Triple
T18480350
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Szegő limit theorem |
E451539
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
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.
|
E1326020
|
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: Fisher–Hartwig conjecture | Statement: [Szegő limit theorem, relatedTo, Fisher–Hartwig conjecture]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Fisher–Hartwig conjecture Context triple: [Szegő limit theorem, relatedTo, Fisher–Hartwig conjecture]
-
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.
Borg–Marchenko theorem
The Borg–Marchenko theorem is a fundamental result in inverse spectral theory that characterizes when a potential in a one-dimensional Schrödinger operator is uniquely determined by its spectral data.
-
C.
May–Wigner stability theorem
The May–Wigner stability theorem is a result in theoretical ecology and random matrix theory showing that large, complex systems with many random interactions are generically unstable beyond a critical level of complexity.
-
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.
Wiener–Hopf equations
Wiener–Hopf equations are integral equations that arise in problems of filtering, prediction, and diffraction, forming the mathematical foundation for optimal linear filters such as the Wiener filter.
- 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: Fisher–Hartwig conjecture Triple: [Szegő limit theorem, relatedTo, Fisher–Hartwig conjecture]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Fisher–Hartwig conjecture Target entity description: 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.
-
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.
Borg–Marchenko theorem
The Borg–Marchenko theorem is a fundamental result in inverse spectral theory that characterizes when a potential in a one-dimensional Schrödinger operator is uniquely determined by its spectral data.
-
C.
May–Wigner stability theorem
The May–Wigner stability theorem is a result in theoretical ecology and random matrix theory showing that large, complex systems with many random interactions are generically unstable beyond a critical level of complexity.
-
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.
Wiener–Hopf equations
Wiener–Hopf equations are integral equations that arise in problems of filtering, prediction, and diffraction, forming the mathematical foundation for optimal linear filters such as the Wiener filter.
- 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_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.