Triple

T7593280
Position Surface form Disambiguated ID Type / Status
Subject Condon–Shortley phase E179791 entity
Predicate relatedTo P37 FINISHED
Object Wigner–Eckart theorem E98261 NE FINISHED

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: [Condon–Shortley phase, relatedTo, Wigner–Eckart theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Wigner–Eckart theorem
Context triple: [Condon–Shortley phase, relatedTo, 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. Wick’s theorem
    Wick’s theorem is a fundamental result in quantum field theory that expresses time-ordered products of field operators as sums of normal-ordered products with all possible contractions, forming the basis for deriving Feynman rules and diagrammatic expansions.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69c69f3487ec8190bf7acdf2dd91e6d6 completed March 27, 2026, 3:16 p.m.
NER Named-entity recognition batch_69c6f9bab3a08190a2c36b2c72a1de25 completed March 27, 2026, 9:42 p.m.
NED1 Entity disambiguation (via context triple) batch_69c86197fe0881908307a411cabdca7f completed March 28, 2026, 11:17 p.m.
Created at: March 27, 2026, 3:53 p.m.