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.