Triple

T3522522
Position Surface form Disambiguated ID Type / Status
Subject PCP theorem E74456 entity
Predicate fullName P16 FINISHED
Object Probabilistically Checkable Proofs 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: Probabilistically Checkable Proofs theorem | Statement: [PCP theorem, fullName, Probabilistically Checkable Proofs theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Probabilistically Checkable Proofs theorem
Context triple: [PCP theorem, fullName, Probabilistically Checkable Proofs 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. 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.
  • C. 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.
  • D. 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.
  • E. 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.
  • 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_69ad85d0c5488190a3d8e02ebd01a1aa completed March 8, 2026, 2:21 p.m.
NER Named-entity recognition batch_69adbc4dd6d48190a5a3f4b86c82b86c completed March 8, 2026, 6:13 p.m.
NED1 Entity disambiguation (via context triple) batch_69b37e87c7948190901d98f34e3987eb completed March 13, 2026, 3:03 a.m.
Created at: March 8, 2026, 3:19 p.m.