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In this case, I think it shows uncommon good sense. There have been how many claims that P=NP?

Ironically, the author being this careful makes me think he's more likely to be right.

I'm not a specialist by any means, but he also ends the paper "All the results show that our polynomial time algorithm can get the same answer as the backtracking algorithm does. No exception.", which doesn't seem to imply a concrete proof.

"Beware of bugs in the above code; I have only proved it correct, not tried it." - Donald Knuth

This appears to be a corollary: "Beware of bugs in the above code; I have only tried it, not proved it correct."