Triple
T4092111
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Hölder inequality |
E87726
|
entity |
| Predicate | usedIn |
P98
|
FINISHED |
| Object | Lebesgue integration |
E59633
|
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 integration | Statement: [Hölder inequality, usedIn, Lebesgue integration]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Lebesgue integration Context triple: [Hölder inequality, usedIn, Lebesgue integration]
-
A.
Lebesgue integration
chosen
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.
-
B.
Lebesgue measure
Lebesgue measure is the standard way of assigning a consistent notion of "length," "area," or "volume" to subsets of Euclidean space, forming the foundation of modern measure theory and integration.
-
C.
Lebesgue spaces
Lebesgue spaces are function spaces, denoted \(L^p\), that consist of measurable functions whose absolute values raised to the \(p\)-th power are integrable, forming a fundamental framework in modern analysis and probability theory.
-
D.
measure theory
Measure theory is a branch of mathematical analysis that rigorously formalizes the concepts of length, area, volume, and integration for very general sets and functions.
-
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_69aed94425148190be337845d56fac22 |
completed | March 9, 2026, 2:29 p.m. |
| NER | Named-entity recognition | batch_69aefcae22a081908af65a960306b78c |
completed | March 9, 2026, 5 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69b56b6cfb288190ac08c3a37327ac9a |
completed | March 14, 2026, 2:06 p.m. |
Created at: March 9, 2026, 3:40 p.m.