That an algorithm is heuristic does not preclude it from being provably correct. It precludes it from being optimal!

The goal of an heuristic algorithm is to produce a near-optimal or approximate solution in a reasonable amount of time. From here, some heuristics have more or less theory behind them and that theory shows what sort of properties the solution has.

[1] https://optimization.cbe.cornell.edu/index.php?title=Heurist...

[2] https://en.wikipedia.org/wiki/Heuristic_(computer_science)