Triple

T6456479
Position Surface form Disambiguated ID Type / Status
Subject Lie group E142004 entity
Predicate hasExample P1259 FINISHED
Object 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.
E595247 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: special linear group SL(n,C) | Statement: [Lie group, hasExample, special linear group SL(n,C)]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: special linear group SL(n,C)
Context triple: [Lie group, hasExample, special linear group SL(n,C)]
  • A. 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.
  • B. SL(2,C)
    SL(2,C) is the complex special linear group of 2×2 matrices with determinant 1, which serves as the double cover and spinor representation group of the proper orthochronous Lorentz group in four-dimensional spacetime.
  • C. 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.
  • D. special unitary group SU(n)
    The special unitary group SU(n) is a fundamental compact Lie group consisting of n×n unitary matrices with determinant 1, central in mathematics and physics, especially in quantum theory and gauge symmetries.
  • E. special orthogonal group SO(n)
    The special orthogonal group SO(n) is the group of all n×n real rotation matrices with determinant 1, representing orientation-preserving isometries of n-dimensional Euclidean space that fix the origin.
  • 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: special linear group SL(n,C)
Triple: [Lie group, hasExample, special linear group SL(n,C)]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: special linear group SL(n,C)
Target entity description: 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.
  • A. 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.
  • B. SL(2,C)
    SL(2,C) is the complex special linear group of 2×2 matrices with determinant 1, which serves as the double cover and spinor representation group of the proper orthochronous Lorentz group in four-dimensional spacetime.
  • C. 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.
  • D. special unitary group SU(n)
    The special unitary group SU(n) is a fundamental compact Lie group consisting of n×n unitary matrices with determinant 1, central in mathematics and physics, especially in quantum theory and gauge symmetries.
  • E. special orthogonal group SO(n)
    The special orthogonal group SO(n) is the group of all n×n real rotation matrices with determinant 1, representing orientation-preserving isometries of n-dimensional Euclidean space that fix the origin.
  • 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_69c008d2f91c8190a8178767a35e08fc completed March 22, 2026, 3:20 p.m.
NER Named-entity recognition batch_69c069d639ec8190bb0a806da4118440 completed March 22, 2026, 10:14 p.m.
NED1 Entity disambiguation (via context triple) batch_69c65394d8b481909868faf79f3d2383 completed March 27, 2026, 9:53 a.m.
NEDg Description generation batch_69c653ffc704819095bb51119917c844 completed March 27, 2026, 9:55 a.m.
NED2 Entity disambiguation (via description) batch_69c654569b3c81909a747bdfe9fd4d17 completed March 27, 2026, 9:56 a.m.
Created at: March 22, 2026, 4:48 p.m.