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.