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.