Am I missing something? A quick read through seems to tell me that this attempts to solve the double-spending problem by... ignoring it?

I see some hand waving about a 24 hour waiting period and some verbiage about how different sub-currencies would handle it, but no actual solution.

Solving that problem is what the block chain is for, so the "without a ledger" bit seems to be missing the point.

Or maybe I didn't skim this carefully enough.