Triple

T17752501
Position Surface form Disambiguated ID Type / Status
Subject Racah algebra E443146 entity
Predicate connectedTo P37 FINISHED
Object Wigner 9-j symbols
Wigner 9-j symbols are mathematical coefficients used in quantum mechanics and angular momentum theory to describe the coupling of three angular momenta and recoupling transformations.
E1288551 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: Wigner 9-j symbols | Statement: [Racah algebra, connectedTo, Wigner 9-j symbols]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Wigner 9-j symbols
Context triple: [Racah algebra, connectedTo, Wigner 9-j symbols]
  • A. Wigner 6-j symbols
    Wigner 6-j symbols are mathematical coefficients in quantum angular momentum theory that encode the recoupling of three angular momenta and play a central role in Racah algebra and the representation theory of rotation groups.
  • B. Wigner 3j symbols
    Wigner 3j symbols are mathematical coefficients used in quantum mechanics and angular momentum theory to describe the coupling and recoupling of three angular momenta with well-defined symmetry properties.
  • C. 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.
  • D. 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.
  • E. Racah polynomials
    Racah polynomials are a family of classical orthogonal polynomials that arise in the representation theory of angular momentum and in the study of exactly solvable models in mathematical 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: Wigner 9-j symbols
Triple: [Racah algebra, connectedTo, Wigner 9-j symbols]
Generated description
Wigner 9-j symbols are mathematical coefficients used in quantum mechanics and angular momentum theory to describe the coupling of three angular momenta and recoupling transformations.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Wigner 9-j symbols
Target entity description: Wigner 9-j symbols are mathematical coefficients used in quantum mechanics and angular momentum theory to describe the coupling of three angular momenta and recoupling transformations.
  • A. Wigner 6-j symbols
    Wigner 6-j symbols are mathematical coefficients in quantum angular momentum theory that encode the recoupling of three angular momenta and play a central role in Racah algebra and the representation theory of rotation groups.
  • B. Wigner 3j symbols
    Wigner 3j symbols are mathematical coefficients used in quantum mechanics and angular momentum theory to describe the coupling and recoupling of three angular momenta with well-defined symmetry properties.
  • C. 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.
  • D. 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.
  • E. Racah polynomials
    Racah polynomials are a family of classical orthogonal polynomials that arise in the representation theory of angular momentum and in the study of exactly solvable models in mathematical 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_69d8b9edf16c8190a59ebd245d378f4f completed April 10, 2026, 8:50 a.m.
NER Named-entity recognition batch_69e4841c0540819093a32d759775c61f completed April 19, 2026, 7:28 a.m.
NED1 Entity disambiguation (via context triple) batch_6a02f82c6b6c81909864f273f85056ba completed May 12, 2026, 9:51 a.m.
NEDg Description generation batch_6a02f9584ca08190b00efcd333c35864 completed May 12, 2026, 9:56 a.m.
NED2 Entity disambiguation (via description) batch_6a02fadc5d4481908f7e7139a83c02bc completed May 12, 2026, 10:03 a.m.
Created at: April 10, 2026, 10:10 a.m.