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.