Attractor-Aware Hyperbolic Lipschitz-Constrained-Reinforcement Learning for FX Market: LLM-Structured Chain of Thought with Lyapunov–Entropy Dynamics

Foreign exchange (FX) markets are non-stationary and event-driven, with heavy tails and regime shifts that complicate generalization and risk control.We introduce an explainable FX trading pipeline that integrates chaotic-systems diagnostics with geometry-aware learning. A Large Language Model (LLM) consolidates several dynamic heterogeneous evidence streams into a Structured Chain-of-Thought (s-CoT) that provides rules, supporting evidence, and uncertainties. The s-CoT is embedded in a hyperbolic space to preserve hierarchical dependencies and to render recurrent price levels geometrically salient. Chaotic and dynamical features, including Lyapunov exponents and permutation entropy, estimate local stability, forecastability horizons, and disorder. Recurrent magnet prices are identified as attractors on the price axis through recurrence density and cross-scale persistence, and they inform entry timing and risk budgeting. A Reinforcement Learning (RL) policy operates on the hyperbolic embedding under Lipschitz constraints that bound geodesic step sizes and stabilize policy updates under distribution shift. The result is an interpretable reasoning-to-action pipeline that produces daily decisions and explicit risk budgets. In pair-averaged non-compounding back-tests across nine major FX pairs from Jan. 2015 to July 2025, the system attains 2.22% monthly return with 10.39% maximum drawdown. An ablation study across components confirms the robustness of the full pipeline, indicating that geometry, Lipschitz control, and s-CoT jointly sustain performance while maintaining controlled drawdown. The empirical evaluation confirmed that encoding structured reasoning in hyperbolic space and steering actions toward magnet-price attractors yields regime-resilient FX trading with strong average performance and transparent risk control.