Triple

T2631192
Position Surface form Disambiguated ID Type / Status
Subject Lebesgue integration E59633 entity
Predicate generalizes P2372 FINISHED
Object Riemann integration E47347 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: Riemann integration | Statement: [Lebesgue integration, generalizes, Riemann integration]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Riemann integration
Context triple: [Lebesgue integration, generalizes, Riemann integration]
  • A. Riemann integral chosen
    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.
  • B. 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.
  • C. Riemann sums
    Riemann sums are a fundamental method in calculus for approximating the area under a curve by summing the areas of a sequence of rectangles, forming the basis of the definition of the definite integral.
  • 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. 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.
  • 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_69ab4ac8596c8190b34997e73d9e991c completed March 6, 2026, 9:44 p.m.
NER Named-entity recognition batch_69abd8c567408190b94ff047efa4bc06 completed March 7, 2026, 7:50 a.m.
NED1 Entity disambiguation (via context triple) batch_69af90a7021081909f81c4ddb48fa00c completed March 10, 2026, 3:31 a.m.
Created at: March 6, 2026, 9:50 p.m.