Triple

T4461376
Position Surface form Disambiguated ID Type / Status
Subject Wigner–Eckart theorem E98261 entity
Predicate relatedTo P37 FINISHED
Object Wigner 3-j symbols E262449 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 3-j symbols | Statement: [Wigner–Eckart theorem, relatedTo, Wigner 3-j symbols]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Wigner 3-j symbols
Context triple: [Wigner–Eckart theorem, relatedTo, Wigner 3-j symbols]
  • 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–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.
  • C. Brillouin–Wigner perturbation theory
    Brillouin–Wigner perturbation theory is a formulation of quantum mechanical perturbation theory that uses an energy-dependent effective Hamiltonian to obtain improved approximations to eigenvalues and eigenstates.
  • D. Infeld–van der Waerden formalism
    The Infeld–van der Waerden formalism is a mathematical framework in general relativity that reformulates the theory using spinor calculus to describe gravitational and electromagnetic fields.
  • E. Jacobi polynomials
    Jacobi polynomials are a family of classical orthogonal polynomials depending on two parameters, widely used in approximation theory, numerical analysis, and solutions of differential equations.
  • 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_69b3454a7c608190944f5455c8031d73 completed March 12, 2026, 10:59 p.m.
NER Named-entity recognition batch_69b35674f718819089388c3924dd1414 completed March 13, 2026, 12:12 a.m.
NED1 Entity disambiguation (via context triple) batch_69b6284b90708190b557b66bd7533f4e completed March 15, 2026, 3:32 a.m.
Created at: March 12, 2026, 11:34 p.m.