Triple

T818200
Position Surface form Disambiguated ID Type / Status
Subject Eugene Wigner E17694 entity
Predicate knownFor P22 FINISHED
Object 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.
E98261 NE FINISHED

How this triple was built (4 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: [Eugene Wigner, knownFor, Wigner–Eckart theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Wigner–Eckart theorem
Context triple: [Eugene Wigner, knownFor, Wigner–Eckart theorem]
  • A. 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.
  • B. Gell-Mann–Nishijima formula
    The Gell-Mann–Nishijima formula is a key relation in particle physics that connects a particle’s electric charge to its isospin and hypercharge, helping classify hadrons within the quark model.
  • C. Feynman–Hellmann theorem
    The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
  • D. Gell-Mann–Low theorem
    The Gell-Mann–Low theorem is a fundamental result in quantum field theory that rigorously connects interacting quantum fields to free fields via the adiabatic switching-on of interactions, underpinning the use of perturbation theory and the Dyson series.
  • E. 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.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Wigner–Eckart theorem
Triple: [Eugene Wigner, knownFor, Wigner–Eckart theorem]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Wigner–Eckart theorem
Target entity description: 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.
  • A. 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.
  • B. Gell-Mann–Nishijima formula
    The Gell-Mann–Nishijima formula is a key relation in particle physics that connects a particle’s electric charge to its isospin and hypercharge, helping classify hadrons within the quark model.
  • C. Feynman–Hellmann theorem
    The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
  • D. Gell-Mann–Low theorem
    The Gell-Mann–Low theorem is a fundamental result in quantum field theory that rigorously connects interacting quantum fields to free fields via the adiabatic switching-on of interactions, underpinning the use of perturbation theory and the Dyson series.
  • E. 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.
  • F. None of above. chosen

Provenance (5 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_69a4937bcaac8190a322524ac6f45a5a completed March 1, 2026, 7:28 p.m.
NER Named-entity recognition batch_69a4ab63f4a48190a61a14c3c41ed641 completed March 1, 2026, 9:11 p.m.
NED1 Entity disambiguation (via context triple) batch_69a76d8f639081909690d1ef4c98680e completed March 3, 2026, 11:23 p.m.
NEDg Description generation batch_69a781f5536c81908175d58b6b75adba completed March 4, 2026, 12:51 a.m.
NED2 Entity disambiguation (via description) batch_69a7860e656c8190a08a9999662ba1f1 completed March 4, 2026, 1:08 a.m.
Created at: March 1, 2026, 7:38 p.m.