If operating as an SPV node then it can check the transactions by querying other nodes.

On an unrelated note, it sounds like your proposal will significantly increase the data size of every transaction, which will create even more contention for block space.

- Jameson

On Wed, Aug 19, 2015 at 7:48 AM, Hector Chu <hectorchu@gmail.com> wrote:
On 19 August 2015 at 12:42, Jameson Lopp <jameson.lopp@gmail.com> wrote:
> If you can actually come up with a technical solution that allows for a node
> operator to prove to the rest of the network that they are running an honest
> full node that hosts the entire blockchain, then you can move forward with a
> direct monetary incentivization proposal. To my knowledge no one has been
> successful in that endeavor. To be more clear, your proposal would need to
> be able to differentiate between a full node and a pseudonode.
> https://github.com/basil00/PseudoNode

The proof is in the validation of transactions. How can a node
reliably validate transactions unless it has the past history of
transactions? Entire blockchain not required or necessary, but that's
a plus.