{
  "id": "exponential-time-hypothesis",
  "org": "OpenAI",
  "topic": "Complexity theory",
  "published": "2026-10-26",
  "status": "independent-review-pending",
  "method": "AI-produced disproof; Lean formalization reported",
  "math": "ETH: 3-SAT ∉ 2^o(n) claimed false",
  "source": "https://openai.com/index/building-scientific-understanding-with-academic-communities/",
  "source_kind": "provider_announcement",
  "checked": "2026-10-29",
  "translations": {
    "en": {
      "title": "A challenge to the Exponential Time Hypothesis",
      "simple": "Some puzzles seem to get overwhelmingly harder as they grow. A new AI-generated argument claims that a famous prediction about how quickly this happens is wrong.",
      "research": "The Exponential Time Hypothesis (ETH) asserts that 3-SAT admits no subexponential-time algorithm in the number of variables. OpenAI announced an AI-generated refutation and a Lean formalization; an external group is studying the implications.",
      "academic": "ETH is a fine-grained complexity assumption, usually expressed as the absence of an algorithm with running time 2^o(n) for 3-SAT on n variables. A verified refutation would unsettle conditional lower bounds across algorithms and parameterized complexity. It would NOT, on its own, establish P=NP or that practical SAT instances are easy.",
      "impact": "Could require re-examining many conditional hardness results, but no practical speedup or cryptographic break is established by this announcement.",
      "caution": "High-impact provider claim. Raw proof material is public; independent technical analysis remains essential."
    },
    "nl": {
      "title": "Een aanval op de exponentiële-tijdhypothese",
      "simple": "Sommige puzzels worden razendsnel moeilijker als ze groter worden. Een nieuw AI-bewijs stelt dat een bekende aanname daarover onjuist is.",
      "research": "ETH stelt dat 3-SAT geen subexponentieel algoritme heeft; OpenAI publiceerde een tegenbewijs en Lean-formalisatie voor onderzoek.",
      "academic": "Formeel gaat het om een looptijd van 2^o(n) voor 3-SAT met n variabelen. Als het klopt, veranderen conditionele complexiteitsgrenzen. Het bewijst NIET dat P=NP.",
      "impact": "Mogelijke herziening van ondergrenzen in de algoritmiek.",
      "caution": "Onafhankelijke inhoudelijke beoordeling is nog nodig."
    },
    "de": {
      "title": "Ein Angriff auf die Exponentialzeithypothese",
      "simple": "Viele Rätsel scheinen mit ihrer Größe explosionsartig schwieriger zu werden. Ein KI-Beweis stellt diese Annahme infrage.",
      "research": "Die ETH schließt subexponentielle Algorithmen für 3-SAT aus; OpenAI meldet eine Widerlegung mit Lean-Formalisation.",
      "academic": "Die konkrete Behauptung betrifft Laufzeiten der Form 2^o(n) für 3-SAT. Eine Widerlegung würde bedingte untere Schranken berühren, aber weder P=NP noch praktische Effizienz beweisen.",
      "impact": "Mögliche Neubewertung theoretischer Komplexitätsgrenzen.",
      "caution": "Externe fachliche Prüfung bleibt erforderlich."
    },
    "fr": {
      "title": "Une remise en cause de l'hypothèse du temps exponentiel",
      "simple": "Certaines énigmes deviennent très vite plus difficiles à mesure qu'elles grandissent. Une preuve produite par IA conteste cette idée.",
      "research": "L'ETH exclut les algorithmes sous-exponentiels pour 3-SAT ; OpenAI annonce une réfutation formalisée en Lean.",
      "academic": "Il s'agit précisément de temps d'exécution en 2^o(n) pour 3-SAT. Une réfutation bouleverserait des bornes conditionnelles, mais ne démontrerait pas P=NP.",
      "impact": "Possibilité de revoir des résultats de complexité théorique.",
      "caution": "Une analyse indépendante reste nécessaire."
    },
    "es": {
      "title": "Una objeción a la hipótesis del tiempo exponencial",
      "simple": "Algunos acertijos se vuelven muchísimo más difíciles al crecer. Un argumento de IA cuestiona esta predicción.",
      "research": "La ETH descarta algoritmos subexponenciales para 3-SAT; OpenAI comunica una refutación con formalización en Lean.",
      "academic": "La afirmación se refiere a tiempos 2^o(n) para 3-SAT. Si se confirma, afectaría a límites inferiores condicionales, pero no probaría P=NP.",
      "impact": "Podría cambiar supuestos clave en teoría de algoritmos.",
      "caution": "Se requiere revisión técnica independiente."
    },
    "it": {
      "title": "Una sfida all'ipotesi del tempo esponenziale",
      "simple": "Alcuni problemi diventano enormemente più difficili quando crescono. Un argomento prodotto dall'IA contesta questa previsione.",
      "research": "L'ETH esclude algoritmi subesponenziali per 3-SAT; OpenAI annuncia una confutazione formalizzata in Lean.",
      "academic": "La tesi riguarda tempi 2^o(n) per 3-SAT. Una confutazione cambierebbe numerosi limiti inferiori condizionati, ma non dimostrerebbe P=NP.",
      "impact": "Potenziale revisione dei risultati di complessità.",
      "caution": "Serve una verifica indipendente approfondita."
    }
  },
  "translation_method": "AI-assisted explanatory translations; not native mathematical peer review",
  "url": "https://appliedfrontier.nl/en/discoveries/exponential-time-hypothesis/",
  "as_of": "2026-10-29"
}