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.