Triple
T14314116
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Bernstein set |
E354908
|
entity |
| Predicate | relatedConcept |
P37
|
FINISHED |
| Object | Vitali set |
E956272
|
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: Vitali set | Statement: [Bernstein set, relatedConcept, Vitali set]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Vitali set Context triple: [Bernstein set, relatedConcept, Vitali set]
-
A.
Vitali set
chosen
A Vitali set is a classic example in real analysis of a subset of the real numbers that is not Lebesgue measurable, constructed using the axiom of choice.
-
B.
Cantor set
The Cantor set is a classic fractal subset of the real line formed by repeatedly removing the open middle third of intervals, notable for being uncountable, perfect, nowhere dense, and having zero Lebesgue measure.
-
C.
Nikodym set
A Nikodym set is a pathological subset of the plane in geometric measure theory that intersects almost every line in a very small (often measure-zero) way while still having full measure in a region, illustrating extreme irregular behavior of measurable sets.
-
D.
Sierpiński set
The Sierpiński set is a subset of the real numbers with the property that it intersects every uncountable closed subset of the reals in only countably many points, illustrating extreme pathological behavior in set theory and real analysis.
-
E.
Vitali covering lemma
The Vitali covering lemma is a fundamental result in measure theory that provides conditions under which a collection of sets can be reduced to a disjoint subcollection that still covers almost all of the original set, and it underpins many key theorems in real analysis and differentiation.
- 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_69d8278ed42c8190b9f882dcce611347 |
completed | April 9, 2026, 10:26 p.m. |
| NER | Named-entity recognition | batch_69de85b49e5481909b9ffab2d922e284 |
completed | April 14, 2026, 6:21 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69fd4687c6bc819088452892128c420e |
completed | May 8, 2026, 2:12 a.m. |
Created at: April 10, 2026, 1:12 a.m.