Dissipative Softening of Chern Plateaus in a Two-Sector Lattice Dirac Model

We study a two-band lattice Dirac model of Qi-Wu-Zhang type coupled to a Lindblad dephasing bath with jump operator L = σz. The main result is a closed-form dissipatively softened Hall response in which dephasing suppresses spectral weight directly rather than acting through thermal occupation. This produces momentum-selective erosion of Chern plateaus that is strongest near local gap closures. The most distinctive prediction is a doubled-cusp enhancement at M = 0, where two high-symmetry gap closures contribute simultaneously, in contrast to the single-point closures at M = ±2. A numerical implementation and figure-generation scripts are included.