superior fit for z(w) with R²=0.9990 against the previous linear model (R²=0.991).
The amplitude of deviation in z is 4.12 times larger than that in y, indicating z-dominant nonlinearity.
Two zero-crossings at w₁ ≈ 0.570 (N=60, p=0.0595) and w₂ ≈ 0.974 were identified.

Abstract

We present PHILIA-EcoSensory Swarm v52+, a comprehensive longitudinal self-audit characterizing the complete nonlinear geometry of the PHINATURAL 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). PHINATURAL = 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∞

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