Triple
T4461379
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Wigner–Eckart theorem |
E98261
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
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.
|
E443146
|
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: Racah algebra | Statement: [Wigner–Eckart theorem, relatedTo, Racah algebra]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Racah algebra Context triple: [Wigner–Eckart theorem, relatedTo, Racah algebra]
-
A.
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.
-
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.
The Classical Groups: Their Invariants and Representations
The Classical Groups: Their Invariants and Representations is a foundational mathematical monograph by Hermann Weyl that systematically develops the theory of classical Lie groups, their invariants, and their representation theory.
-
D.
Onsager algebra
The Onsager algebra is an infinite-dimensional Lie algebra introduced in the study of exactly solvable models in statistical mechanics, particularly the two-dimensional Ising model.
-
E.
Methods of Representation Theory
Methods of Representation Theory is a foundational multi-volume work in mathematics that systematically develops the theory of group and algebra representations, coauthored by Israel Gelfand and collaborators.
- 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: Racah algebra Triple: [Wigner–Eckart theorem, relatedTo, Racah algebra]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Racah algebra Target entity description: 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.
-
A.
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.
-
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.
The Classical Groups: Their Invariants and Representations
The Classical Groups: Their Invariants and Representations is a foundational mathematical monograph by Hermann Weyl that systematically develops the theory of classical Lie groups, their invariants, and their representation theory.
-
D.
Onsager algebra
The Onsager algebra is an infinite-dimensional Lie algebra introduced in the study of exactly solvable models in statistical mechanics, particularly the two-dimensional Ising model.
-
E.
Methods of Representation Theory
Methods of Representation Theory is a foundational multi-volume work in mathematics that systematically develops the theory of group and algebra representations, coauthored by Israel Gelfand and collaborators.
- 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_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. |
| NEDg | Description generation | batch_69b629532cac8190b959adc0ef13305a |
completed | March 15, 2026, 3:36 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69b62d9c287c8190a305f9d21517f913 |
completed | March 15, 2026, 3:55 a.m. |
Created at: March 12, 2026, 11:34 p.m.