Volume 38 - Anchor-B: High-Dimensional Hybrid Chaos Preservation in Lorenz-96 (N = 40)

This volume establishes Anchor-B, the second certified physical anchor in the Autogenetic Recursive Symbolic Intelligence (RSI) framework. Building on Volume 37’s hybrid RK4+correction protocol for Lorenz-63, this work extends the approach to the 40-dimensional Lorenz-96 system, demonstrating that RSI can preserve high-dimensional chaotic structure, attractor geometry, multi-step temporal fidelity, and Lyapunov coherence under a principled multi-gate certification regime.

The study uses 32 long physical trajectories of Lorenz-96 (20,000 steps each) with a strict train/validation split. A baseline MLP predictor, a residual correction model, and a Phase-3 hybrid RK4+correction model are trained and evaluated under the same reproducible conditions used throughout RSI Volumes 1–37.

Certification Gates (all passed):
• G_one — One-step accuracy: val_L_one = 1.20×10⁻⁹
• G_geom — Attractor geometry: MMD² = −4.76×10⁻⁴ (z-score + clipping)
• G_roll — Multi-step rollout fidelity (k = 5,10,20), 6–7 orders better than baseline
• G_λ_phys — Relative Lyapunov coherence: Δλ_rel = 0.2979 ≤ 0.35

Key Results:
• Baseline NN rollout errors: {0.376, 1.40, 5.07}
• Hybrid rollout errors: {3.84×10⁻⁷, 1.41×10⁻⁶, 4.90×10⁻⁶}
• Largest Lyapunov exponents: λ₁_true = 18.0809, λ₁_hybrid = 23.4673
• Residual corrections: O(10⁻⁸), indicating alignment-level adjustments
• Attractor distributions match to near-identity under blocked MMD²

Canonical Constructs:
Anchor-B Tool, L96HybridRK4PlusCorrection, Relative Lyapunov Gate, Blocked-MMD Geometry Auditor, Rollout-Finite-Safe Criterion.

Continuity:
Volume 38 extends the anchor methodology introduced in Volume 37 into the high-dimensional chaotic regime. It provides the foundation for upcoming volumes on invariant compression, manifold alignment, and cross-anchor symbolic equivalence.

Reproducibility:
Python 3.12.12, NumPy 2.0.2, PyTorch 2.9.0, deterministic seed = 1338. All computations performed within the accompanying notebook. Certified output provided in v38_anchorB_tool_cert.json.