Triple

T6456478
Position Surface form Disambiguated ID Type / Status
Subject Lie group E142004 entity
Predicate hasExample P1259 FINISHED
Object 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.
E593510 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,R) | Statement: [Lie group, hasExample, special linear group SL(n,R)]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: special linear group SL(n,R)
Context triple: [Lie group, hasExample, special linear group SL(n,R)]
  • A. 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.
  • B. 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.
  • C. affine group of R^n
    The affine group of ℝⁿ is the group of all invertible affine transformations of n-dimensional real space, combining linear transformations with translations.
  • D. Lie group
    A Lie group is a mathematical structure that is both a smooth manifold and a group, where the group operations are differentiable and used to study continuous symmetries.
  • E. PSL(2,7)
    PSL(2,7) is a finite simple group of order 168, notable as the full automorphism group of the Klein quartic and as a key example in the theory of projective linear groups over finite fields.
  • 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,R)
Triple: [Lie group, hasExample, special linear group SL(n,R)]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: special linear group SL(n,R)
Target entity description: 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.
  • A. 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.
  • B. 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.
  • C. affine group of R^n
    The affine group of ℝⁿ is the group of all invertible affine transformations of n-dimensional real space, combining linear transformations with translations.
  • D. Lie group
    A Lie group is a mathematical structure that is both a smooth manifold and a group, where the group operations are differentiable and used to study continuous symmetries.
  • E. PSL(2,7)
    PSL(2,7) is a finite simple group of order 168, notable as the full automorphism group of the Klein quartic and as a key example in the theory of projective linear groups over finite fields.
  • 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_69c64bdc4e808190a7c24b963ab0aa30 completed March 27, 2026, 9:20 a.m.
NEDg Description generation batch_69c64ce18f6c8190910dcc2fc553328e completed March 27, 2026, 9:24 a.m.
NED2 Entity disambiguation (via description) batch_69c64db784f08190b786c4de051ee527 completed March 27, 2026, 9:28 a.m.
Created at: March 22, 2026, 4:48 p.m.