Triple

T18480250
Position Surface form Disambiguated ID Type / Status
Subject Orthogonal Polynomials E451537 entity
Predicate contains P35 FINISHED
Object Hermite polynomials — NE NERFINISHED

How this triple was built (3 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: Hermite polynomials | Statement: [Orthogonal Polynomials, contains, Hermite polynomials]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Hermite polynomials
Context triple: [Orthogonal Polynomials, contains, Hermite polynomials]
  • A. 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.
  • B. Hermite
    Hermite is a French surname most famously associated with the 19th-century mathematician Charles Hermite, known for his contributions to number theory, algebra, and analysis.
  • C. Hermite functions
    Hermite functions are a family of orthogonal functions built from Hermite polynomials and a Gaussian weight, widely used in quantum mechanics, signal processing, and approximation theory.
  • D. 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.
  • 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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: Hermite polynomials
Target entity description: Hermite polynomials are a classical family of orthogonal polynomials that arise prominently in probability theory and quantum mechanics, particularly in the analysis of the Gaussian distribution and the quantum harmonic oscillator.
  • A. 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.
  • B. Hermite
    Hermite is a French surname most famously associated with the 19th-century mathematician Charles Hermite, known for his contributions to number theory, algebra, and analysis.
  • C. Hermite functions
    Hermite functions are a family of orthogonal functions built from Hermite polynomials and a Gaussian weight, widely used in quantum mechanics, signal processing, and approximation theory.
  • D. 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.
  • 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 (2 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.
Created at: April 10, 2026, 11:35 a.m.