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.