it takes 10 minutes to find a solution, but only after 12 solutions have been found (the chain has been extended 12 times total), can the authenticity of the first of those 12 be guaranteed.
The existence of the 12-block chain is proof that a majority of them has participated in its creation.
Why is the existence of 12 verifications proof that a majority of N have participated?
he can even be lucky twice or thrice. but to be lucky 12 times against everyone else with less than 50% of the resources, is statistically improbable.
2 hours is the result of those two values (12 being statistically relevant, and 10 minutes a chosen parameter of problem difficulty), not an input variable.