Triple

T4461356
Position Surface form Disambiguated ID Type / Status
Subject Wigner–Eckart theorem E98261 entity
Predicate involves P1256 FINISHED
Object 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.
E443145 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: rotation group SU(2) | Statement: [Wigner–Eckart theorem, involves, rotation group SU(2)]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: rotation group SU(2)
Context triple: [Wigner–Eckart theorem, involves, rotation group SU(2)]
  • A. rotation group SO(3)
    The rotation group SO(3) is the group of all rotations in three-dimensional space, represented by 3×3 orthogonal matrices with determinant 1, and plays a central role in classical mechanics, quantum mechanics, and geometry.
  • B. 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.
  • C. Lorentz group
    The Lorentz group is the mathematical group of spacetime symmetries in special relativity, consisting of all rotations and boosts that preserve the Minkowski spacetime interval.
  • 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. Poincaré group
    The Poincaré group is the fundamental symmetry group of special relativity, combining spacetime translations with Lorentz transformations in four-dimensional Minkowski space.
  • 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: rotation group SU(2)
Triple: [Wigner–Eckart theorem, involves, rotation group SU(2)]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: rotation group SU(2)
Target entity description: 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.
  • A. rotation group SO(3)
    The rotation group SO(3) is the group of all rotations in three-dimensional space, represented by 3×3 orthogonal matrices with determinant 1, and plays a central role in classical mechanics, quantum mechanics, and geometry.
  • B. 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.
  • C. Lorentz group
    The Lorentz group is the mathematical group of spacetime symmetries in special relativity, consisting of all rotations and boosts that preserve the Minkowski spacetime interval.
  • 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. Poincaré group
    The Poincaré group is the fundamental symmetry group of special relativity, combining spacetime translations with Lorentz transformations in four-dimensional Minkowski space.
  • 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_69b3454a7c608190944f5455c8031d73 completed March 12, 2026, 10:59 p.m.
NER Named-entity recognition batch_69b35674f718819089388c3924dd1414 completed March 13, 2026, 12:12 a.m.
NED1 Entity disambiguation (via context triple) batch_69b6284b90708190b557b66bd7533f4e completed March 15, 2026, 3:32 a.m.
NEDg Description generation batch_69b629532cac8190b959adc0ef13305a completed March 15, 2026, 3:36 a.m.
NED2 Entity disambiguation (via description) batch_69b62d9c287c8190a305f9d21517f913 completed March 15, 2026, 3:55 a.m.
Created at: March 12, 2026, 11:34 p.m.