Triple

T17752499
Position Surface form Disambiguated ID Type / Status
Subject Racah algebra E443146 entity
Predicate connectedTo P37 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: [Racah algebra, connectedTo, Clebsch–Gordan coefficients]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Clebsch–Gordan coefficients
Context triple: [Racah algebra, connectedTo, 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–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.
  • D. Clebsch representation
    The Clebsch representation is a mathematical formulation in fluid dynamics and vector calculus that expresses a three-dimensional vector field, particularly a velocity field, in terms of scalar potential functions.
  • E. 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.
  • 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_69d8b9edf16c8190a59ebd245d378f4f completed April 10, 2026, 8:50 a.m.
NER Named-entity recognition batch_69e4841c0540819093a32d759775c61f completed April 19, 2026, 7:28 a.m.
Created at: April 10, 2026, 10:10 a.m.