Triple

T23372443
Position Surface form Disambiguated ID Type / Status
Subject GL(n,ℝ) E593509 entity
Predicate hasLieAlgebra P28830 FINISHED
Object gl(n,ℝ)
gl(n,ℝ) is the Lie algebra of all n×n real matrices under the commutator bracket, forming a fundamental example in linear algebra and Lie theory.
 E1583642 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: gl(n,ℝ) | Statement: [GL(n,ℝ), hasLieAlgebra, gl(n,ℝ)]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: gl(n,ℝ)
Context triple: [GL(n,ℝ), hasLieAlgebra, gl(n,ℝ)]
  • A. general linear group GL(n,R)
    The general linear group GL(n,ℝ) is the Lie group consisting of all invertible n×n real matrices under matrix multiplication, fundamental in linear algebra and differential geometry.
  • B. general linear group GL(n,C)
    The general linear group GL(n,ℂ) is the Lie group consisting of all invertible n×n complex matrices under matrix multiplication, fundamental in linear algebra and representation theory.
  • C. special linear group SL(n,R)
    The special linear group SL(n,ℝ) is the Lie group of all n×n real matrices with determinant 1, fundamental in linear algebra and differential geometry as the group of volume-preserving linear transformations.
  • D. special linear group SL(n,C)
    The special linear group SL(n,ℂ) is the Lie group of n×n complex matrices with determinant 1, fundamental in representation theory, geometry, and many areas of modern mathematics and physics.
  • E. GL_n(Q_l)
    GL_n(Q_l) is the group of invertible n×n matrices over the field of ℓ-adic numbers, fundamental in the study of ℓ-adic Galois representations and arithmetic 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: gl(n,ℝ)
Triple: [GL(n,ℝ), hasLieAlgebra, gl(n,ℝ)]
Generated description
gl(n,ℝ) is the Lie algebra of all n×n real matrices under the commutator bracket, forming a fundamental example in linear algebra and Lie theory.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: gl(n,ℝ)
Target entity description: gl(n,ℝ) is the Lie algebra of all n×n real matrices under the commutator bracket, forming a fundamental example in linear algebra and Lie theory.
  • A. general linear group GL(n,R)
    The general linear group GL(n,ℝ) is the Lie group consisting of all invertible n×n real matrices under matrix multiplication, fundamental in linear algebra and differential geometry.
  • B. general linear group GL(n,C)
    The general linear group GL(n,ℂ) is the Lie group consisting of all invertible n×n complex matrices under matrix multiplication, fundamental in linear algebra and representation theory.
  • C. special linear group SL(n,R)
    The special linear group SL(n,ℝ) is the Lie group of all n×n real matrices with determinant 1, fundamental in linear algebra and differential geometry as the group of volume-preserving linear transformations.
  • D. special linear group SL(n,C)
    The special linear group SL(n,ℂ) is the Lie group of n×n complex matrices with determinant 1, fundamental in representation theory, geometry, and many areas of modern mathematics and physics.
  • E. GL_n(Q_l)
    GL_n(Q_l) is the group of invertible n×n matrices over the field of ℓ-adic numbers, fundamental in the study of ℓ-adic Galois representations and arithmetic 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_69e25d2593c88190bcdf4a716a94ccb2 completed April 17, 2026, 4:17 p.m.
NER Named-entity recognition batch_69f1a3af45ec8190a32aa4e5f04f6756 completed April 29, 2026, 6:22 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0c5ddde5608190acd427c4b8740733 completed May 19, 2026, 12:55 p.m.
NEDg Description generation batch_6a0c5f3e57308190865e48b43cc83d10 completed May 19, 2026, 1:01 p.m.
NED2 Entity disambiguation (via description) batch_6a0c5ffbea40819088a5a01a3763c718 completed May 19, 2026, 1:05 p.m.
Created at: April 17, 2026, 5:32 p.m.