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.