Triple

T5896710
Position Surface form Disambiguated ID Type / Status
Subject Pál Erdős E131117 entity
Predicate knownFor P22 FINISHED
Object Erdős–Turán conjecture
The Erdős–Turán conjecture is an unsolved problem in additive number theory asserting that any subset of the positive integers with divergent sum of reciprocals must contain arbitrarily long arithmetic progressions.
E554303 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: Erdős–Turán conjecture | Statement: [Pál Erdős, knownFor, Erdős–Turán conjecture]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Erdős–Turán conjecture
Context triple: [Pál Erdős, knownFor, Erdős–Turán conjecture]
  • A. Hardy–Littlewood conjectures
    The Hardy–Littlewood conjectures are a collection of influential unproven hypotheses in analytic number theory that generalize the prime number theorem to describe the distribution of prime numbers and prime constellations.
  • B. Bateman–Horn conjecture
    The Bateman–Horn conjecture is a far-reaching unproven statement in number theory that predicts how often sets of polynomial expressions simultaneously take prime values, generalizing several earlier conjectures about the distribution of prime numbers.
  • C. Waring's problem
    Waring's problem is a famous conjecture in number theory that concerns representing natural numbers as sums of fixed powers of integers and determining how many such powers are needed.
  • D. Green–Tao theorem
    The Green–Tao theorem is a landmark result in number theory proving that the sequence of prime numbers contains arbitrarily long arithmetic progressions.
  • E. Deuring–Heilbronn phenomenon
    The Deuring–Heilbronn phenomenon is a result in analytic number theory describing how the presence of an exceptional (Siegel) zero of a Dirichlet L-function forces other zeros away from the real axis, sharpening zero-free regions and affecting the distribution of primes in arithmetic progressions.
  • 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: Erdős–Turán conjecture
Triple: [Pál Erdős, knownFor, Erdős–Turán conjecture]
Generated description
The Erdős–Turán conjecture is an unsolved problem in additive number theory asserting that any subset of the positive integers with divergent sum of reciprocals must contain arbitrarily long arithmetic progressions.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Erdős–Turán conjecture
Target entity description: The Erdős–Turán conjecture is an unsolved problem in additive number theory asserting that any subset of the positive integers with divergent sum of reciprocals must contain arbitrarily long arithmetic progressions.
  • A. Hardy–Littlewood conjectures
    The Hardy–Littlewood conjectures are a collection of influential unproven hypotheses in analytic number theory that generalize the prime number theorem to describe the distribution of prime numbers and prime constellations.
  • B. Bateman–Horn conjecture
    The Bateman–Horn conjecture is a far-reaching unproven statement in number theory that predicts how often sets of polynomial expressions simultaneously take prime values, generalizing several earlier conjectures about the distribution of prime numbers.
  • C. Waring's problem
    Waring's problem is a famous conjecture in number theory that concerns representing natural numbers as sums of fixed powers of integers and determining how many such powers are needed.
  • D. Green–Tao theorem
    The Green–Tao theorem is a landmark result in number theory proving that the sequence of prime numbers contains arbitrarily long arithmetic progressions.
  • E. Deuring–Heilbronn phenomenon
    The Deuring–Heilbronn phenomenon is a result in analytic number theory describing how the presence of an exceptional (Siegel) zero of a Dirichlet L-function forces other zeros away from the real axis, sharpening zero-free regions and affecting the distribution of primes in arithmetic progressions.
  • 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_69c00857439c819095950754176aa58a completed March 22, 2026, 3:18 p.m.
NER Named-entity recognition batch_69c036f4b56c8190aa52c9460eae8fbe completed March 22, 2026, 6:37 p.m.
NED1 Entity disambiguation (via context triple) batch_69c0b159cb908190b78b78d1e854212b completed March 23, 2026, 3:19 a.m.
NEDg Description generation batch_69c0b22d661c8190a055abd3ca6fa92f completed March 23, 2026, 3:23 a.m.
NED2 Entity disambiguation (via description) batch_69c0b608a10881908c9bca7d09a99b05 completed March 23, 2026, 3:39 a.m.
Created at: March 22, 2026, 3:58 p.m.