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.