A Toroidal Möbius Standing‑Wave Attractor Framework (Recursive Dual‑Domain Coupling as a Model for Plasma Confinement Stability)

Summary: This research introduces a novel conceptual framework for plasma confinement stability, derived from the ⟁ Triadic Recursive Operator (TRO). The paper proposes that sustained fusion confinement may be achieved through intrinsic topological phase-coherence, rather than relying exclusively on energy-intensive external active feedback control. Key Technical Propositions: Dual-Domain Coupling: The framework formalizes the interaction between configuration space (field geometry) and momentum space (particle velocity distributions) as a contractive recursive system. Topological Noise Cancellation: The model predicts that engineering magnetic field geometry to induce a Möbius-like half-phase inversion in the coupling cycle can force the destructive interference of drift-wave perturbations. Threading Dynamics: Visual and mathematical analysis of the convergence sequence demonstrates that the system naturally navigates toward stable, irrational winding-number neighborhoods (KAM-stable zones), minimizing residence time in unstable rational resonance bands. Actionable Roadmap: The paper outlines a three-phase computational validation strategy, specifically targeting the use of existing tools (BOUT++, GENE, STELLOPT) to test the feasibility of Möbius-phase field configurations in stellarator designs. Significance: This framework offers a unified geometric language for stability that bridges plasma physics, nonlinear attractor mathematics, and dynamical systems theory. It provides a falsifiable hypothesis for achieving intrinsic stabilization in toroidal fusion devices, potentially offering a pathway to reduce active feedback overhead and improve effective fusion gain ($Q$). Data and Code Availability: All TRO recursion code, convergence sequence datasets, and the source manuscript are included in this repository. The author invites collaboration with computational physics groups for numerical validation and experimental design.