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If the signatures are enough, you don't need the chain. If the signatures aren't enough, you need the chain and a proof of work.

You can use a "blockchain", an enforcer of security deposit against double spending rather than as the raw double spend prevention mechanism.[0]

"Soothly we live in mighty years!"

It looks like the underlying mechanism that they use for this was described in

I'll try to think of a counterexample, but your observation may well be right in all or almost all cases.