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.