Nuclear Spectral Triples in Fracton Phases and Higher-Form Symmetry Extensions

With this paper a new framework for fracton–spectral triples is introduced, extending the nuclear spectral triple formalism to capture subdimensional excitations and higher–form symmetry effects in fracton topological phases. The construction yields a universal invariant $\mathcal{U}(X)$ that decomposes into global and local components and is invariant under fracton $\Sigma$–preserving deformations. A holographic bulk–boundary correspondence is established via colimit constructions, and an extended index pairing unifies contributions from both fracton and higher–form sectors.