Common-domain commutation versus strong commutation

Here $D$ is dense and invariant, but is not asserted to be a graph core for both self-adjoint realizations. The example proves the precise common-domain nonimplication used in the plan. It is not a counterexample to a theorem with additional common-core, analytic-vector, or VOA hypotheses.

The corrected optimal-energy locality criterion of Carpi–Tanimoto–Weiner operates inside its chiral field hypotheses, including the Hermitian condition emphasized in the correction CTW,CTWCorrection. It cannot be applied to Proposition prop:unbounded by merely naming $H_D$ an energy.