Proved
Established implication or scoped theorem in cited mathematics ↗
Observed Oct 10, 2026
Theorem · version 1
If P = NP, the polynomial hierarchy collapses to P
Earlier version 1. View current version 2 →
Statement
If P = NP, then PH = P.
Assumptions
- The classical finite-level polynomial hierarchy and deterministic polynomial time.
Scope
An asymptotic complexity-class consequence, not a practical algorithm implementation.
Evidence
Source reports
Connections
In this problem · publication v4 · Selected context
P versus NP →
Conditional implication · Proved
This statement contributes context in its stated scope; it does not settle the canonical P versus NP question.
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 v7
P versus NP →
Conditional implication · Proved
This statement contributes context in its stated scope; it does not settle the canonical P versus NP question.
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
Avi Wigderson · Mathematics and Computation →
- §4.1, polynomial hierarchy; P = NP collapse discussion → · Original passage ↗
Recorded wording
If P = NP, then PH = P.
paraphrase · Only metadata and original OpenMath paraphrases are published; proof PDFs remain at their source.
Avi Wigderson · Published · Publication date 2019
Published author exposition or original paper.
Avi Wigderson · Mathematics and Computation — proof text ↗Manuscript / exposition · external
Revision & attribution
Source revision: author-draft-2019-08-06. Observed Oct 10, 2026.
AI involvement is not reported by this cited source; this is not a claim of its absence.
Avi Wigderson · Mathematics and Computation — proof text: author-draft-2019-08-06. External source text. Its mathematical claims and independent OpenMath review are assessed separately.
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-hierarchy-collapse
- Statement version
- 1
- SHA-256
- 2f515646ba1473044030da34f70e610100520b40c199123f2df375c5062ebd98