High-Precision Spectral Analysis of the Local Edge-Flip Hamiltonian at k=16

We extend the spectral analysis of 2+1D quantum gravity to level k=16 (N=969) using a local Edge-Flip Hamiltonian. We demonstrate that while this discretization leads to a more rapid gap collapse than the global vertex model, it preserves the topological vacuum manifold of the torus (34 zero-modes). We conclude that while the existence of the gap is robust, the specific scaling exponent is discretization-dependent on coarse lattices, requiring further triangulation refinement to identify a universal continuum value.