Cuts and entanglement

Fix a finite graph cut with a nonempty vertex set on each side, and attach one qubit to each vertex. The all-zero product state has zero entanglement entropy across that cut. A Bell pair between one selected vertex on each side, with every other qubit in $|0⟩$, has entropy one bit across the same cut. The graph metric and degree measure are identical.

Hence an articulation cut, even in a tree, does not determine quantum entanglement. The exact corner mass is classical sampling mass, not a density operator and not an entropy.

Family 265's stated gapped-lattice area-law and PEPS results remain separate documentary records Dossier,Oai265A. They provide neither a state on this map nor a radiation history. A graph cut is not a horizon, and a size index $n$ is not an evaporation clock.