Triple

T2408487
Position Surface form Disambiguated ID Type / Status
Subject Alfred Clebsch E50330 entity
Predicate notableWork P4 FINISHED
Object Clebsch–Gordan coefficients
Clebsch–Gordan coefficients are numerical factors in quantum mechanics and representation theory that describe how to combine two angular momenta (or group representations) into a single resultant one.
E262449 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: Clebsch–Gordan coefficients | Statement: [Alfred Clebsch, notableWork, Clebsch–Gordan coefficients]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Clebsch–Gordan coefficients
Context triple: [Alfred Clebsch, notableWork, Clebsch–Gordan coefficients]
  • A. Wigner–Eckart theorem
    The Wigner–Eckart theorem is a fundamental result in quantum mechanics that factorizes matrix elements of tensor operators into a reduced matrix element and a purely geometric part given by Clebsch–Gordan coefficients, greatly simplifying angular momentum calculations.
  • B. Jacobi polynomials
    Jacobi polynomials are a family of classical orthogonal polynomials depending on two parameters, widely used in approximation theory, numerical analysis, and solutions of differential equations.
  • C. Russell–Saunders coupling
    Russell–Saunders coupling is an atomic physics scheme that describes how individual electron orbital and spin angular momenta combine to determine the total angular momentum of an atom, especially in light atoms.
  • D. Weyl character formula
    The Weyl character formula is a fundamental result in representation theory that gives an explicit expression for the characters of irreducible finite-dimensional representations of semisimple Lie algebras and Lie groups.
  • E. Gell-Mann matrices
    Gell-Mann matrices are a set of eight 3×3 traceless Hermitian matrices that serve as the generators of the SU(3) Lie algebra in quantum chromodynamics and other areas of particle physics.
  • 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: Clebsch–Gordan coefficients
Triple: [Alfred Clebsch, notableWork, Clebsch–Gordan coefficients]
Generated description
Clebsch–Gordan coefficients are numerical factors in quantum mechanics and representation theory that describe how to combine two angular momenta (or group representations) into a single resultant one.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Clebsch–Gordan coefficients
Target entity description: Clebsch–Gordan coefficients are numerical factors in quantum mechanics and representation theory that describe how to combine two angular momenta (or group representations) into a single resultant one.
  • A. Wigner–Eckart theorem
    The Wigner–Eckart theorem is a fundamental result in quantum mechanics that factorizes matrix elements of tensor operators into a reduced matrix element and a purely geometric part given by Clebsch–Gordan coefficients, greatly simplifying angular momentum calculations.
  • B. Jacobi polynomials
    Jacobi polynomials are a family of classical orthogonal polynomials depending on two parameters, widely used in approximation theory, numerical analysis, and solutions of differential equations.
  • C. Russell–Saunders coupling
    Russell–Saunders coupling is an atomic physics scheme that describes how individual electron orbital and spin angular momenta combine to determine the total angular momentum of an atom, especially in light atoms.
  • D. Weyl character formula
    The Weyl character formula is a fundamental result in representation theory that gives an explicit expression for the characters of irreducible finite-dimensional representations of semisimple Lie algebras and Lie groups.
  • E. Gell-Mann matrices
    Gell-Mann matrices are a set of eight 3×3 traceless Hermitian matrices that serve as the generators of the SU(3) Lie algebra in quantum chromodynamics and other areas of particle physics.
  • 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_69a88b0339a88190a1207333cd271cc9 completed March 4, 2026, 7:41 p.m.
NER Named-entity recognition batch_69abc92408308190ad2d331ebee71d15 completed March 7, 2026, 6:43 a.m.
NED1 Entity disambiguation (via context triple) batch_69aeb3eba9d08190a2c63e590e08b4df completed March 9, 2026, 11:50 a.m.
NEDg Description generation batch_69aeb4a5e9c481908426fe51343a1342 completed March 9, 2026, 11:53 a.m.
NED2 Entity disambiguation (via description) batch_69aeb52bec1881909c589aea2af3684c completed March 9, 2026, 11:55 a.m.
Created at: March 4, 2026, 7:58 p.m.