Triple

T10991500
Position Surface form Disambiguated ID Type / Status
Subject Riemann–Stieltjes integral E259762 entity
Predicate relatedConcept P37 FINISHED
Object Young integral
The Young integral is a generalization of the Riemann–Stieltjes integral that allows integration with respect to functions of limited regularity, such as those with Hölder continuity.
E259762 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: Young integral | Statement: [Riemann–Stieltjes integral, relatedConcept, Young integral]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Young integral
Context triple: [Riemann–Stieltjes integral, relatedConcept, Young integral]
  • A. Itô integral
    The Itô integral is a fundamental stochastic integral used in probability theory and mathematical finance to rigorously define integration with respect to Brownian motion and more general semimartingales.
  • B. Stratonovich integral
    The Stratonovich integral is a formulation of stochastic integration that preserves the classical chain rule of calculus and is widely used in physics and engineering for modeling systems with noise.
  • C. Riemann–Stieltjes integral
    The Riemann–Stieltjes integral is a generalization of the Riemann integral in which integration is taken with respect to a function of bounded variation rather than just the identity function, allowing more flexible treatment of sums and distributions.
  • D. 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.
  • E. 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.
  • 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: Young integral
Triple: [Riemann–Stieltjes integral, relatedConcept, Young integral]
Generated description
The Young integral is a generalization of the Riemann–Stieltjes integral that allows integration with respect to functions of limited regularity, such as those with Hölder continuity.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Young integral
Target entity description: The Young integral is a generalization of the Riemann–Stieltjes integral that allows integration with respect to functions of limited regularity, such as those with Hölder continuity.
  • A. Itô integral
    The Itô integral is a fundamental stochastic integral used in probability theory and mathematical finance to rigorously define integration with respect to Brownian motion and more general semimartingales.
  • B. Stratonovich integral
    The Stratonovich integral is a formulation of stochastic integration that preserves the classical chain rule of calculus and is widely used in physics and engineering for modeling systems with noise.
  • C. Riemann–Stieltjes integral chosen
    The Riemann–Stieltjes integral is a generalization of the Riemann integral in which integration is taken with respect to a function of bounded variation rather than just the identity function, allowing more flexible treatment of sums and distributions.
  • D. 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.
  • E. 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.
  • F. None of above.

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_69d6aa8a6a548190a750f944ccdc8064 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d795d1e918819090c71f5a077fa15a completed April 9, 2026, 12:04 p.m.
NED1 Entity disambiguation (via context triple) batch_69e34504ebec8190a78e4795765b0c24 completed April 18, 2026, 8:47 a.m.
NEDg Description generation batch_69e3556fd3548190a33f04604be947cf completed April 18, 2026, 9:57 a.m.
NED2 Entity disambiguation (via description) batch_69e3593b0f8481909ed7a90f8bb9839d completed April 18, 2026, 10:13 a.m.
Created at: April 8, 2026, 9:24 p.m.