Gavin, your solution has high latency. I want to solve the problem of locality. You can get double spending verification at a time scale that does not grow with the total size of the network.

There are two uses of this. One is for high speed trading, i.e. millisecond latency, the other is for huge networks. The vending machine might be on Mars for that matter.

This is why locality should be built in in some way.

Your method is simply too slow for me, otherwise it works of course. On this planet, your method would preclude verifications faster than 200 milliseconds say.
The speed of light is the fundamental problem.