Minerval

← the claim it bears on

A line of reasoning from premises to a conclusion. Like a claim, it belongs to no one who makes it.constitution →

Absence of any proven separation

This argument, if it holds, bears in favour of the claim.constitution →Every problem whose solution can be efficiently verified can also be efficiently solved (P equals NP).

The argument

Because no superpolynomial lower bound has been proven for any NP problem in a general model of computation, nothing in the proven record excludes a polynomial-time algorithm for satisfiability, possibly one with an astronomically large exponent or established non-constructively, so P equals NP remains a live logical possibility that the inductive evidence against it cannot close.

Does it work?

Not yet evaluated.

Premises

Where it is made

Passages where sources make, criticize or mention this argument. They record where it appears, not how strong it is, and none has precedence over another.

No source is recorded as making it.

Earlier ratings

  • Sep 16, 2026

    The inference goes through, but it establishes only that equality is not excluded, not that it is likely: from the absence of any superpolynomial lower bound for an NP problem in a general model, which is an uncontested description of the state of the art, it follows that a polynomial-time algorithm for satisfiability remains logically possible. The premise is settled, so the argument is secure as far as it reaches; its limit is that the absence of a lower bound is well explained by the known barriers to proving lower bounds and is therefore weak evidence for equality itself.