Triple
T11098844
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Clebsch–Gordan coefficients |
E262449
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Wigner 6j symbols |
E674699
|
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 6j symbols | Statement: [Clebsch–Gordan coefficients, relatedTo, Wigner 6j symbols]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Wigner 6j symbols Context triple: [Clebsch–Gordan coefficients, relatedTo, Wigner 6j symbols]
-
A.
Wigner 3j symbols
chosen
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.
Schur–Weyl duality
Schur–Weyl duality is a fundamental result in representation theory that links representations of the symmetric group and the general linear group via their commuting actions on tensor powers of a vector space.
-
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 (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_69d6aa9a40d88190a373e2c7e48285db |
completed | April 8, 2026, 7:20 p.m. |
| NER | Named-entity recognition | batch_69d79a0c46308190889b94c23ebaca62 |
completed | April 9, 2026, 12:22 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69e42d69c8b4819092614e83e855430e |
completed | April 19, 2026, 1:18 a.m. |
Created at: April 8, 2026, 9:27 p.m.