Lemma: Kinematic master identity

The Hamiltonian (eq:kinham) satisfies

Proof. Its Hamiltonian vector field restricts to $s$ on the fields. The bracket of two antifield-linear Hamiltonians is antifield-linear, and its coefficient at ${{\Phi }_A}^{‡}$ is the coefficient of $s^2{\Phi }^A$, with the fixed canonical ordering. Theorem thm:kinematic makes every coefficient zero.