Triple
T10991198
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | random matrix theory |
E259756
|
entity |
| Predicate | hasKeyConcept |
P533
|
FINISHED |
| Object |
Stieltjes transform
The Stieltjes transform is an integral transform that encodes a measure or distribution via a complex-analytic function, widely used in random matrix theory to study limiting spectral distributions and resolvents.
|
E898466
|
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: Stieltjes transform | Statement: [random matrix theory, hasKeyConcept, Stieltjes transform]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Stieltjes transform Context triple: [random matrix theory, hasKeyConcept, Stieltjes transform]
-
A.
Mellin transforms
Mellin transforms are integral transforms that convert functions into complex-variable representations, playing a central role in analytic number theory by linking arithmetic functions to Dirichlet series and zeta functions.
-
B.
Hilbert transform
The Hilbert transform is an integral transform that produces the harmonic conjugate of a real-valued function, playing a central role in signal processing, harmonic analysis, and the theory of analytic signals.
-
C.
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.
-
D.
Mittag-Leffler function
The Mittag-Leffler function is a complex function that generalizes the exponential function and plays a central role in fractional calculus and the theory of differential and integral equations.
-
E.
Sommerfeld-Watson transform
The Sommerfeld-Watson transform is a complex-analysis technique that converts discrete sums over angular momentum into contour integrals, widely used in scattering theory and Regge theory to study analytic properties of amplitudes.
- 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: Stieltjes transform Triple: [random matrix theory, hasKeyConcept, Stieltjes transform]
Generated description
The Stieltjes transform is an integral transform that encodes a measure or distribution via a complex-analytic function, widely used in random matrix theory to study limiting spectral distributions and resolvents.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Stieltjes transform Target entity description: The Stieltjes transform is an integral transform that encodes a measure or distribution via a complex-analytic function, widely used in random matrix theory to study limiting spectral distributions and resolvents.
-
A.
Mellin transforms
Mellin transforms are integral transforms that convert functions into complex-variable representations, playing a central role in analytic number theory by linking arithmetic functions to Dirichlet series and zeta functions.
-
B.
Hilbert transform
The Hilbert transform is an integral transform that produces the harmonic conjugate of a real-valued function, playing a central role in signal processing, harmonic analysis, and the theory of analytic signals.
-
C.
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.
-
D.
Mittag-Leffler function
The Mittag-Leffler function is a complex function that generalizes the exponential function and plays a central role in fractional calculus and the theory of differential and integral equations.
-
E.
Sommerfeld-Watson transform
The Sommerfeld-Watson transform is a complex-analysis technique that converts discrete sums over angular momentum into contour integrals, widely used in scattering theory and Regge theory to study analytic properties of amplitudes.
- 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_69d6aa8a6a548190a750f944ccdc8064 |
completed | April 8, 2026, 7:20 p.m. |
| NER | Named-entity recognition | batch_69d787b8d7088190b7d6b63c3bac4ad1 |
completed | April 9, 2026, 11:04 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69e34504ebec8190a78e4795765b0c24 |
completed | April 18, 2026, 8:47 a.m. |
| NEDg | Description generation | batch_69e3556fd3548190a33f04604be947cf |
completed | April 18, 2026, 9:57 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69e3593b0f8481909ed7a90f8bb9839d |
completed | April 18, 2026, 10:13 a.m. |
Created at: April 8, 2026, 9:24 p.m.