Triple
T16474968
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | measure theory |
E400163
|
entity |
| Predicate | usesConcept |
P531
|
FINISHED |
| Object | Borel sets |
E681623
|
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: Borel sets | Statement: [measure theory, usesConcept, Borel sets]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Borel sets Context triple: [measure theory, usesConcept, Borel sets]
-
A.
Borel set
chosen
A Borel set is any set that can be formed from open (or equivalently closed) sets of a topological space through countable unions, intersections, and complements, forming the smallest σ-algebra containing all open sets.
-
B.
Borel measure
A Borel measure is a measure defined on the σ-algebra generated by the open sets of a topological space, fundamental in modern measure theory and probability.
-
C.
Baire space
Baire space is a fundamental topological space—typically the set of all infinite sequences of natural numbers with the product topology—that serves as a central object in descriptive set theory and general topology.
-
D.
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.
-
E.
Borel
Borel is a French surname most notably associated with Émile Borel, a pioneering mathematician in measure theory and probability.
- 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.