No.9525598 ViewReplyOriginalReport
Here's a new attempt after my last one got wrecked by you guys. I'm curious what you think.

Statement

S1. P ? NP.

Proof

P1. Let there be natural non-zero inputs n and k such that the complexity of the input is the sum of the bit lengths of n and k.

P2. Let there be irrational a such that a must be calculated before a. For example, if a is 0.01011110…, 0.010[1]1110… must be calculated before 0.0101[1]110…. Note that not all irrationals require such calculation.

P3. For each natural c such that 0 ? c ? 2 ^ n, let natural chunk[c] be bits a[k × c + 1] to a[k × c + k + 1].

P4. Let the problem be as follows: does d and e exist such that d ? e and chunk[d] = chunk[e]? Note that, as n and k change, the solution to the problem can change between YES and NO, so no general solution exists.

P5. P2 and P3 imply that solving the problem requires ? O(2 ^ n) time. This is because chunk[c] must be calculated before chunk[c + 1] and there are O(2 ^ n) chunks to check for equality.

P6. A solution to the problem can be verified in O(k) time by a comparison between chunk[d] and chunk[e] returning YES.

P7. P5 and P6 imply S1, because the problem requires ? O(2 ^ n) time to find a solution but O(k) time to verify a solution.

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