Triple
T16474951
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | measure theory |
E400163
|
entity |
| Predicate | usesConcept |
P531
|
FINISHED |
| Object | Lebesgue measure |
E284674
|
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 measure | Statement: [measure theory, usesConcept, Lebesgue measure]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Lebesgue measure Context triple: [measure theory, usesConcept, Lebesgue measure]
-
A.
Lebesgue measure
chosen
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.
-
B.
Lebesgue measurable set
A Lebesgue measurable set is a subset of Euclidean space for which a consistent, translation-invariant notion of "size" (Lebesgue measure) can be assigned, forming the foundation of modern measure theory and integration.
-
C.
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.
-
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.
Hausdorff measure
Hausdorff measure is a fundamental concept in geometric measure theory that generalizes the notion of length, area, and volume to sets with arbitrary fractal or irregular structure in metric spaces.
- 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_69d883813098819084f5409539723b59 |
completed | April 10, 2026, 4:58 a.m. |
| NER | Named-entity recognition | batch_69e32dd43cf88190881a5cbc80da1490 |
completed | April 18, 2026, 7:08 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a004f5f238881909b5f2fb41da3f932 |
completed | May 10, 2026, 9:26 a.m. |
Created at: April 10, 2026, 5:13 a.m.