Relativizing techniques cannot settle P versus NP

Statement

There are recursive oracles A and B with P^A = NP^A and P^B ≠ NP^B.

A limitation of relativizing proofs for the unrelativized question.

Proved

Observed Oct 10, 2026

In this problem · publication v7

Proof barrier · Proved

This statement contributes context in its stated scope; it does not settle the canonical P versus NP question.

Scope: Relativizing techniques cannot settle P versus NP.

This is one indexed assertion in its own scope. No disjoint solved fraction, strongest-known ranking or additional parent resolution is inferred.

Relationship not independently reviewed. This concerns its use in this problem.

Original paper abstract, SIAM J. Comput. 4(4), 431–442, DOI 10.1137/0204037 → · Original passage ↗
Recorded wording
There are recursive oracles A and B with P^A = NP^A and P^B ≠ NP^B.
paraphrase · Only metadata and original OpenMath paraphrases are published; proof PDFs remain at their source.

Theodore Baker · John Gill · Robert Solovay · Published · Publication date Dec 1975

Published author exposition or original paper.

Revision & attribution

Source revision: doi-10.1137/0204037-abstract-observed-2026-10-10. Observed Oct 10, 2026.

AI involvement is not reported by this cited source; this is not a claim of its absence.

Statement versions and problem publication versions are separate. A new publication can update context or sources while retaining the same statement.

Assessment history · 1

Assessments retained in these publication records. Earlier statement versions retain their own source histories.

Proved

Observed Oct 10, 2026 · Source passage →

Record details