Triple
T10462103
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Selberg integral |
E246700
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
Jack polynomials
Jack polynomials are a family of symmetric polynomials depending on a continuous parameter that generalize several classical symmetric functions and play a key role in algebraic combinatorics, representation theory, and mathematical physics.
|
E865107
|
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: Jack polynomials | Statement: [Selberg integral, relatedTo, Jack polynomials]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Jack polynomials Context triple: [Selberg integral, relatedTo, Jack polynomials]
-
A.
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.
-
B.
Symanzik polynomials
Symanzik polynomials are graph-based polynomials that arise in the parametric representation of Feynman integrals in quantum field theory, encoding the topology and kinematic dependence of Feynman diagrams.
-
C.
Orthogonal Polynomials
Orthogonal Polynomials is a classic mathematical monograph by Gábor Szegő that systematically develops the theory and applications of orthogonal polynomial systems in analysis and approximation theory.
-
D.
Gegenbauer polynomials
Gegenbauer polynomials are a family of orthogonal polynomials on the interval [-1, 1] that generalize Legendre polynomials and play a key role in harmonic analysis and solutions of differential equations with spherical symmetry.
-
E.
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.
- 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: Jack polynomials Triple: [Selberg integral, relatedTo, Jack polynomials]
Generated description
Jack polynomials are a family of symmetric polynomials depending on a continuous parameter that generalize several classical symmetric functions and play a key role in algebraic combinatorics, representation theory, and mathematical physics.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Jack polynomials Target entity description: Jack polynomials are a family of symmetric polynomials depending on a continuous parameter that generalize several classical symmetric functions and play a key role in algebraic combinatorics, representation theory, and mathematical physics.
-
A.
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.
-
B.
Symanzik polynomials
Symanzik polynomials are graph-based polynomials that arise in the parametric representation of Feynman integrals in quantum field theory, encoding the topology and kinematic dependence of Feynman diagrams.
-
C.
Orthogonal Polynomials
Orthogonal Polynomials is a classic mathematical monograph by Gábor Szegő that systematically develops the theory and applications of orthogonal polynomial systems in analysis and approximation theory.
-
D.
Gegenbauer polynomials
Gegenbauer polynomials are a family of orthogonal polynomials on the interval [-1, 1] that generalize Legendre polynomials and play a key role in harmonic analysis and solutions of differential equations with spherical symmetry.
-
E.
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.
- 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.