Triple
T18480214
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Toeplitz matrix |
E451536
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Szegő limit theorem |
—
|
NE NERFINISHED |
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: Szegő limit theorem | Statement: [Toeplitz matrix, relatedTo, Szegő limit theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Szegő limit theorem Context triple: [Toeplitz matrix, relatedTo, Szegő limit theorem]
-
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.
Szegő polynomials
Szegő polynomials are a fundamental family of orthogonal polynomials on the unit circle that play a key role in complex analysis, approximation theory, and spectral theory.
-
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.
Tauberian theorems
Tauberian theorems are results in mathematical analysis that connect the behavior of transformed series or integrals (such as those summed by Abel or Cesàro methods) back to the asymptotic behavior or convergence of the original sequences or series.
-
E.
Fisher–Hartwig conjecture
The Fisher–Hartwig conjecture is a result in mathematical analysis that predicts the asymptotic behavior of Toeplitz determinants with singular symbols, extending the classical Szegő limit theorem.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (2 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. |
Created at: April 10, 2026, 11:35 a.m.