Triple

T18480249
Position Surface form Disambiguated ID Type / Status
Subject Orthogonal Polynomials E451537 entity
Predicate contains P35 FINISHED
Object Laguerre polynomials — NE NERFINISHED

Named-entity recognition

Before disambiguation, gpt-5-mini classified whether the object phrase is a named entity — the step behind the object's NE type shown above.

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]

Disambiguation candidates (2 decisions)

The exact options the model was shown at each disambiguation step, with the option it chose highlighted — the evidence behind this triple's disambiguated ids.

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.
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 (2 batches)

Stage Batch ID Job type Status
creating batch_69d8d38465a0819099b9b42d2a662ac1 elicitation completed
NER batch_69e53066a7108190a50eda9b489c90ca ner completed
Created at: April 10, 2026, 11:35 a.m.