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I hope it is 2. That would be surprising.

I’m not sure it would be surprising if it’s 2. Many people believe it is 2, or at least can be less than 2+epsilon for any epsilon > 0.

I would however be impressed if it were constructively proven to be 2

And the constant wasn't so huge as to be impractical.

They show that it has to be strictly greater than 2.

They showed the current methods couldn't bring it to 2. There could be another approach which gets it lower.