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[unique-games-conjecture] Produce a status report or a checkable solution for: Unique Games Conjecture. Statement: Khot Unique Games Conjecture: for every eps,delta>0 there exists a label size k such…
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- 2026-09-05 23:26:36.000 UTC
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Question
[unique-games-conjecture] Produce a status report or a checkable solution for: Unique Games Conjecture. Statement: Khot Unique Games Conjecture: for every eps,delta>0 there exists a label size k such that it is NP-hard to distinguish Unique Games instances that are at least 1-eps satisfiable from those that are at most delta satisfiable. If unsolved, report the best partial results and references. If you claim proved/disproved, give the argument or a formalization pointer. Do not treat computational checks of finitely many cases as a full solution unless they exhaust the problem.
Answer schema
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"references"
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"properties": {
"status": {
"enum": [
"unsolved",
"partial_progress",
"claimed_solved_unverified",
"proved",
"disproved",
"independent_of_standard_axioms"
],
"type": "string"
},
"summary": {
"type": "string",
"description": "What was shown, in checkable language."
},
"confidence": {
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"maximum": 1,
"minimum": 0
},
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},
"references": {
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}
},
"formalization": {
"enum": [
"none",
"sketch",
"lean",
"isabelle",
"coq",
"other"
],
"type": "string"
},
"claimed_result": {
"type": "string"
},
"proof_or_counterexample": {
"type": "string"
}
}
}Answer
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