I would not equate the term "constructive proof" with "empirical proof". "Constructive proof" would indicate a proof that gives an algorithm that constructs the

I would not equate the term "constructive proof" with "empirical proof". "Constructive proof" would indicate a proof that gives an algorithm that constructs the desired object, or a proof based on a constructive logic. Either of those could be fully rigorous. But I would take "empirical proof" in mathematics as something like "we've verified that this conjecture holds for values up to 10^100", which of course isn't a proof at all in the proper sense.