Proved
Established implication or scoped theorem in cited mathematics ↗
Observed Oct 10, 2026
Theorem · version 2
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.
Assumptions
- Both machine classes receive the same unit-cost oracle-query mechanism.
Scope
A limitation of relativizing proofs for the unrelativized question.
Evidence
Source reports
Connections
In this problem · publication v13 · Selected context
P versus NP →
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.
In this problem · publication v14
P versus NP →
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.
Sources
Baker–Gill–Solovay · Relativizations of the P =? NP question →
- 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.
History
Statement versions
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
Established implication or scoped theorem in cited mathematics ↗
Observed Oct 10, 2026 · Source passage →
Record details
- Claim ID
- claim-pnp-relativization
- Statement version
- 2
- SHA-256
- 4376ba453ceaf6da292b8c2ca4a9fa5e9a8332dd4e56edb417e8a2057d320e78