Triple
T4552549
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Gábor Szegő |
E120398
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Orthogonal Polynomials
Orthogonal Polynomials is a classic mathematical monograph by Gábor Szegő that systematically develops the theory and applications of orthogonal polynomial systems in analysis and approximation theory.
|
E451537
|
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: Orthogonal Polynomials | Statement: [Gábor Szegő, notableWork, Orthogonal Polynomials]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Orthogonal Polynomials Context triple: [Gábor Szegő, notableWork, Orthogonal Polynomials]
-
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.
Carathéodory–Fejér interpolation
Carathéodory–Fejér interpolation is a classical result in complex analysis and approximation theory that concerns constructing analytic functions, typically with bounded or positive real part, that match prescribed initial Taylor coefficients.
-
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.
Selberg integral
The Selberg integral is a fundamental multidimensional generalization of Euler’s beta integral that plays a central role in random matrix theory, combinatorics, and special functions.
-
E.
Bernstein inequalities
Bernstein inequalities are fundamental results in approximation theory and probability that provide bounds on the derivatives or deviations of functions and random variables under certain smoothness or moment conditions.
- 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: Orthogonal Polynomials Triple: [Gábor Szegő, notableWork, Orthogonal Polynomials]
Generated description
Orthogonal Polynomials is a classic mathematical monograph by Gábor Szegő that systematically develops the theory and applications of orthogonal polynomial systems in analysis and approximation theory.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Orthogonal Polynomials Target entity description: Orthogonal Polynomials is a classic mathematical monograph by Gábor Szegő that systematically develops the theory and applications of orthogonal polynomial systems in analysis and approximation theory.
-
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.
Carathéodory–Fejér interpolation
Carathéodory–Fejér interpolation is a classical result in complex analysis and approximation theory that concerns constructing analytic functions, typically with bounded or positive real part, that match prescribed initial Taylor coefficients.
-
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.
Selberg integral
The Selberg integral is a fundamental multidimensional generalization of Euler’s beta integral that plays a central role in random matrix theory, combinatorics, and special functions.
-
E.
Bernstein inequalities
Bernstein inequalities are fundamental results in approximation theory and probability that provide bounds on the derivatives or deviations of functions and random variables under certain smoothness or moment conditions.
- 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_69bd4636f1648190a701445c2fcd9c17 |
completed | March 20, 2026, 1:05 p.m. |
| NER | Named-entity recognition | batch_69bd581160e08190b715a8ce5c3e6c9b |
completed | March 20, 2026, 2:22 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69bdb95b01b0819094a600752e41aa09 |
completed | March 20, 2026, 9:17 p.m. |
| NEDg | Description generation | batch_69bdbdbf73508190b64a78ff9274ee6d |
completed | March 20, 2026, 9:35 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69bdbe1bcd8c819094adea59c91c6f5b |
completed | March 20, 2026, 9:37 p.m. |
Created at: March 20, 2026, 1:09 p.m.