Triple

T2364437
Position Surface form Disambiguated ID Type / Status
Subject Riemann integral E47347 entity
Predicate contrastedWith P278 FINISHED
Object Henstock–Kurzweil integral
The Henstock–Kurzweil integral is a highly general integration theory that extends and refines the Riemann integral, capable of integrating a broader class of functions while retaining many of the intuitive properties of Riemann integration.
E259763 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: Henstock–Kurzweil integral | Statement: [Riemann integral, contrastedWith, Henstock–Kurzweil integral]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Henstock–Kurzweil integral
Context triple: [Riemann integral, contrastedWith, Henstock–Kurzweil integral]
  • A. Riemann–Liouville integral
    The Riemann–Liouville integral is a fundamental operator in fractional calculus that generalizes the concept of an n-fold repeated integral to non-integer (fractional) orders.
  • B. Riemann integral
    The Riemann integral is a fundamental concept in calculus that defines the integral of a function as the limit of sums of function values over increasingly fine partitions of an interval.
  • C. Lebesgue integration
    Lebesgue integration is a foundational measure-theoretic framework for defining and analyzing integrals, particularly suited to handling limits, convergence, and more general functions than those allowed by Riemann integration.
  • D. Radon–Nikodym derivative
    The Radon–Nikodym derivative is a function that represents how one measure changes with respect to another absolutely continuous measure, playing a central role in modern probability theory and measure theory.
  • E. Hardy–Littlewood maximal function
    The Hardy–Littlewood maximal function is a fundamental operator in real analysis and harmonic analysis that controls the local averages of a function and plays a key role in differentiation theorems and singular integral theory.
  • 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: Henstock–Kurzweil integral
Triple: [Riemann integral, contrastedWith, Henstock–Kurzweil integral]
Generated description
The Henstock–Kurzweil integral is a highly general integration theory that extends and refines the Riemann integral, capable of integrating a broader class of functions while retaining many of the intuitive properties of Riemann integration.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Henstock–Kurzweil integral
Target entity description: The Henstock–Kurzweil integral is a highly general integration theory that extends and refines the Riemann integral, capable of integrating a broader class of functions while retaining many of the intuitive properties of Riemann integration.
  • A. Riemann–Liouville integral
    The Riemann–Liouville integral is a fundamental operator in fractional calculus that generalizes the concept of an n-fold repeated integral to non-integer (fractional) orders.
  • B. Riemann integral
    The Riemann integral is a fundamental concept in calculus that defines the integral of a function as the limit of sums of function values over increasingly fine partitions of an interval.
  • C. Lebesgue integration
    Lebesgue integration is a foundational measure-theoretic framework for defining and analyzing integrals, particularly suited to handling limits, convergence, and more general functions than those allowed by Riemann integration.
  • D. Radon–Nikodym derivative
    The Radon–Nikodym derivative is a function that represents how one measure changes with respect to another absolutely continuous measure, playing a central role in modern probability theory and measure theory.
  • E. Hardy–Littlewood maximal function
    The Hardy–Littlewood maximal function is a fundamental operator in real analysis and harmonic analysis that controls the local averages of a function and plays a key role in differentiation theorems and singular integral theory.
  • 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_69a88a1a4a6081908645b0f2914521ab completed March 4, 2026, 7:38 p.m.
NER Named-entity recognition batch_69abc7486cb48190acef1891cc87bdb1 completed March 7, 2026, 6:35 a.m.
NED1 Entity disambiguation (via context triple) batch_69aea896e0388190aabff2d70787dc43 completed March 9, 2026, 11:01 a.m.
NEDg Description generation batch_69aea91ce164819091aa24b287f9fb8e completed March 9, 2026, 11:03 a.m.
NED2 Entity disambiguation (via description) batch_69aea999b864819084134c670e7c5d9c completed March 9, 2026, 11:06 a.m.
Created at: March 4, 2026, 7:55 p.m.