The non-unital version of Connes' theorem on the Hochschild class of the Chern character

We offer a short proof of Connes' Hochschild class of the Chern character formula for non-unital semifinite spectral triples. The proof is simple due to its reliance on the authors' extensive work on a refined version of the local index formula, and the consequent understanding of the passage from generalised residues of zeta functions to representations in terms of singular traces.