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.