Triple
T9070968
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Johannes G. van der Corput |
E217363
|
entity |
| Predicate | notableConcept |
P201
|
FINISHED |
| Object |
van der Corput method for estimating exponential sums
The van der Corput method for estimating exponential sums is a classical analytic number theory technique that provides bounds for oscillatory sums by exploiting differencing and smoothness properties of the phase function.
|
E776136
|
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: van der Corput method for estimating exponential sums | Statement: [Johannes G. van der Corput, notableConcept, van der Corput method for estimating exponential sums]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: van der Corput method for estimating exponential sums Context triple: [Johannes G. van der Corput, notableConcept, van der Corput method for estimating exponential sums]
-
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–Delange method results
Selberg–Delange method results are asymptotic formulas in analytic number theory that precisely describe the average order and distribution of multiplicative arithmetic functions using complex-analytic techniques.
-
C.
Dirichlet hyperbola method
The Dirichlet hyperbola method is a technique in analytic number theory used to estimate sums of arithmetic functions by splitting double sums along a hyperbola to obtain asymptotic formulas.
-
D.
Bombieri–Vinogradov theorem
The Bombieri–Vinogradov theorem is a major result in analytic number theory that gives strong average estimates for the distribution of prime numbers in arithmetic progressions, approaching what is predicted by the Generalized Riemann Hypothesis.
-
E.
Linnik’s theorem on the least prime in an arithmetic progression
Linnik’s theorem on the least prime in an arithmetic progression is a result in analytic number theory that gives an explicit upper bound, depending only on the modulus, for the size of the smallest prime in any given coprime residue class.
- 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: van der Corput method for estimating exponential sums Triple: [Johannes G. van der Corput, notableConcept, van der Corput method for estimating exponential sums]
Generated description
The van der Corput method for estimating exponential sums is a classical analytic number theory technique that provides bounds for oscillatory sums by exploiting differencing and smoothness properties of the phase function.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: van der Corput method for estimating exponential sums Target entity description: The van der Corput method for estimating exponential sums is a classical analytic number theory technique that provides bounds for oscillatory sums by exploiting differencing and smoothness properties of the phase function.
-
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–Delange method results
Selberg–Delange method results are asymptotic formulas in analytic number theory that precisely describe the average order and distribution of multiplicative arithmetic functions using complex-analytic techniques.
-
C.
Dirichlet hyperbola method
The Dirichlet hyperbola method is a technique in analytic number theory used to estimate sums of arithmetic functions by splitting double sums along a hyperbola to obtain asymptotic formulas.
-
D.
Bombieri–Vinogradov theorem
The Bombieri–Vinogradov theorem is a major result in analytic number theory that gives strong average estimates for the distribution of prime numbers in arithmetic progressions, approaching what is predicted by the Generalized Riemann Hypothesis.
-
E.
Linnik’s theorem on the least prime in an arithmetic progression
Linnik’s theorem on the least prime in an arithmetic progression is a result in analytic number theory that gives an explicit upper bound, depending only on the modulus, for the size of the smallest prime in any given coprime residue class.
- 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_69ca83d5a7f48190b16c1e59bd43ede0 |
completed | March 30, 2026, 2:08 p.m. |
| NER | Named-entity recognition | batch_69cc955ec5c0819089bb42448edf391e |
completed | April 1, 2026, 3:47 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69cffde470388190ae88a96654404410 |
completed | April 3, 2026, 5:50 p.m. |
| NEDg | Description generation | batch_69d000d4a4548190939a9a9946be469b |
completed | April 3, 2026, 6:03 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69d001b245f08190a8e5c53c570b20a0 |
completed | April 3, 2026, 6:06 p.m. |
Created at: March 30, 2026, 7:12 p.m.