Triple
T4461375
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Wigner–Eckart theorem |
E98261
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Clebsch–Gordan decomposition |
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: Clebsch–Gordan decomposition | Statement: [Wigner–Eckart theorem, relatedTo, Clebsch–Gordan decomposition]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Clebsch–Gordan decomposition Context triple: [Wigner–Eckart theorem, relatedTo, Clebsch–Gordan decomposition]
-
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.
Schmidt decomposition
The Schmidt decomposition is a mathematical technique in functional analysis and quantum information theory that expresses a bipartite vector (such as a quantum state) as a sum of orthogonal product states with nonnegative coefficients, revealing its entanglement structure.
-
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 (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_69b6511439c08190965afc1107ae24f4 |
completed | March 15, 2026, 6:26 a.m. |
Created at: March 12, 2026, 11:34 p.m.