Triple
T738058
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | von Neumann universe |
E14977
|
entity |
| Predicate | relatedConcept |
P37
|
FINISHED |
| Object |
Grothendieck universe
A Grothendieck universe is a set-theoretic construct large enough to contain all the usual objects and operations of mathematics, used to rigorously handle "large" categories while avoiding paradoxes.
|
E98601
|
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: Grothendieck universe | Statement: [von Neumann universe, relatedConcept, Grothendieck universe]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Grothendieck universe Context triple: [von Neumann universe, relatedConcept, Grothendieck universe]
-
A.
von Neumann universe
The von Neumann universe is a cumulative, well-founded hierarchy of sets used as a standard model of the set-theoretic universe in axiomatic set theory.
-
B.
von Neumann–Bernays–Gödel set theory
Von Neumann–Bernays–Gödel set theory is an axiomatic set theory extending Zermelo–Fraenkel set theory by formally distinguishing between sets and classes, widely used in foundational studies of mathematics.
-
C.
Zermelo–Fraenkel set theory
Zermelo–Fraenkel set theory is the standard axiomatic framework for modern set theory, designed to avoid paradoxes and provide a rigorous foundation for much of mathematics.
-
D.
Morse–Kelley set theory by class–set distinction
Morse–Kelley set theory by class–set distinction is a foundational system that avoids certain set-theoretic paradoxes by rigorously distinguishing between sets and proper classes within a powerful axiomatic framework.
-
E.
Zermelo set theory
Zermelo set theory is an early axiomatic system for set theory, introduced by Ernst Zermelo to rigorously formalize the concept of sets and avoid known paradoxes.
- 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: Grothendieck universe Triple: [von Neumann universe, relatedConcept, Grothendieck universe]
Generated description
A Grothendieck universe is a set-theoretic construct large enough to contain all the usual objects and operations of mathematics, used to rigorously handle "large" categories while avoiding paradoxes.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Grothendieck universe Target entity description: A Grothendieck universe is a set-theoretic construct large enough to contain all the usual objects and operations of mathematics, used to rigorously handle "large" categories while avoiding paradoxes.
-
A.
von Neumann universe
The von Neumann universe is a cumulative, well-founded hierarchy of sets used as a standard model of the set-theoretic universe in axiomatic set theory.
-
B.
von Neumann–Bernays–Gödel set theory
Von Neumann–Bernays–Gödel set theory is an axiomatic set theory extending Zermelo–Fraenkel set theory by formally distinguishing between sets and classes, widely used in foundational studies of mathematics.
-
C.
Zermelo–Fraenkel set theory
Zermelo–Fraenkel set theory is the standard axiomatic framework for modern set theory, designed to avoid paradoxes and provide a rigorous foundation for much of mathematics.
-
D.
Morse–Kelley set theory by class–set distinction
Morse–Kelley set theory by class–set distinction is a foundational system that avoids certain set-theoretic paradoxes by rigorously distinguishing between sets and proper classes within a powerful axiomatic framework.
-
E.
Zermelo set theory
Zermelo set theory is an early axiomatic system for set theory, introduced by Ernst Zermelo to rigorously formalize the concept of sets and avoid known paradoxes.
- 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_69a4934d9930819099eed80096b0597d |
completed | March 1, 2026, 7:28 p.m. |
| NER | Named-entity recognition | batch_69a4a5f1c9888190b2817138c6893cfe |
completed | March 1, 2026, 8:47 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69a76d742ef08190bb9405a1cde84eb1 |
completed | March 3, 2026, 11:23 p.m. |
| NEDg | Description generation | batch_69a78f03a1a081909087f72e8342cba1 |
completed | March 4, 2026, 1:46 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69a78f632cd88190856e24d5f33d914c |
completed | March 4, 2026, 1:48 a.m. |
Created at: March 1, 2026, 7:37 p.m.