Proposed
Provider proposes this result; assessment pending ↗
Observed Oct 10, 2026
Theorem · version 2
Proposed Unique Games gap reductions
Statement
For every fixed ε, δ in (0,1/2), there is a deterministic polynomial-time reduction from binary 3SAT to unique games over a fixed alphabet, with completeness at least 1−ε and soundness at most δ.
Assumptions
- Alphabet depends on ε and δ; translation constraints in the provider’s formalization scope.
Scope
Provider proposal for Unique Games hardness; a hardness reduction does not prove P ≠ NP.
This source presents a theorem with a proposed proof. Its wording does not establish acceptance or independent mathematical review.
Evidence
Source reports
Connections
In this problem · publication v13 · Selected context
P versus NP →
Different statement · related variant · Proposed
This statement contributes context in its stated scope; it does not settle the canonical P versus NP question.
Relationship not independently reviewed. This concerns its use in this problem.
In this problem · publication v14
P versus NP →
Different statement · related variant · Proposed
This statement contributes context in its stated scope; it does not settle the canonical P versus NP question.
Relationship not independently reviewed. This concerns its use in this problem.
Sources
OpenAI · Mathematics release: complexity proposals →
- Family 102; lean/docs/102.md and linked paper/comparator → · Original passage ↗
Recorded wording
For every fixed ε, δ in (0,1/2), there is a deterministic polynomial-time reduction from binary 3SAT to unique games over a fixed alphabet, with completeness at least 1−ε and soundness at most δ.
paraphrase · Only metadata and original OpenMath paraphrases are published; proof PDFs remain at their source.
OpenAI internal model; author attribution per manuscript · Project documentation · Publication date Oct 6, 2026
Source-reported preprint/project; independent mathematical assessment pending.
Unique Games gap reductions — formalization scope ↗Source-reported evidence
Revision & attribution
Source revision: fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. Observed Oct 10, 2026.
OpenAI reports internal-model production and accompanying formalizations at mixed stages of assessment. These Claims remain proposed in this curation; external formal evidence does not become an OpenMath check.
Unique Games gap reductions — formalization scope: fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. Pinned provider scope document and comparator links. OpenMath has not executed the code or independently reviewed the mathematical correspondence.
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.
Proposed
Provider proposes this result; assessment pending ↗
Observed Oct 10, 2026 · Source passage →
Record details
- Claim ID
- claim-pnp-ugc-proposal
- Statement version
- 2
- SHA-256
- 8aa5a4829cbdb23aa71d9f539b4a3e337ef39a05b7cb6a0df2a53c02178938a3