Triple

T2252105
Position Surface form Disambiguated ID Type / Status
Subject Atle Selberg E49639 entity
Predicate knownFor P22 FINISHED
Object Selberg sieve
The Selberg sieve is a powerful analytic number theory method developed by Atle Selberg for estimating the size of sets of integers filtered by divisibility conditions, particularly in the study of prime numbers.
E246699 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: Selberg sieve | Statement: [Atle Selberg, knownFor, Selberg sieve]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Selberg sieve
Context triple: [Atle Selberg, knownFor, Selberg sieve]
  • A. Hardy–Littlewood circle method
    The Hardy–Littlewood circle method is a powerful analytic number theory technique that uses complex analysis and Fourier series to study additive problems such as Waring’s problem and the Goldbach conjecture.
  • B. Multiplicative Number Theory
    Multiplicative Number Theory is a branch of analytic number theory that studies arithmetic functions and prime number distributions through their multiplicative properties and associated Dirichlet series.
  • C. 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.
  • D. Chebotarev density theorem
    The Chebotarev density theorem is a fundamental result in algebraic number theory that generalizes the prime number theorem to describe how often primes in a number field have a given Frobenius conjugacy class in its Galois group.
  • E. Riemann–Siegel formula
    The Riemann–Siegel formula is an asymptotic expression that efficiently approximates the Riemann zeta function on the critical line, playing a key role in the numerical study of its zeros.
  • 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: Selberg sieve
Triple: [Atle Selberg, knownFor, Selberg sieve]
Generated description
The Selberg sieve is a powerful analytic number theory method developed by Atle Selberg for estimating the size of sets of integers filtered by divisibility conditions, particularly in the study of prime numbers.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Selberg sieve
Target entity description: The Selberg sieve is a powerful analytic number theory method developed by Atle Selberg for estimating the size of sets of integers filtered by divisibility conditions, particularly in the study of prime numbers.
  • A. Hardy–Littlewood circle method
    The Hardy–Littlewood circle method is a powerful analytic number theory technique that uses complex analysis and Fourier series to study additive problems such as Waring’s problem and the Goldbach conjecture.
  • B. Multiplicative Number Theory
    Multiplicative Number Theory is a branch of analytic number theory that studies arithmetic functions and prime number distributions through their multiplicative properties and associated Dirichlet series.
  • C. 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.
  • D. Chebotarev density theorem
    The Chebotarev density theorem is a fundamental result in algebraic number theory that generalizes the prime number theorem to describe how often primes in a number field have a given Frobenius conjugacy class in its Galois group.
  • E. Riemann–Siegel formula
    The Riemann–Siegel formula is an asymptotic expression that efficiently approximates the Riemann zeta function on the critical line, playing a key role in the numerical study of its zeros.
  • 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_69a88aaa9250819095e127d0d77e8a32 completed March 4, 2026, 7:40 p.m.
NER Named-entity recognition batch_69abc11eb2708190bc5a3d152a3bb133 completed March 7, 2026, 6:09 a.m.
NED1 Entity disambiguation (via context triple) batch_69ae6b1bc424819087b2ce9a6256a180 completed March 9, 2026, 6:39 a.m.
NEDg Description generation batch_69ae6be0d108819085cf8c531d08db65 completed March 9, 2026, 6:42 a.m.
NED2 Entity disambiguation (via description) batch_69ae6c0fc220819090b254cc20b1bc26 completed March 9, 2026, 6:43 a.m.
Created at: March 4, 2026, 7:47 p.m.