Triple
T18480352
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Szegő limit theorem |
E451539
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
Szegő–Kolmogorov formula
The Szegő–Kolmogorov formula is a fundamental result in prediction theory and stationary stochastic processes that expresses the minimum mean-square prediction error in terms of the spectral density of the process.
|
E451539
|
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: Szegő–Kolmogorov formula | Statement: [Szegő limit theorem, relatedTo, Szegő–Kolmogorov formula]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Szegő–Kolmogorov formula Context triple: [Szegő limit theorem, relatedTo, Szegő–Kolmogorov formula]
-
A.
Szegő limit theorem
The Szegő limit theorem is a fundamental result in analysis and operator theory that describes the asymptotic behavior of determinants of large Toeplitz matrices in terms of the symbol’s integral.
-
B.
Christoffel–Darboux formula
The Christoffel–Darboux formula is a key result in the theory of orthogonal polynomials that provides an explicit expression for sums of products of such polynomials, with important applications in approximation theory and mathematical physics.
-
C.
Szegő kernel
The Szegő kernel is a fundamental reproducing kernel in complex analysis and operator theory, associated with Hardy spaces on the boundary of a domain and central to the study of orthogonal polynomials and boundary behavior of analytic functions.
-
D.
Christoffel–Schwarz formula
The Christoffel–Schwarz formula is a fundamental result in complex analysis that provides an explicit conformal mapping from the upper half-plane onto polygonal regions in the complex plane.
-
E.
Bochner–Martinelli formula
The Bochner–Martinelli formula is a fundamental integral representation in several complex variables that generalizes the Cauchy integral formula to higher dimensions.
- 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: Szegő–Kolmogorov formula Triple: [Szegő limit theorem, relatedTo, Szegő–Kolmogorov formula]
Generated description
The Szegő–Kolmogorov formula is a fundamental result in prediction theory and stationary stochastic processes that expresses the minimum mean-square prediction error in terms of the spectral density of the process.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Szegő–Kolmogorov formula Target entity description: The Szegő–Kolmogorov formula is a fundamental result in prediction theory and stationary stochastic processes that expresses the minimum mean-square prediction error in terms of the spectral density of the process.
-
A.
Szegő limit theorem
chosen
The Szegő limit theorem is a fundamental result in analysis and operator theory that describes the asymptotic behavior of determinants of large Toeplitz matrices in terms of the symbol’s integral.
-
B.
Christoffel–Darboux formula
The Christoffel–Darboux formula is a key result in the theory of orthogonal polynomials that provides an explicit expression for sums of products of such polynomials, with important applications in approximation theory and mathematical physics.
-
C.
Szegő kernel
The Szegő kernel is a fundamental reproducing kernel in complex analysis and operator theory, associated with Hardy spaces on the boundary of a domain and central to the study of orthogonal polynomials and boundary behavior of analytic functions.
-
D.
Christoffel–Schwarz formula
The Christoffel–Schwarz formula is a fundamental result in complex analysis that provides an explicit conformal mapping from the upper half-plane onto polygonal regions in the complex plane.
-
E.
Bochner–Martinelli formula
The Bochner–Martinelli formula is a fundamental integral representation in several complex variables that generalizes the Cauchy integral formula to higher dimensions.
- F. None of above.
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_69d8d38465a0819099b9b42d2a662ac1 |
completed | April 10, 2026, 10:40 a.m. |
| NER | Named-entity recognition | batch_69e53066a7108190a50eda9b489c90ca |
completed | April 19, 2026, 7:43 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a043f2f64848190808075254008e6e1 |
completed | May 13, 2026, 9:06 a.m. |
| NEDg | Description generation | batch_6a043fb7db388190bb50cfade4f025f9 |
completed | May 13, 2026, 9:09 a.m. |
| NED2 | Entity disambiguation (via description) | batch_6a044063c6048190b65620af8ceed897 |
completed | May 13, 2026, 9:12 a.m. |
Created at: April 10, 2026, 11:35 a.m.