P equals NP (Abridged proof)

The original, non-abridged, incarnation of this proof was first published to the Blockchain on 2015-05-30. Solving the Byzantine Generals’ Problem was the first step towards a Node passing the Turing test in a mathematically provable way. The next ? years in computer science will be beautiful thanks to Satoshi.

I'm willing to wager M $BTC that P=NP is proven TRUE within N years, AND that multiple independent proofs already exists currently on mainnet blockchain (https://poex.io/). Will escrow funds. Contact me for more details.


P = NP


P != NP

I am not mad.

P = NP is true.

What follows is a non-constructive proof of such. There, however, does not exist a constructive proof. Therefore an efficient computational method is impossible within the real 4-dimensional universe.

P = NP != MAD is true.
P = NP = MAD is also true.

Therefore MAD != MAD.

The MAD paradox can be observed in nature, i.e. the MAD doctrine is unstable on an infinite timeline.

Therefore P = NP.


While P=NP is provable non-constructively within M-theory, an efficient method will most likely never be found given a finite N dimensions. Due to Gödel's incompleteness theorems, as argued by Stephen Hawking in “Gödel and the end of physics,” it is likely N is infinite.

Solving the MAD paradox would lead to a constructive proof. Stated another way, the MAD paradox is unsolvable within a finite number N dimensions. Being solvable within N finite dimensions leads to the principle of explosion within N dimensions. Therefore, N is most likely unbounded i.e. the multiverse is infinite.

Clay Mathematics Institute


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