Triple

T10991498
Position Surface form Disambiguated ID Type / Status
Subject Riemann–Stieltjes integral E259762 entity
Predicate relatedConcept P37 FINISHED
Object Lebesgue–Stieltjes integral E898477 NE FINISHED

How this triple was built (2 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: Lebesgue–Stieltjes integral | Statement: [Riemann–Stieltjes integral, relatedConcept, Lebesgue–Stieltjes integral]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Lebesgue–Stieltjes integral
Context triple: [Riemann–Stieltjes integral, relatedConcept, Lebesgue–Stieltjes integral]
  • A. 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.
  • B. Stieltjes measure chosen
    A Stieltjes measure is a measure on the real line constructed from a nondecreasing, right-continuous function, providing the measure-theoretic foundation for the Riemann–Stieltjes and Lebesgue–Stieltjes integrals.
  • C. 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.
  • D. 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.
  • E. Bochner integral
    The Bochner integral is a generalization of the Lebesgue integral to functions taking values in Banach spaces, widely used in functional analysis and probability theory.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69e374639f1481908ea372b81a834f6f completed April 18, 2026, 12:09 p.m.
Created at: April 8, 2026, 9:24 p.m.