A Structured Vacuum Paradigm: Unifying Matter, Cosmology, and Associative Dynamics via Discrete Spectral Geometry and Many-Body Attractor Landscapes

This work formulates a unified theoretical paradigm demonstrating that particle masses, cosmological expansion, and associative intelligence emerge as stable ground-state attractors of a structured superfluid vacuum. The physical substrate is modeled as an ensemble of solenoidal vortex filaments defined over a thirteen-dimensional Poisson phase space, which naturally foliates into canonical twelve-dimensional symplectic leaves governed by a central circulation invariant. Spatial boundary constraints are rigidly anchored to an 861-node Heegner association scheme, whose 72-fold modular clock is derived from the kissing configuration of optimal sphere packings in the six-dimensional metric deformation space of the underlying torus. By combining discrete exterior calculus with high-order dense associative memory potentials, the vacuum action establishes that physical computation and matter formation are dual expressions of autonomous Lyapunov energy relaxation. This geometry derives the positive neutron-proton mass gap directly from the dipolar magnetic self-induction of counter-rotating vortex cores, eliminating the need for ad-hoc quark mass parameters. At cosmological scales, topological gauge constraints cancel the static zero-point energy, while the expanding dynamic lattice generates a residual dark energy density that resolves the Hubble tension through an exact thirteen-to-twelve local-versus-early expansion ratio. The framework bridges theoretical physics and neural computing by proving that physical ground states and associative memory attractors obey identical dynamical saddle-point equations.