Triple
T12138859
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Pafnuty Chebyshev |
E289130
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object | Chebyshev polynomials |
E697760
|
NE FINISHED |
How this triple was built (2 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 | Statement: [Pafnuty Chebyshev, notableWork, Chebyshev polynomials]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Chebyshev polynomials Context triple: [Pafnuty Chebyshev, notableWork, Chebyshev polynomials]
-
A.
Chebyshev polynomials of the first kind
chosen
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.
-
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.
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.
-
D.
Legendre polynomials
Legendre polynomials are a sequence of orthogonal polynomials that arise in solving Legendre’s differential equation, playing a central role in mathematical physics, especially in problems with spherical symmetry such as potential theory and quantum mechanics.
-
E.
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.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (3 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_69d6ab4b5e4c81909950b17151eb0951 |
completed | April 8, 2026, 7:23 p.m. |
| NER | Named-entity recognition | batch_69d9158eef48819083bdce283a363414 |
completed | April 10, 2026, 3:21 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f60a7baee88190a32a5a3cd0b8a326 |
completed | May 2, 2026, 2:30 p.m. |
Created at: April 8, 2026, 9:49 p.m.