Triple
T7871817
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Jacobi polynomials |
E182753
|
entity |
| Predicate | generalizes |
P2372
|
FINISHED |
| Object |
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.
|
E697760
|
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 polynomials of the first kind | Statement: [Jacobi polynomials, generalizes, Chebyshev polynomials of the first kind]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Chebyshev polynomials of the first kind Context triple: [Jacobi polynomials, generalizes, Chebyshev polynomials of the first kind]
-
A.
Bernstein polynomials
Bernstein polynomials are a family of polynomials used in approximation theory that provide a constructive proof of the Weierstrass approximation theorem by uniformly approximating continuous functions on a closed interval.
-
B.
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.
-
C.
Chebyshev functions
Chebyshev functions are arithmetic functions in number theory that encode information about the distribution of prime numbers and play a key role in analytic approaches to the prime number theorem.
-
D.
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.
-
E.
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.
- 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 polynomials of the first kind Triple: [Jacobi polynomials, generalizes, Chebyshev polynomials of the first kind]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Chebyshev polynomials of the first kind Target entity description: 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.
-
A.
Bernstein polynomials
Bernstein polynomials are a family of polynomials used in approximation theory that provide a constructive proof of the Weierstrass approximation theorem by uniformly approximating continuous functions on a closed interval.
-
B.
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.
-
C.
Chebyshev functions
Chebyshev functions are arithmetic functions in number theory that encode information about the distribution of prime numbers and play a key role in analytic approaches to the prime number theorem.
-
D.
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.
-
E.
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.
- 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.