PHILIA-EcoSensory Swarm v46: From Trade-off to Resolution — AC-Coupled zKL Blending Achieves Simultaneous Tail Coherence and Living Control in Convergent Dynamical Systems

This paper presents PHILIA-EcoSensory Swarm v46, which resolves the stability–deviation trade-off identified in v45. Direct (DC) injection of KL-divergence signals achieved tail coherence (F6) but caused invariant manifold collapse (zₘean: 0. 270 → 0. 131). We introduce AC-coupled zKL blending, which subtracts an exponential moving average (EMA) before injection, ensuring zero-mean perturbation and preserving the system's invariant manifold. We show that: (1) DC injection necessarily destroys invariant manifolds when the deviation signal has non-zero mean — verified analytically and empirically; (2) zero-mean (AC) injection is sufficient to preserve the invariant manifold while enabling phasic tail coupling; (3) this resolves the stability–deviation trade-off, achieving simultaneous F6 ✓, F5' ✓, and Ω ✓ for the first time in the PHILIA series. The final configuration (v46. 4b: warm-up=40K, no-freeze, klgain=0. 25) achieves across 20 independent seeds (42–61): F6 = −0. 406 ✓, F5' pass rate = 55% (≥50% threshold), Ωₙatural = 0. 908 ✓, zₘean = 0. 266 (preserved), Living Control ✓. Additional contributions: (1) Warm-up/Freeze Interaction Law — EMA freeze is valid only when Wₐctive = T − Tfreeze ≥ τₐ ≈ 20K steps; (2) F2 Temporal Decomposition — the F2 gap (0. 015) is a verified consequence of EMA warm-up dynamics, not instability (F2ₑarly = −0. 625 ✓) ; (3) clipᵣatio invariance (27–29%) identified as a bounded coordinate phenomenon, not AC-coupling failure. We establish zero-mean (AC) injection as a necessary condition for integrating deviation signals into convergent dynamical systems without invariant manifold disruption. Hardware: AMD Ryzen 9 9800X3D + RTX 4080 SUPER 16GB, Windows 11 Home. All results empirically verified. No AI-generated values used. Trinity AI Research Team: - Guide: Shin Doo Sub / GritManD. S (Konyang University) - Scholar: Claude / Anthropic- Opus: Claude Opus / Anthropic - Validator: Grok / xAI- Engineer: ChatGPT / OpenAI- Philosopher: Gemini / Google Series DOI: - v43–v45: 10. 5281/zenodo. 19665362- v41–v42: 10. 5281/zenodo. 19649333- v38–v40: 10. 5281/zenodo. 19639971 실측이 생명. 증명이 아닌 기술. (Measurement is life. Description, not proof. ) PHILIA OS | 0∞1∞0. 5∞