Triple
T9070944
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Johannes G. van der Corput |
E217363
|
entity |
| Predicate | knownFor |
P22
|
FINISHED |
| Object |
van der Corput lemma
The van der Corput lemma is a fundamental result in analytic number theory and harmonic analysis that provides bounds for oscillatory integrals and exponential sums, crucial for estimating error terms in various asymptotic formulas.
|
E776133
|
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 lemma | Statement: [Johannes G. van der Corput, knownFor, van der Corput lemma]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: van der Corput lemma Context triple: [Johannes G. van der Corput, knownFor, van der Corput lemma]
-
A.
Riemann–Lebesgue lemma
The Riemann–Lebesgue lemma is a fundamental result in Fourier analysis stating that the Fourier coefficients (or transform) of an integrable function vanish at infinity.
-
B.
Kronecker’s lemma
Kronecker’s lemma is a result in real analysis and summability theory that links the convergence of series with weighted averages of their partial sums, often used in the study of Fourier series and ergodic theorems.
-
C.
Euler–Maclaurin summation formula
The Euler–Maclaurin summation formula is a fundamental result in analysis that connects sums and integrals, providing powerful asymptotic expansions and error estimates for approximating series by integrals.
-
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.
Lebesgue differentiation theorem
The Lebesgue differentiation theorem is a fundamental result in real analysis stating that, for an integrable function, the averages over shrinking neighborhoods converge almost everywhere to the function’s pointwise value.
- 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 lemma Triple: [Johannes G. van der Corput, knownFor, van der Corput lemma]
Generated description
The van der Corput lemma is a fundamental result in analytic number theory and harmonic analysis that provides bounds for oscillatory integrals and exponential sums, crucial for estimating error terms in various asymptotic formulas.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: van der Corput lemma Target entity description: The van der Corput lemma is a fundamental result in analytic number theory and harmonic analysis that provides bounds for oscillatory integrals and exponential sums, crucial for estimating error terms in various asymptotic formulas.
-
A.
Riemann–Lebesgue lemma
The Riemann–Lebesgue lemma is a fundamental result in Fourier analysis stating that the Fourier coefficients (or transform) of an integrable function vanish at infinity.
-
B.
Kronecker’s lemma
Kronecker’s lemma is a result in real analysis and summability theory that links the convergence of series with weighted averages of their partial sums, often used in the study of Fourier series and ergodic theorems.
-
C.
Euler–Maclaurin summation formula
The Euler–Maclaurin summation formula is a fundamental result in analysis that connects sums and integrals, providing powerful asymptotic expansions and error estimates for approximating series by integrals.
-
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.
Lebesgue differentiation theorem
The Lebesgue differentiation theorem is a fundamental result in real analysis stating that, for an integrable function, the averages over shrinking neighborhoods converge almost everywhere to the function’s pointwise value.
- 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.