Triple

T18480249
Position Surface form Disambiguated ID Type / Status
Subject Orthogonal Polynomials E451537 entity
Predicate contains P35 FINISHED
Object Laguerre polynomials
Laguerre polynomials are a classical family of orthogonal polynomials that arise in solutions of differential equations and play a key role in quantum mechanics and numerical analysis.
 E1326017 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: Laguerre polynomials | Statement: [Orthogonal Polynomials, contains, Laguerre polynomials]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Laguerre polynomials
Context triple: [Orthogonal Polynomials, contains, Laguerre polynomials]
  • A. Legendre polynomials
    Legendre polynomials are a sequence of orthogonal polynomials that arise in solving Legendre’s differential equation, playing a central role in mathematical physics, especially in problems with spherical symmetry such as potential theory and quantum mechanics.
  • B. 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.
  • C. 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.
  • D. 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.
  • E. Racah polynomials
    Racah polynomials are a family of classical orthogonal polynomials that arise in the representation theory of angular momentum and in the study of exactly solvable models in mathematical physics.
  • 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: Laguerre polynomials
Triple: [Orthogonal Polynomials, contains, Laguerre polynomials]
Generated description
Laguerre polynomials are a classical family of orthogonal polynomials that arise in solutions of differential equations and play a key role in quantum mechanics and numerical analysis.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: Laguerre polynomials
Target entity description: Laguerre polynomials are a classical family of orthogonal polynomials that arise in solutions of differential equations and play a key role in quantum mechanics and numerical analysis.
  • A. Legendre polynomials
    Legendre polynomials are a sequence of orthogonal polynomials that arise in solving Legendre’s differential equation, playing a central role in mathematical physics, especially in problems with spherical symmetry such as potential theory and quantum mechanics.
  • B. 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.
  • C. 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.
  • D. 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.
  • E. Racah polynomials
    Racah polynomials are a family of classical orthogonal polynomials that arise in the representation theory of angular momentum and in the study of exactly solvable models in mathematical physics.
  • 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_69d8d38465a0819099b9b42d2a662ac1 completed April 10, 2026, 10:40 a.m.
NER Named-entity recognition batch_69e53066a7108190a50eda9b489c90ca completed April 19, 2026, 7:43 p.m.
NED1 Entity disambiguation (via context triple) batch_6a043f2f64848190808075254008e6e1 completed May 13, 2026, 9:06 a.m.
NEDg Description generation batch_6a043fb7db388190bb50cfade4f025f9 completed May 13, 2026, 9:09 a.m.
NED2 Entity disambiguation (via description) batch_6a044063c6048190b65620af8ceed897 completed May 13, 2026, 9:12 a.m.
Created at: April 10, 2026, 11:35 a.m.