Triple
T14704225
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Émile Borel |
E345382
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Borel–Lebesgue theorem
The Borel–Lebesgue theorem is a fundamental result in real analysis and topology that characterizes compact subsets of Euclidean space via the property that every open cover admits a finite subcover.
|
E1116059
|
NE FINISHED |
How this triple was built (4 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–Lebesgue theorem | Statement: [Émile Borel, notableWork, Borel–Lebesgue theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Borel–Lebesgue theorem Context triple: [Émile Borel, notableWork, Borel–Lebesgue theorem]
-
A.
Arzelà–Ascoli theorem
The Arzelà–Ascoli theorem is a fundamental result in analysis that characterizes the relative compactness of families of functions via uniform boundedness and equicontinuity.
-
B.
Bolzano–Weierstrass theorem
The Bolzano–Weierstrass theorem is a fundamental result in real analysis stating that every bounded infinite sequence in ℝⁿ has a convergent subsequence.
-
C.
Banach–Alaoglu theorem
The Banach–Alaoglu theorem is a fundamental result in functional analysis stating that the closed unit ball in the dual of a normed space is compact in the weak-* topology.
-
D.
Banach–Mazur theorem
The Banach–Mazur theorem is a fundamental result in functional analysis that characterizes separable Banach spaces as isometrically isomorphic to closed subspaces of spaces of continuous functions on compact metric spaces.
-
E.
Krein–Milman theorem
The Krein–Milman theorem is a fundamental result in functional analysis and convex geometry stating that a compact convex set in a locally convex topological vector space is the closed convex hull of its extreme points.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Borel–Lebesgue theorem Triple: [Émile Borel, notableWork, Borel–Lebesgue theorem]
Generated description
The Borel–Lebesgue theorem is a fundamental result in real analysis and topology that characterizes compact subsets of Euclidean space via the property that every open cover admits a finite subcover.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Borel–Lebesgue theorem Target entity description: The Borel–Lebesgue theorem is a fundamental result in real analysis and topology that characterizes compact subsets of Euclidean space via the property that every open cover admits a finite subcover.
-
A.
Arzelà–Ascoli theorem
The Arzelà–Ascoli theorem is a fundamental result in analysis that characterizes the relative compactness of families of functions via uniform boundedness and equicontinuity.
-
B.
Bolzano–Weierstrass theorem
The Bolzano–Weierstrass theorem is a fundamental result in real analysis stating that every bounded infinite sequence in ℝⁿ has a convergent subsequence.
-
C.
Banach–Alaoglu theorem
The Banach–Alaoglu theorem is a fundamental result in functional analysis stating that the closed unit ball in the dual of a normed space is compact in the weak-* topology.
-
D.
Banach–Mazur theorem
The Banach–Mazur theorem is a fundamental result in functional analysis that characterizes separable Banach spaces as isometrically isomorphic to closed subspaces of spaces of continuous functions on compact metric spaces.
-
E.
Krein–Milman theorem
The Krein–Milman theorem is a fundamental result in functional analysis and convex geometry stating that a compact convex set in a locally convex topological vector space is the closed convex hull of its extreme points.
- F. None of above. chosen
Provenance (5 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_69d822e4a8c08190a155df736bb7bc13 |
completed | April 9, 2026, 10:06 p.m. |
| NER | Named-entity recognition | batch_69deb6071e5c8190bb5509c859135c2d |
completed | April 14, 2026, 9:47 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69fdf087ce8c819081a7186df67bcf1f |
completed | May 8, 2026, 2:17 p.m. |
| NEDg | Description generation | batch_69fdf2a63cc88190b3670378c54c96b6 |
completed | May 8, 2026, 2:26 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69fdf31fcb4081908a88cf4d4c5ddced |
completed | May 8, 2026, 2:28 p.m. |
Created at: April 10, 2026, 1:28 a.m.