AIProofWatch
← Explore interestsIndividual problem

The Unique Games Conjecture

The conjecture requires simultaneously near-perfect completeness and arbitrarily small soundness with an alphabet fixed for those errors.

Progress records 1

Understand the problem ↓

1 record · How we rate progress

Understanding the problem

Read the background

The conjecture requires simultaneously near-perfect completeness and arbitrarily small soundness with an alphabet fixed for those errors. A weaker gap theorem does not establish that quantifier pattern.

The alphabet and reduction constants depend on the fixed errors. NP-hardness does not prove P≠NP, and companion approximation consequences are not separate discoveries in this record.

Why it matters

If correct, establishes the full stated Unique Games hardness target underlying many approximation thresholds.

What counts as progress

A sourced resolution or substantial advance on the precise target, with hypotheses, prior context, and verification evidence stated separately.

What to watch for

  • Assess the precise statement and assumptions before comparing results.
  • The alphabet and reduction constants depend on the fixed errors. NP-hardness does not prove P≠NP, and companion approximation consequences are not separate discoveries in this record.
  • Track independent assessments, dependencies, corrections, and withdrawals separately from importance.

Background review: 2026-10-11. Selected sources:

Website timeline

Publication dates and editorial changes.