Triple

T9070946
Position Surface form Disambiguated ID Type / Status
Subject Johannes G. van der Corput E217363 entity
Predicate knownFor P22 FINISHED
Object van der Corput inequality
The van der Corput inequality is a fundamental result in analytic number theory that provides bounds for exponential sums, playing a key role in estimating trigonometric sums and studying uniform distribution.
E776135 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 inequality | Statement: [Johannes G. van der Corput, knownFor, van der Corput inequality]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: van der Corput inequality
Context triple: [Johannes G. van der Corput, knownFor, van der Corput inequality]
  • A. Korn inequality
    Korn inequality is a fundamental result in functional analysis and the mathematical theory of elasticity that provides bounds relating the full gradient of a vector field to its symmetric part, ensuring control of deformations by their strains.
  • B. Bernstein inequalities
    Bernstein inequalities are fundamental results in approximation theory and probability that provide bounds on the derivatives or deviations of functions and random variables under certain smoothness or moment conditions.
  • C. Cauchy–Schwarz inequality
    The Cauchy–Schwarz inequality is a fundamental result in linear algebra and analysis that bounds the inner product of two vectors by the product of their magnitudes, underpinning many concepts in geometry, probability, and functional analysis.
  • D. Turán–Kubilius inequality
    The Turán–Kubilius inequality is a fundamental result in probabilistic number theory that provides bounds on the distribution of additive arithmetic functions.
  • E. Hadamard inequality
    The Hadamard inequality is a fundamental result in linear algebra and analysis that bounds the absolute value of a determinant by the product of the Euclidean norms of its row or column vectors.
  • 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 inequality
Triple: [Johannes G. van der Corput, knownFor, van der Corput inequality]
Generated description
The van der Corput inequality is a fundamental result in analytic number theory that provides bounds for exponential sums, playing a key role in estimating trigonometric sums and studying uniform distribution.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: van der Corput inequality
Target entity description: The van der Corput inequality is a fundamental result in analytic number theory that provides bounds for exponential sums, playing a key role in estimating trigonometric sums and studying uniform distribution.
  • A. Korn inequality
    Korn inequality is a fundamental result in functional analysis and the mathematical theory of elasticity that provides bounds relating the full gradient of a vector field to its symmetric part, ensuring control of deformations by their strains.
  • B. Bernstein inequalities
    Bernstein inequalities are fundamental results in approximation theory and probability that provide bounds on the derivatives or deviations of functions and random variables under certain smoothness or moment conditions.
  • C. Cauchy–Schwarz inequality
    The Cauchy–Schwarz inequality is a fundamental result in linear algebra and analysis that bounds the inner product of two vectors by the product of their magnitudes, underpinning many concepts in geometry, probability, and functional analysis.
  • D. Turán–Kubilius inequality
    The Turán–Kubilius inequality is a fundamental result in probabilistic number theory that provides bounds on the distribution of additive arithmetic functions.
  • E. Hadamard inequality
    The Hadamard inequality is a fundamental result in linear algebra and analysis that bounds the absolute value of a determinant by the product of the Euclidean norms of its row or column vectors.
  • 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.