Topological Gauge Dynamics of the DSM-861 Vacuum: Complete Mathematical Closure, Variational Stability, and Spectral Mass Gap Proofs

Metriplectic Relaxation Engine: The conservative Hamiltonian flow is augmented by a localized dissipation tensor that activates exclusively during filament collisions, breaking phase-space volume conservation and steering turbulent vacuum states onto low-dimensional geometric attractors. Terminal Attractor Selection: Dissipative reconnections act as a topological ratchet, shedding enstrophy and acoustic shear waves until reaching the Borromean ground state, where geometric ropelength packing permanently prevents filament cores from intersecting and extinguishes further dissipation. Derrick Evasion and Scale Invariance: Integrating out heavy off-diagonal gauge fluctuations derives the non-linear four-derivative stabilizing term directly from non-Abelian curvature, which balances localized magnetic bending against string tension to lock a unique, stable equilibrium radius. Three-Body Color Confinement: Vanishing pairwise Gauss linking numbers combined with a non-zero Milnor triple-linking invariant enforce an inseparable three-loop geometry, reproducing baryon-like color confinement without isolated diquark states. Matter-Radiation Ledger Invariance: Matter particles are singular topological defects with zero-density cores, whereas photons and neutrinos are smooth, nonsingular shear and torsional wave packets whose emission, propagation, and absorption strictly preserve the net matter vorton count. Automorphic Mass Gap: Formulating the gauge-covariant Dirac operator over the single-cusp Bianchi orbifold of the maximal class-number-one imaginary quadratic field establishes a strictly positive lower bound on discrete eigenvalues, yielding a non-zero physical mass gap without spontaneous symmetry breaking.