Triple
T4552382
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Hardy–Littlewood circle method |
E120394
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
Vinogradov's method
Vinogradov's method is a powerful analytic number theory technique, closely related to the Hardy–Littlewood circle method, used to estimate exponential sums and solve additive problems such as Waring’s problem and the Goldbach conjecture.
|
E120394
|
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: Vinogradov's method | Statement: [Hardy–Littlewood circle method, relatedTo, Vinogradov's method]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Vinogradov's method Context triple: [Hardy–Littlewood circle method, relatedTo, Vinogradov's method]
-
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.
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.
-
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.
Hardy–Ramanujan asymptotic formula
The Hardy–Ramanujan asymptotic formula is a landmark result in number theory that gives an approximate expression for the partition function p(n), describing how the number of integer partitions of n grows rapidly with n.
-
E.
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.
- 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: Vinogradov's method Triple: [Hardy–Littlewood circle method, relatedTo, Vinogradov's method]
Generated description
Vinogradov's method is a powerful analytic number theory technique, closely related to the Hardy–Littlewood circle method, used to estimate exponential sums and solve additive problems such as Waring’s problem and the Goldbach conjecture.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Vinogradov's method Target entity description: Vinogradov's method is a powerful analytic number theory technique, closely related to the Hardy–Littlewood circle method, used to estimate exponential sums and solve additive problems such as Waring’s problem and the Goldbach conjecture.
-
A.
Hardy–Littlewood circle method
chosen
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.
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.
-
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.
Hardy–Ramanujan asymptotic formula
The Hardy–Ramanujan asymptotic formula is a landmark result in number theory that gives an approximate expression for the partition function p(n), describing how the number of integer partitions of n grows rapidly with n.
-
E.
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.
- F. None of above.
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_69bd4636f1648190a701445c2fcd9c17 |
completed | March 20, 2026, 1:05 p.m. |
| NER | Named-entity recognition | batch_69bd57f7b9748190af29d02fc77b02e0 |
completed | March 20, 2026, 2:21 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69bdb95b01b0819094a600752e41aa09 |
completed | March 20, 2026, 9:17 p.m. |
| NEDg | Description generation | batch_69bdbdbf73508190b64a78ff9274ee6d |
completed | March 20, 2026, 9:35 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69bdbe1bcd8c819094adea59c91c6f5b |
completed | March 20, 2026, 9:37 p.m. |
Created at: March 20, 2026, 1:09 p.m.