Isodynamicity as a Dirac Constraint on the Ideal-MHD Lie-Poisson Bracket: a Jalon Addendum on the (Non-) Degeneracy of the Constraint Matrix, from the Axisymmetric X-Point to the Homoclinic Tangle (v2)

Motivated by correspondence with A. Gruber and Sina (Sandia National Laboratories) on extending Lie-Poisson bracket reductions to semidirect-product groups, and with D. Peralta-Salas (ICMAT) on the geometry of isodynamic equilibria, this Jalon note examines whether the isodynamic constraint ||B||^2 = B_0(\psi)^2 on a magnetic flux surface can be treated as a genuine second-class constraint, à la Dirac, on the noncanonical (Morrison-Greene-Newcomb) Poisson bracket of ideal MHD.Version 2 (September 10, 2026, superseding September 8, 2026 v1) includes:- Formal generalization and symbolic re-verification of the Dirac secondary constraint \Phi_2 and its principal symbol \sigma_{12}(x,k) = -(4|B|^2/\rho)|B x k|^2 across orthogonal curvilinear coordinates (fixing two index/tensor contraction script bugs in the verification pipeline without changing the underlying physical tensor identity).- Corrected numerical validation on a VMEC++ equilibrium of Wendelstein 7-X (fixing a Fourier Nyquist mode indexing error and clarifying the distinction between a local magnetic-well minimum and an island-chain topological X-point).- Negative finding on natural resonance overlap: natural driving harmonics for low-order rational surfaces on W7-X and a ConStellaration quasi-isodynamic equilibrium carry negligible amplitude (~0.03%), placing Chirikov overlap parameters ~30x below the chaos threshold.- A novel hybrid real-field / prescribed-chaos triangulation demonstrating that when a controlled perturbation is applied to realistic 3D metric-weighted fields, all dynamically active directions (resonant wavevector, Lyapunov stretching, unstable homoclinic manifold) remain within 10 degrees of k \perp B, confirming the maximal non-degeneracy of the constraint matrix away from the gauge direction k || B.AI-contribution disclosure: Produced in collaborative dialogue with an AI language model (Anthropic Claude), which assisted with symbolic verification (sympy), numerical integrations, manifold tracing, and VMEC++ equilibrium analysis. All physical framing, decision to pursue and correct conjectures, and responsibility for final content rest with the human author.