Triple
T7871807
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Jacobi polynomials |
E182753
|
entity |
| Predicate | satisfies |
P4233
|
FINISHED |
| Object |
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.
|
E697757
|
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: Rodrigues formula | Statement: [Jacobi polynomials, satisfies, Rodrigues formula]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Rodrigues formula Context triple: [Jacobi polynomials, satisfies, Rodrigues formula]
-
A.
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.
-
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.
Gauss multiplication formula
The Gauss multiplication formula is a classical identity in complex analysis that expresses the gamma function of a multiple of a variable as a product of gamma functions evaluated at shifted fractions of that variable.
-
D.
Gauss hypergeometric function
The Gauss hypergeometric function is a special function defined by a power series that generalizes many elementary and higher transcendental functions and plays a central role in mathematical analysis, differential equations, and mathematical physics.
-
E.
Bernoulli polynomials
Bernoulli polynomials are a sequence of polynomials deeply connected to number theory and analysis, appearing in the study of special functions, series expansions, and the evaluation of sums of powers of integers.
- 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: Rodrigues formula Triple: [Jacobi polynomials, satisfies, Rodrigues formula]
Generated description
Rodrigues formula is a classical representation that expresses certain families of orthogonal polynomials, such as Jacobi polynomials, in terms of derivatives of weight functions.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Rodrigues formula Target entity description: Rodrigues formula is a classical representation that expresses certain families of orthogonal polynomials, such as Jacobi polynomials, in terms of derivatives of weight functions.
-
A.
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.
-
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.
Gauss multiplication formula
The Gauss multiplication formula is a classical identity in complex analysis that expresses the gamma function of a multiple of a variable as a product of gamma functions evaluated at shifted fractions of that variable.
-
D.
Gauss hypergeometric function
The Gauss hypergeometric function is a special function defined by a power series that generalizes many elementary and higher transcendental functions and plays a central role in mathematical analysis, differential equations, and mathematical physics.
-
E.
Bernoulli polynomials
Bernoulli polynomials are a sequence of polynomials deeply connected to number theory and analysis, appearing in the study of special functions, series expansions, and the evaluation of sums of powers of integers.
- 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_69ca82894d9081908a832bfce71a4714 |
completed | March 30, 2026, 2:02 p.m. |
| NER | Named-entity recognition | batch_69cb39a5950481908399211c5dfe2569 |
completed | March 31, 2026, 3:04 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69cb5b6bc7248190adbf4377c52e16a9 |
completed | March 31, 2026, 5:28 a.m. |
| NEDg | Description generation | batch_69cb5f1daac88190a162132bbd40fdc6 |
completed | March 31, 2026, 5:43 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69cb768ac1a48190bc6a59a64adf7144 |
completed | March 31, 2026, 7:23 a.m. |
Created at: March 30, 2026, 4:56 p.m.