The longest heaviest proof-of-luck chain.
Discussion
From an individual miners perspective, sure; but from the perspective of the whole network, it's proof of work.
Proof that miners participated in the hashing competition targeting the appropriate difficulty.
No, it is not.
There is no mathematical proof, or logocal proof that says this much works was done.
In fact sometimes you find a block faster than you should.
As far as you know the miner found the nonce on the street(im sure statistically this never happens).