Triple
T10462129
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Selberg integral |
E246700
|
entity |
| Predicate | hasVariant |
P455
|
FINISHED |
| Object |
q-Selberg integral
The q-Selberg integral is a q-analogue of the classical Selberg integral, expressing a multivariate basic hypergeometric integral that generalizes many important identities in q-series and special function theory.
|
E865111
|
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: q-Selberg integral | Statement: [Selberg integral, hasVariant, q-Selberg integral]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: q-Selberg integral Context triple: [Selberg integral, hasVariant, q-Selberg integral]
-
A.
Selberg integral
The Selberg integral is a fundamental multidimensional generalization of Euler’s beta integral that plays a central role in random matrix theory, combinatorics, and special functions.
-
B.
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.
-
C.
Askey scheme of hypergeometric orthogonal polynomials
The Askey scheme of hypergeometric orthogonal polynomials is a hierarchical classification of families of (basic) hypergeometric orthogonal polynomials, organized by limit relations between them.
-
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.
Jacobi polynomials
Jacobi polynomials are a family of classical orthogonal polynomials depending on two parameters, widely used in approximation theory, numerical analysis, and solutions of differential equations.
- 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: q-Selberg integral Triple: [Selberg integral, hasVariant, q-Selberg integral]
Generated description
The q-Selberg integral is a q-analogue of the classical Selberg integral, expressing a multivariate basic hypergeometric integral that generalizes many important identities in q-series and special function theory.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: q-Selberg integral Target entity description: The q-Selberg integral is a q-analogue of the classical Selberg integral, expressing a multivariate basic hypergeometric integral that generalizes many important identities in q-series and special function theory.
-
A.
Selberg integral
The Selberg integral is a fundamental multidimensional generalization of Euler’s beta integral that plays a central role in random matrix theory, combinatorics, and special functions.
-
B.
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.
-
C.
Askey scheme of hypergeometric orthogonal polynomials
The Askey scheme of hypergeometric orthogonal polynomials is a hierarchical classification of families of (basic) hypergeometric orthogonal polynomials, organized by limit relations between them.
-
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.
Jacobi polynomials
Jacobi polynomials are a family of classical orthogonal polynomials depending on two parameters, widely used in approximation theory, numerical analysis, and solutions of differential equations.
- 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_69d381c16c248190a2fe5b471e584e9c |
completed | April 6, 2026, 9:49 a.m. |
| NER | Named-entity recognition | batch_69d50884fac48190af22e181b1492557 |
completed | April 7, 2026, 1:37 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69d89fcc84b48190a39de0d9b9111ebd |
completed | April 10, 2026, 6:59 a.m. |
| NEDg | Description generation | batch_69d8a1656b348190ba932d03402d6a4d |
completed | April 10, 2026, 7:06 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69d8a2b82bb48190899f37a967fef444 |
completed | April 10, 2026, 7:11 a.m. |
Created at: April 6, 2026, 12:19 p.m.