Triple
T17752482
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Racah algebra |
E443146
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
Wigner 6-j symbols
Wigner 6-j symbols are mathematical coefficients in quantum angular momentum theory that encode the recoupling of three angular momenta and play a central role in Racah algebra and the representation theory of rotation groups.
|
E1284813
|
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 6-j symbols | Statement: [Racah algebra, relatedTo, Wigner 6-j symbols]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Wigner 6-j symbols Context triple: [Racah algebra, relatedTo, Wigner 6-j symbols]
-
A.
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.
-
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.
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.
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.
-
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 6-j symbols Triple: [Racah algebra, relatedTo, Wigner 6-j symbols]
Generated description
Wigner 6-j symbols are mathematical coefficients in quantum angular momentum theory that encode the recoupling of three angular momenta and play a central role in Racah algebra and the representation theory of rotation groups.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Wigner 6-j symbols Target entity description: Wigner 6-j symbols are mathematical coefficients in quantum angular momentum theory that encode the recoupling of three angular momenta and play a central role in Racah algebra and the representation theory of rotation groups.
-
A.
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.
-
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.
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.
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.
-
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_69d8b9edf16c8190a59ebd245d378f4f |
completed | April 10, 2026, 8:50 a.m. |
| NER | Named-entity recognition | batch_69e4841b3ccc8190b3241b3e0fa4b2e8 |
completed | April 19, 2026, 7:28 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a0243067e6c8190b94113eb4785faae |
completed | May 11, 2026, 8:58 p.m. |
| NEDg | Description generation | batch_6a0244ca6b348190a1c68dc3bf873f1d |
completed | May 11, 2026, 9:06 p.m. |
| NED2 | Entity disambiguation (via description) | batch_6a024530b5dc8190a4776863cc01babf |
completed | May 11, 2026, 9:08 p.m. |
Created at: April 10, 2026, 10:10 a.m.