Triple

T11812503
Position Surface form Disambiguated ID Type / Status
Subject Elwin Bruno Christoffel E280907 entity
Predicate notableWork P4 FINISHED
Object Christoffel–Darboux formula
The Christoffel–Darboux formula is a key result in the theory of orthogonal polynomials that provides an explicit expression for sums of products of such polynomials, with important applications in approximation theory and mathematical physics.
E947533 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: Christoffel–Darboux formula | Statement: [Elwin Bruno Christoffel, notableWork, Christoffel–Darboux formula]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Christoffel–Darboux formula
Context triple: [Elwin Bruno Christoffel, notableWork, Christoffel–Darboux formula]
  • A. Rodrigues formula
    Rodrigues formula is a classical representation that expresses certain families of orthogonal polynomials, such as Jacobi polynomials, in terms of derivatives of weight functions.
  • B. 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.
  • C. 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.
  • 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. Cauchy–Binet formula
    The Cauchy–Binet formula is a fundamental result in linear algebra that expresses the determinant of a product of two rectangular matrices as a sum of products of determinants of their square submatrices.
  • 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: Christoffel–Darboux formula
Triple: [Elwin Bruno Christoffel, notableWork, Christoffel–Darboux formula]
Generated description
The Christoffel–Darboux formula is a key result in the theory of orthogonal polynomials that provides an explicit expression for sums of products of such polynomials, with important applications in approximation theory and mathematical physics.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Christoffel–Darboux formula
Target entity description: The Christoffel–Darboux formula is a key result in the theory of orthogonal polynomials that provides an explicit expression for sums of products of such polynomials, with important applications in approximation theory and mathematical physics.
  • A. Rodrigues formula
    Rodrigues formula is a classical representation that expresses certain families of orthogonal polynomials, such as Jacobi polynomials, in terms of derivatives of weight functions.
  • B. 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.
  • C. 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.
  • 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. Cauchy–Binet formula
    The Cauchy–Binet formula is a fundamental result in linear algebra that expresses the determinant of a product of two rectangular matrices as a sum of products of determinants of their square submatrices.
  • 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_69d6ab26aae88190b2489efcb2a24234 completed April 8, 2026, 7:23 p.m.
NER Named-entity recognition batch_69d8a5cba708819097467bb7aca7fc65 completed April 10, 2026, 7:24 a.m.
NED1 Entity disambiguation (via context triple) batch_69f131a01aa48190bf5a70759ac886f6 completed April 28, 2026, 10:16 p.m.
NEDg Description generation batch_69f141b31c9081908f19ff870f5f3c33 completed April 28, 2026, 11:24 p.m.
NED2 Entity disambiguation (via description) batch_69f14fdb39d48190828668fc535d7f6a completed April 29, 2026, 12:24 a.m.
Created at: April 8, 2026, 9:42 p.m.