Triple
T7287606
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Onsager algebra |
E163912
|
entity |
| Predicate | connectedTo |
P37
|
FINISHED |
| Object |
Askey–Wilson algebra
The Askey–Wilson algebra is a quadratic algebra arising in the theory of orthogonal polynomials and quantum groups, closely linked to the Askey–Wilson polynomials and related integrable models.
|
E653520
|
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: Askey–Wilson algebra | Statement: [Onsager algebra, connectedTo, Askey–Wilson algebra]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Askey–Wilson algebra Context triple: [Onsager algebra, connectedTo, Askey–Wilson algebra]
-
A.
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.
-
B.
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.
-
C.
Yang–Baxter equation
The Yang–Baxter equation is a fundamental consistency condition in mathematical physics and integrable systems that underlies exactly solvable models, quantum groups, and braid group representations.
-
D.
Rogers–Ramanujan-type identities
Rogers–Ramanujan-type identities are a class of deep q-series and partition identities generalizing the classical Rogers–Ramanujan identities, with rich connections to combinatorics, number theory, and modular forms.
-
E.
Gelfand–Tsetlin basis
The Gelfand–Tsetlin basis is a canonical, combinatorially defined basis for representations of certain Lie algebras and groups, particularly used in the representation theory of GL(n) and related structures.
- 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: Askey–Wilson algebra Triple: [Onsager algebra, connectedTo, Askey–Wilson algebra]
Generated description
The Askey–Wilson algebra is a quadratic algebra arising in the theory of orthogonal polynomials and quantum groups, closely linked to the Askey–Wilson polynomials and related integrable models.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Askey–Wilson algebra Target entity description: The Askey–Wilson algebra is a quadratic algebra arising in the theory of orthogonal polynomials and quantum groups, closely linked to the Askey–Wilson polynomials and related integrable models.
-
A.
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.
-
B.
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.
-
C.
Yang–Baxter equation
The Yang–Baxter equation is a fundamental consistency condition in mathematical physics and integrable systems that underlies exactly solvable models, quantum groups, and braid group representations.
-
D.
Rogers–Ramanujan-type identities
Rogers–Ramanujan-type identities are a class of deep q-series and partition identities generalizing the classical Rogers–Ramanujan identities, with rich connections to combinatorics, number theory, and modular forms.
-
E.
Gelfand–Tsetlin basis
The Gelfand–Tsetlin basis is a canonical, combinatorially defined basis for representations of certain Lie algebras and groups, particularly used in the representation theory of GL(n) and related structures.
- 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_69c6886093b88190a254b1ce6db8bae7 |
completed | March 27, 2026, 1:38 p.m. |
| NER | Named-entity recognition | batch_69c6eb6a73fc8190ae5ce81fd3e46d87 |
completed | March 27, 2026, 8:41 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c7db42c8d48190a548c4242b07fb40 |
completed | March 28, 2026, 1:44 p.m. |
| NEDg | Description generation | batch_69c7dc794bec819094d848497bd11fc1 |
completed | March 28, 2026, 1:49 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69c7dd8117f881908c982c33b3f0e71a |
completed | March 28, 2026, 1:54 p.m. |
Created at: March 27, 2026, 2:59 p.m.