OK, I just upvoted purely for the reason of keeping it on the front page a little longer so someone more qualified has a chance to glance at this. Without any evidence and no qualification to judge myself, it seems highly unlikely.
The prior probability of it being correct is so low that we should be flagging it, not upvoting it. There's many, many false "proofs" of P=?NP out there.
If I write a paper formatted in LaTeX saying that I cloned a T-Rex in my backyard, should it be upvoted so that an expert in cloning can take a look at it?
If this were the situation I would agree with you, however an independent programmer has implemented his algorithm and posted it on github with instructions (https://github.com/anjlab/sat3) on how to run it on k-SAT instances. Because of this, I believe it increases the claim's reputability; it is easier to confirm or reject his algorithm and claim.
First, it doesn't appear to be independent as the author on the blog says he/we prepared it.
Second, doesn't mean much. It's almost as likely there's a bug in the code as in a proof. The only advantage is you can run some tets on it, but if it's wrong the tests may actually give you a false sense of security.
Lastly, if you prove P=NP you submit to FOCS or STOC. Let them review it.
Perhaps you're right regarding the first point, I'm just going off what he states in the OP: "Also two independent versions of the algorithm in programming languages have been implemented."
My point is that a constructivist proof that P=NP along with working code (again I'm assuming it's implemented correctly, as it appears vetted by Romanov) is easier to prove incorrect as it's easier for someone who perhaps doesn't have the theoretical background to find pathological examples where it breaks down (and a much wider audience fits in this category, including most of HN).
I agree with your point about the false sense of security however--an inability to find such pathological cases is not sufficient to prove P=NP. In order to truly verify the claim a rigorous analysis of the proof will be necessary--but in this situation it's much easier to show what this guy is saying is false than in the Deolalikar case.
