Triple

T12138865
Position Surface form Disambiguated ID Type / Status
Subject Pafnuty Chebyshev E289130 entity
Predicate notableWork P4 FINISHED
Object Chebyshev quadrature
Chebyshev quadrature is a numerical integration method that approximates definite integrals using specially chosen nodes and equal weights to achieve high accuracy.
E968217 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: Chebyshev quadrature | Statement: [Pafnuty Chebyshev, notableWork, Chebyshev quadrature]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Chebyshev quadrature
Context triple: [Pafnuty Chebyshev, notableWork, Chebyshev quadrature]
  • A. Gaussian quadrature rules
    Gaussian quadrature rules are numerical integration methods that approximate definite integrals by optimally choosing evaluation points and weights to achieve exactness for polynomials up to a high degree.
  • B. Newton–Cotes formulas
    Newton–Cotes formulas are a family of numerical integration methods that approximate definite integrals by interpolating the integrand with equally spaced polynomial points.
  • C. Chebyshev polynomials of the first kind
    Chebyshev polynomials of the first kind are a classical family of orthogonal polynomials on the interval [-1, 1] that play a central role in approximation theory, numerical analysis, and spectral methods.
  • D. 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.
  • E. 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.
  • 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: Chebyshev quadrature
Triple: [Pafnuty Chebyshev, notableWork, Chebyshev quadrature]
Generated description
Chebyshev quadrature is a numerical integration method that approximates definite integrals using specially chosen nodes and equal weights to achieve high accuracy.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Chebyshev quadrature
Target entity description: Chebyshev quadrature is a numerical integration method that approximates definite integrals using specially chosen nodes and equal weights to achieve high accuracy.
  • A. Gaussian quadrature rules
    Gaussian quadrature rules are numerical integration methods that approximate definite integrals by optimally choosing evaluation points and weights to achieve exactness for polynomials up to a high degree.
  • B. Newton–Cotes formulas
    Newton–Cotes formulas are a family of numerical integration methods that approximate definite integrals by interpolating the integrand with equally spaced polynomial points.
  • C. Chebyshev polynomials of the first kind
    Chebyshev polynomials of the first kind are a classical family of orthogonal polynomials on the interval [-1, 1] that play a central role in approximation theory, numerical analysis, and spectral methods.
  • D. 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.
  • E. 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.
  • 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_69d6ab4b5e4c81909950b17151eb0951 completed April 8, 2026, 7:23 p.m.
NER Named-entity recognition batch_69d9158eef48819083bdce283a363414 completed April 10, 2026, 3:21 p.m.
NED1 Entity disambiguation (via context triple) batch_69f5f690ae408190966bb4fe8feaa7d2 completed May 2, 2026, 1:05 p.m.
NEDg Description generation batch_69f6022ecf38819080f0eb6a3a815c5b completed May 2, 2026, 1:54 p.m.
NED2 Entity disambiguation (via description) batch_69f606560934819092ba4d4fa162b799 completed May 2, 2026, 2:12 p.m.
Created at: April 8, 2026, 9:49 p.m.