Triple

T18930745
Position Surface form Disambiguated ID Type / Status
Subject Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra E463101 entity
Predicate topic P261 FINISHED
Object Clebsch–Gordan coefficients — NE NERFINISHED

How this triple was built (2 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: [Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra, topic, Clebsch–Gordan coefficients]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Clebsch–Gordan coefficients
Context triple: [Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra, topic, Clebsch–Gordan coefficients]
  • A. Clebsch–Gordan coefficients chosen
    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.
  • 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. 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.
  • D. 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.
  • 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.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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_69d8dcfdbbb881909964fa5a75bd0b48 completed April 10, 2026, 11:20 a.m.
NER Named-entity recognition batch_69e5c9bfaee881908d701c5a05528939 completed April 20, 2026, 6:37 a.m.
Created at: April 10, 2026, 11:59 a.m.