Closure of the Constraint Algebra in 1+1D Chrono-Grid Dynamics (Version 2 – corrected)

Abstract

This preprint presents a consistency check for Chrono‑Grid Dynamics (CGD) in 1+1 dimensions: the closure of the Dirac constraint algebra. Starting from the fermionic representation obtained via the Jordan–Wigner transformation, exact lattice operator identities are derived and verified. The commutator of neighbouring Hamiltonian densities yields a symmetric combination of diffeomorphism generators, and when the constraints are smeared with lapse functions, the algebra reproduces exactly the Dirac algebra of 1+1D gravity.