Triple

T20563930
Position Surface form Disambiguated ID Type / Status
Subject Borel–Weil theorem E504917 entity
Predicate usesConcept P531 FINISHED
Object Borel subgroup
A Borel subgroup is a maximal connected solvable algebraic subgroup of a linear algebraic group, playing a central role in the structure and representation theory of such groups.
E1438706 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 subgroup | Statement: [Borel–Weil theorem, usesConcept, Borel subgroup]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Borel subgroup
Context triple: [Borel–Weil theorem, usesConcept, Borel subgroup]
  • A. Borel subalgebras
    Borel subalgebras are maximal solvable subalgebras of a Lie algebra that play a central role in the classification and representation theory of Lie algebras and algebraic groups.
  • B. Bruhat decomposition
    Bruhat decomposition is a fundamental result in algebraic group theory that expresses a group as a union of double cosets indexed by elements of its Weyl group, revealing a deep combinatorial structure.
  • C. Lie subgroup
    A Lie subgroup is a subgroup of a Lie group that is itself a Lie group and an embedded submanifold, inheriting compatible smooth and group structures from the ambient Lie group.
  • D. Fitting subgroup
    The Fitting subgroup is a characteristic subgroup of a finite group formed by the product of all its nilpotent normal subgroups, playing a central role in the structure theory of finite groups.
  • E. Weyl group
    A Weyl group is a finite reflection group associated with a root system that encodes the symmetries of Lie algebras and Lie groups in representation theory and geometry.
  • 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 subgroup
Triple: [Borel–Weil theorem, usesConcept, Borel subgroup]
Generated description
A Borel subgroup is a maximal connected solvable algebraic subgroup of a linear algebraic group, playing a central role in the structure and representation theory of such groups.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Borel subgroup
Target entity description: A Borel subgroup is a maximal connected solvable algebraic subgroup of a linear algebraic group, playing a central role in the structure and representation theory of such groups.
  • A. Borel subalgebras
    Borel subalgebras are maximal solvable subalgebras of a Lie algebra that play a central role in the classification and representation theory of Lie algebras and algebraic groups.
  • B. Bruhat decomposition
    Bruhat decomposition is a fundamental result in algebraic group theory that expresses a group as a union of double cosets indexed by elements of its Weyl group, revealing a deep combinatorial structure.
  • C. Lie subgroup
    A Lie subgroup is a subgroup of a Lie group that is itself a Lie group and an embedded submanifold, inheriting compatible smooth and group structures from the ambient Lie group.
  • D. Fitting subgroup
    The Fitting subgroup is a characteristic subgroup of a finite group formed by the product of all its nilpotent normal subgroups, playing a central role in the structure theory of finite groups.
  • E. Weyl group
    A Weyl group is a finite reflection group associated with a root system that encodes the symmetries of Lie algebras and Lie groups in representation theory and geometry.
  • 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_69e0b4b6587c8190aee63dc7cff244ea completed April 16, 2026, 10:06 a.m.
NER Named-entity recognition batch_69e6a7a0a0488190a534050b40ff47da completed April 20, 2026, 10:24 p.m.
NED1 Entity disambiguation (via context triple) batch_6a08acde0880819091934642e4440621 completed May 16, 2026, 5:43 p.m.
NEDg Description generation batch_6a08adf778fc819087fa57048192829e completed May 16, 2026, 5:48 p.m.
NED2 Entity disambiguation (via description) batch_6a08aeaf2be88190bac218c7de1544fc completed May 16, 2026, 5:51 p.m.
Created at: April 16, 2026, 11:39 a.m.