Triple

T15244895
Position Surface form Disambiguated ID Type / Status
Subject MIP = NEXP E364352 entity
Predicate isCitedAs P771 FINISHED
Object Babai–Fortnow–Lund–Safra–Szegedy theorem
The Babai–Fortnow–Lund–Safra–Szegedy theorem is a landmark result in computational complexity theory that characterizes the power of multi-prover interactive proofs by showing they capture exactly the class of nondeterministic exponential-time problems.
E1145567 NE FINISHED

How this triple was built (4 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Babai–Fortnow–Lund–Safra–Szegedy theorem | Statement: [MIP = NEXP, isCitedAs, Babai–Fortnow–Lund–Safra–Szegedy theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Babai–Fortnow–Lund–Safra–Szegedy theorem
Context triple: [MIP = NEXP, isCitedAs, Babai–Fortnow–Lund–Safra–Szegedy theorem]
  • A. Håstad’s switching lemma
    Håstad’s switching lemma is a fundamental result in computational complexity theory that provides powerful bounds on the simplification of Boolean formulas under random restrictions, with major applications in circuit lower bounds.
  • B. Furst–Saxe–Sipser lower bounds
    Furst–Saxe–Sipser lower bounds are foundational results in circuit complexity theory that established superpolynomial lower bounds for constant-depth Boolean circuits (AC⁰), demonstrating inherent limitations of such circuits for computing certain functions.
  • C. Valiant–Vazirani theorem
    The Valiant–Vazirani theorem is a fundamental result in computational complexity theory showing that solving unique solutions of NP problems is, under randomized reductions, as hard as solving general NP problems, with major implications for the study of randomness and hardness of approximation.
  • D. Interactive Proofs and the Hardness of Approximating Cliques
    "Interactive Proofs and the Hardness of Approximating Cliques" is a seminal theoretical computer science paper that introduced powerful interactive proof techniques to show that finding near-maximum cliques in graphs is computationally intractable to approximate within strong bounds.
  • E. The Knowledge Complexity of Interactive Proof Systems
    "The Knowledge Complexity of Interactive Proof Systems" is a seminal theoretical computer science paper that introduced the notion of zero-knowledge proofs, fundamentally shaping modern cryptography and complexity theory.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Babai–Fortnow–Lund–Safra–Szegedy theorem
Triple: [MIP = NEXP, isCitedAs, Babai–Fortnow–Lund–Safra–Szegedy theorem]
Generated description
The Babai–Fortnow–Lund–Safra–Szegedy theorem is a landmark result in computational complexity theory that characterizes the power of multi-prover interactive proofs by showing they capture exactly the class of nondeterministic exponential-time problems.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Babai–Fortnow–Lund–Safra–Szegedy theorem
Target entity description: The Babai–Fortnow–Lund–Safra–Szegedy theorem is a landmark result in computational complexity theory that characterizes the power of multi-prover interactive proofs by showing they capture exactly the class of nondeterministic exponential-time problems.
  • A. Håstad’s switching lemma
    Håstad’s switching lemma is a fundamental result in computational complexity theory that provides powerful bounds on the simplification of Boolean formulas under random restrictions, with major applications in circuit lower bounds.
  • B. Furst–Saxe–Sipser lower bounds
    Furst–Saxe–Sipser lower bounds are foundational results in circuit complexity theory that established superpolynomial lower bounds for constant-depth Boolean circuits (AC⁰), demonstrating inherent limitations of such circuits for computing certain functions.
  • C. Valiant–Vazirani theorem
    The Valiant–Vazirani theorem is a fundamental result in computational complexity theory showing that solving unique solutions of NP problems is, under randomized reductions, as hard as solving general NP problems, with major implications for the study of randomness and hardness of approximation.
  • D. Interactive Proofs and the Hardness of Approximating Cliques
    "Interactive Proofs and the Hardness of Approximating Cliques" is a seminal theoretical computer science paper that introduced powerful interactive proof techniques to show that finding near-maximum cliques in graphs is computationally intractable to approximate within strong bounds.
  • E. The Knowledge Complexity of Interactive Proof Systems
    "The Knowledge Complexity of Interactive Proof Systems" is a seminal theoretical computer science paper that introduced the notion of zero-knowledge proofs, fundamentally shaping modern cryptography and complexity theory.
  • F. None of above. chosen

Provenance (5 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69d85a0dde7481908fc64d1e82d5d20d completed April 10, 2026, 2:01 a.m.
NER Named-entity recognition batch_69e007f306f08190be448b215d6c9b6c completed April 15, 2026, 9:49 p.m.
NED1 Entity disambiguation (via context triple) batch_69fedd461cf08190a506aac2f0cec83a completed May 9, 2026, 7:07 a.m.
NEDg Description generation batch_69fedf6ee3f081909553078cd3e9d243 completed May 9, 2026, 7:17 a.m.
NED2 Entity disambiguation (via description) batch_69fee0016a088190ad87268e035f677e completed May 9, 2026, 7:19 a.m.
Created at: April 10, 2026, 3:13 a.m.