Triple

T5642190
Position Surface form Disambiguated ID Type / Status
Subject Inapproximability results for SAT and other problems E124291 entity
Predicate topic P261 FINISHED
Object PCP theorem E74456 NE FINISHED

How this triple was built (2 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: PCP theorem | Statement: [Inapproximability results for SAT and other problems, topic, PCP theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: PCP theorem
Context triple: [Inapproximability results for SAT and other problems, topic, PCP theorem]
  • A. PCP theorem chosen
    The PCP theorem is a fundamental result in computational complexity theory stating that every problem in NP has probabilistically checkable proofs that can be verified by examining only a constant number of bits, with major implications for the hardness of approximation.
  • B. Cook–Levin theorem
    The Cook–Levin theorem is a foundational result in computational complexity theory that established the Boolean satisfiability problem (SAT) as the first NP-complete problem, launching the theory of NP-completeness.
  • C. NP-completeness
    NP-completeness is a central concept in computational complexity theory that classifies decision problems believed to be among the hardest in NP, such that a polynomial-time solution to any one of them would yield polynomial-time solutions to all problems in NP.
  • D. “Inapproximability results for SAT and other problems”
    “Inapproximability results for SAT and other problems” is a seminal theoretical computer science paper by Johan Håstad that establishes tight hardness-of-approximation bounds for satisfiability and related optimization problems using probabilistically checkable proofs.
  • E. 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.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69c00824643c81909ffdb888a2d35189 completed March 22, 2026, 3:17 p.m.
NER Named-entity recognition batch_69c022a6a22881908d16f4df564ed2a2 completed March 22, 2026, 5:11 p.m.
NED1 Entity disambiguation (via context triple) batch_69c04d7c98008190b79528596eca4208 completed March 22, 2026, 8:13 p.m.
Created at: March 22, 2026, 3:41 p.m.