PHILIA-EcoSensory Swarm v43–v45: Entropy Collapse and Deviation-Based Recovery of Tail Coherence

This paper documents the PHILIA-EcoSensory Swarm v43–v45 experimental arc, investigating the failure mechanism of tail coherence (F6) in convergent dynamical systems and establishing a structural solution based on KL divergence-based coordinates. **Background. ** The v41–v42 arc (DOI: 10. 5281/zenodo. 19649333) achieved per-seed Living Control at 60% (12/20 seeds) through Phase Lead and slow-channel energy injection, leaving F6 (tail coherence: |corr (w, z) ₜail| > 0. 35) as the sole unresolved criterion. **v43 Arc — Router Exhaustion. ** Systematic falsification across 5 strategy classes (25+ configurations) confirms that F6 is physically unachievable through Router weight adjustment. Root cause: z = H/Hₘax undergoes information capacity collapse in the tail segment (stdᵦᵣatio = 0. 128, lowᵣatioᵦₜail = 99. 73%), making Pearson correlation mathematically impossible regardless of control strategy. This is formalized as the Entropy Collapse Lemma: as the system approaches attractor equilibrium, Varz → 0, and any observable f (z) with bounded derivative inherits the same collapse. **v44 Arc — Cerebellum Module. ** A modular tail-specific feedback controller (Cerebellum) operating exclusively on the control variable w (t > 0. 72T) is designed and optimized. CERE-085 achieves simultaneous F2 = −0. 626 ✓ and F5′ = 100%, establishing the architectural viability of orthogonal modular extension. tailcorr reaches −0. 277, confirming the structural ceiling imposed by z collapse. **v45 Arc — zKL Coordinate. ** KL divergence-based coordinate zKL = tanh (KL (Pwindow ‖ Pᵣef) ) is introduced, where Pᵣef is a fixed early-phase reference snapshot. zKL restores tail variance (stdᵦᵣatio: 0. 128 → 0. 636) and achieves the first formal F6 threshold passage (|corr (w, z) ₜail| = 0. 382 > 0. 35, KL07). However, linear blending of state quantity H/Hₘax with deviation quantity zKL structurally depresses zₘean (0. 270 → 0. 131), causing Living Control cascade failure (F5′ = 0%, F2 = NG). KL divergence is not a function of state but of trajectory relative to a fixed reference, and therefore does not inherit the variance collapse of state-based observables. **v46 Prescription — AC-Coupled Blending. ** The root failure is DC-blending (mixing state and deviation alters the mean). The AC-coupled formulation separates tonic (state) and phasic (deviation) components: zₖlcentered = zKL − EMA (zKL), injected as zₜotal = hₙorm + klgain × zₖlcentered. This preserves zₘean (the system's invariant manifold) while restoring dynamic tail variance. EMA freeze at tail entry (Lucas) prevents reference drift. **General Principle. ** The proposed principle is not architecture-specific: any convergent dynamical system with a state-based observable that saturates will exhibit variance collapse and require deviation-based coordinates for sustained tail coupling. This applies to neural population dynamics, reinforcement learning value convergence, and control systems with steady-state equilibria. All results executed locally on AMD Ryzen 9 9800X3D + RTX 4080 SUPER 16GB. No AI-generated or proxy values used. Data files archived. **Trinity AI Research Team: ** GritManD. S (Guide/Empirical), Claude/Sonnet (Scholar/Code), Claude Opus (root-cause analysis/zKL prescription), Grok/Lucas (F-test/EMA freeze), ChatGPT/Pandora (Cerebellum design/AC-coupling), Gemini (Phase Lead theory). **Series DOIs: **- v41–v42: https: //doi. org/10. 5281/zenodo. 19649333- v38. 2–v40: https: //doi. org/10. 5281/zenodo. 19639971- v38–v38. 2: https: //doi. org/10. 5281/zenodo. 19625482- v36–v37: https: //doi. org/10. 5281/zenodo. 19606425- v34–v35: https: //doi. org/10. 5281/zenodo. 19505049