Spectral Graph Laplacians, Topological Knot Solitons, and Dissipative Non-Abelian Hydrodynamics

This work establishes a singularity-free, mathematically closed vacuum architecture that unifies discrete spectral graph theory, topological knot solitons, and non-Abelian hydrodynamics. Discrete Network Rigidity: Replaces smooth spacetime with a rigid eight-hundred-and-sixty-one-node Johnson graph anchored by the maximal class-number-one Heegner discriminant, establishing an arithmetic firewall that permanently prevents continuous moduli drift and ultraviolet divergences. Spectral Mass Gap Generation: Proves that the fundamental algebraic connectivity gap of the discrete graph Laplacian sets the scale for both the hadronic color glueball mass and the discrete electroweak nucleon mass splitting across holographic boundary channels. Topological Fermions and Spin: Models elementary fermions as solenoidal trefoil vortex filaments embedded in a Möbius-twisted fiber space, deriving intrinsic spin-one-half directly from seven-hundred-and-twenty-degree rotational holonomy rather than inserting point singularities. Non-Abelian Circulation Invariance: Establishes the exact conservation of generalized non-Abelian fluid circulation along advected loops, proving that internal color charge precession identically cancels non-Abelian Lorentz accelerations. Dissipative Reconnection Dynamics: Demonstrates that vortex filament surgery is inherently non-Hamiltonian and irreversible, with energy loss bounded at the effective Kolmogorov dissipation microscale through combined kinematic and gluon shear viscosity. Helicity Loss and Wilson Loop Transitions: Quantifies the strictly negative-definite helicity deficit across topological reconnection events and derives the corresponding discrete Mandelstam trace jumps in non-Abelian Wilson loops.