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P ≠ NP under Closure of the Saturated SAT Layer

A conditional separation of P and NP that hangs on one hidden thing.

In plain words

Take all fast SAT computations together with their audit data as one layer. Look at it through a fast instrument that decides what counts as a current observation.

Two translation theorems turn the statement SAT is in P into a statement about that layer: the thing that produces witnesses would have to be a lawful current observable. The Hiddenness paper argues it is not.

Under that single hypothesis the chain closes: SAT is not in P, so P is not NP. Outside the framework the result is the conditional theorem, stated exactly.

What it shows

  • Two translations from standard SAT semantics into the framework.
  • A four step contradiction chain under the hiddenness hypothesis.
  • The hypothesis localized to one residual about lexicographic branching.

What it does not claim

It is conditional. The hiddenness hypothesis is not proved here.

Cite

Tsiokos, I. (2026). P ≠ NP under Closure of the Saturated SAT Layer. Zenodo. https://doi.org/10.5281/zenodo.20713602