Fractal deconfinement and confinement in Sierpinski ice

What the math gives to ML

The paper provides a constructive real-space recursion for a six-vertex model on a Sierpinski gasket, retaining charge-free and charged boundary partition functions as coarse-grained state variables. Its transferable asset is a two-channel hierarchical renormalization map whose fixed points and Jacobian determine confinement, deconfinement, and sharp regime changes. A neural implementation can use repeated ternary aggregation blocks with neutral and defect channels, while monitoring the recursion Jacobian to obtain a measurable stability boundary. The noninteger path dimension reported at the deconfined point also suggests a concrete sparsity and routing diagnostic for hierarchical networks.