The TPM elementary-excitation and connectivity conjecture

Let a $2D$ topological phase of matter (TPM) be an equivalence class of connected stable topological Hamiltonian schemas, and let its topological order be the unitary modular category (UMC) derived from the ground-state unitary topological modular functor. TPM excitation and connectivity conjecture. Elementary excitations of a TPM form a UMC, and connected stable Hamiltonian schemas are equivalent. The source gives no resolution or further evidence for this conjecture.