Triple

T18930743
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 Wigner–Eckart theorem — 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: Wigner–Eckart theorem | Statement: [Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra, topic, Wigner–Eckart theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Wigner–Eckart theorem
Context triple: [Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra, topic, Wigner–Eckart theorem]
  • A. Wigner–Eckart theorem chosen
    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. 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.
  • C. Racah algebra
    Racah algebra is a mathematical structure in representation theory and quantum mechanics that encodes the symmetries and coupling properties of angular momenta, particularly through Racah coefficients and related special functions.
  • D. Wigner’s theorem on symmetry transformations
    Wigner’s theorem on symmetry transformations is a fundamental result in quantum mechanics stating that any symmetry of transition probabilities is represented by either a unitary or antiunitary operator on the system’s Hilbert space.
  • E. 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.
  • 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.