Triple

T15169022
Position Surface form Disambiguated ID Type / Status
Subject Carl Eckart E362435 entity
Predicate coDeveloperOf P6901 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: [Carl Eckart, coDeveloperOf, Wigner–Eckart theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Wigner–Eckart theorem
Context triple: [Carl Eckart, coDeveloperOf, 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_69d85a087b7c81908baa94a53dac8d68 completed April 10, 2026, 2:01 a.m.
NER Named-entity recognition batch_69e0064dba588190a4341775b472a6d3 completed April 15, 2026, 9:42 p.m.
NED1 Entity disambiguation (via context triple) batch_69fed3286a2c8190ac73b68cefd0191d completed May 9, 2026, 6:24 a.m.
Created at: April 10, 2026, 3:08 a.m.