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.