Darkon-Augmented Lagrangian Dynamics, Ecliptic Confinement Breaking, and Novel Lagrangian Equilibria L 6 –L 9 for Efficient Deep-Space Navigation

We apply the complete Darkon-sector Euler–Lagrange equations of motion (Darkon EoM) derived within Big Boot Gauge Theory (BBGT) and its non-associative octonionic action (OZIP) to the classical restricted three-body problem (CR3BP). We first prove the Ecliptic Confinement Theorem: in the classical CR3BP, no equilibrium can exist off the orbital plane, because the z-restoring coefficient is strictly positive everywhere. The Darkon Yukawa field generated by the primaries breaks this confinement, lifting the equilibrium landscape from 2 to 2.5 dimensions and producing two off-plane equilibria L₆, L₇ and the collinear impulse manifold L_imp. The extended dark matter halo condensate, modelled as a tilted, spinning Darkon condensate governed by the non-associative associator e₄, breaks the remaining y-symmetry and completes the transition to fully three-dimensional dynamics, producing the Dark Apex equilibrium L₉ — the first genuinely 3D Lagrangian point whose existence requires both the Darkon Yukawa sector and the extended halo. We establish nine transitive inference chains (I₁)–(I₉) from first-principles BBGT premises to each novel equilibrium, and derive the Darkon–Jacobi conserved integral C_D governing all low-energy spacecraft transfers between them. The Phi-Molniya geometric orbit model supplies the discrete preferred curvature surfaces; the momentum-conserved derivation of G the gravitational coupling; the discrete coupling-constant ladder the dark-sector coupling α₄ = 8α; the Axiomatic Node Locking framework the planetary discrete geometry; the Darkon Homotopy Corrector the non-associative phase regularisation; and the Topological Belt Fracture model the deterministic orbital-zone structure. All source documents are deposited on Zenodo under CC BY 4.0.