Quantum Lichnerowicz complex

The paper defines the quantum Lichnerowicz current j_L from P^{ij}(γ) and shows, by an explicit Wick-contraction/OPE computation, that the simple-pole coefficient in j_L(z)j_L(w) assembles into the Jacobiator and its derivatives, hence vanishes when P is Poisson; this yields (d^q_L)^2=0 (Proposition 1; definitions and OPEs are in Section 2) , with the final cancellations explicitly tied to (derivatives of) the Jacobi identity (see the grouped terms and their cancellation) . In Section 4, after switching the βγ sign to the chiral de Rham convention, they introduce J_{dR}(z)=∂γ_i c_i and prove δ_{dR}^2=0 and [δ_{dR},d^q_L]=0 by observing that the mixed OPE produces only a total z-derivative (Proposition 2) . The candidate solution reproduces the same structure: it writes the same current, uses the same OPE sign conventions in each part, identifies the Jacobiator J^{ijk} as the simple-pole coefficient, and shows that the mixed OPE with J_{dR} is a total derivative. One minor imprecision is the model’s claim that the B–B channel has “no simple pole”; the paper’s detailed expansion shows cccb-type simple-pole terms that cancel by (derivatives of) the Jacobi identity rather than being absent a priori . This does not affect the final conclusion. Overall, both the paper and the model present essentially the same proof strategy and reach the same results.