This release documents the current state of the HAOS–IIP operator program, which investigates whether multiple continuum-like operator sectors can emerge from a single discrete interaction substrate defined by a Gaussian kernel graph. The repository tests a sequence of operator constructions: • a kernel-induced scalar operator that converges to the continuum Laplacian under appropriate normalization • an edge/Hodge operator sector separating exact, harmonic, and coexact components • a restricted transverse operator T = d₁* d₁ | ker(d₀*) ∩ (H₁)⊥ A series of numerical experiments is included: • kernel Laplacian convergence tests • defect transverse tests • transverse scaling tests • transverse band tests including a flux-tube branch Across these experiments the restricted transverse sector shows: • a descending eigenvalue floor with lattice size • decreasing inverse participation ratio (IPR) • decreasing defect concentration • partial n² spectral collapse of the lowest eigenvalues Within the tested lattice range, this provides operator-level numerical evidence for a low transverse spectral band consistent with continuum scaling. This work does not claim emergent gauge dynamics or physical photon modes. The results are presented as numerical evidence for the operator architecture only. Future work will test larger lattice sizes, transverse spectral density, and continuum operator comparisons. https://tomislav-rupic.com/
Tomislav Rupić (Tue,) studied this question.