Triple
T6456475
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Lie group |
E142004
|
entity |
| Predicate | hasExample |
P1259
|
FINISHED |
| Object |
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.
|
E593508
|
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 unitary group SU(n) | Statement: [Lie group, hasExample, special unitary group SU(n)]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: special unitary group SU(n) Context triple: [Lie group, hasExample, special unitary group SU(n)]
-
A.
SU(3)
SU(3) is the special unitary group of degree three, a Lie group fundamental to the mathematical description of the strong interaction and the classification of hadrons in particle physics.
-
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.
rotation group SU(2)
The rotation group SU(2) is the Lie group of 2×2 unitary matrices with determinant 1 that serves as the double cover of the three-dimensional rotation group SO(3) and underlies the quantum theory of angular momentum and spin.
-
D.
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.
-
E.
U(1)
U(1) is the group of complex numbers with absolute value 1 under multiplication, commonly representing the symmetry group of electromagnetism and other abelian gauge theories.
- 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 unitary group SU(n) Triple: [Lie group, hasExample, special unitary group SU(n)]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: special unitary group SU(n) Target entity description: 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.
-
A.
SU(3)
SU(3) is the special unitary group of degree three, a Lie group fundamental to the mathematical description of the strong interaction and the classification of hadrons in particle physics.
-
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.
rotation group SU(2)
The rotation group SU(2) is the Lie group of 2×2 unitary matrices with determinant 1 that serves as the double cover of the three-dimensional rotation group SO(3) and underlies the quantum theory of angular momentum and spin.
-
D.
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.
-
E.
U(1)
U(1) is the group of complex numbers with absolute value 1 under multiplication, commonly representing the symmetry group of electromagnetism and other abelian gauge theories.
- 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.