Triple
T10991190
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | random matrix theory |
E259756
|
entity |
| Predicate | hasKeyConcept |
P533
|
FINISHED |
| Object |
Tracy–Widom distribution
The Tracy–Widom distribution is a probability distribution that describes the fluctuations of the largest eigenvalue in many classes of large random matrices and appears widely in random matrix theory and related probabilistic limit theorems.
|
E898464
|
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: Tracy–Widom distribution | Statement: [random matrix theory, hasKeyConcept, Tracy–Widom distribution]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Tracy–Widom distribution Context triple: [random matrix theory, hasKeyConcept, Tracy–Widom distribution]
-
A.
Wigner surmise
The Wigner surmise is an approximate formula in random matrix theory that describes the statistical distribution of spacings between neighboring energy levels in complex quantum systems.
-
B.
Gaussian unitary ensemble
The Gaussian unitary ensemble is a fundamental random matrix ensemble of complex Hermitian matrices with statistically independent, Gaussian-distributed entries, central to quantum chaos and random matrix theory.
-
C.
Jacobi ensemble
The Jacobi ensemble is a family of random matrix models whose eigenvalue distributions are supported on a finite interval and are closely connected to classical orthogonal polynomials and beta-type probability measures.
-
D.
Gaussian orthogonal ensemble
The Gaussian orthogonal ensemble is a fundamental random matrix ensemble of real symmetric matrices with Gaussian-distributed entries, central to the study of eigenvalue statistics and universality in random matrix theory.
-
E.
Tukey's lambda distribution
Tukey's lambda distribution is a flexible family of probability distributions used primarily for exploratory data analysis and modeling diverse shapes of data, including varying degrees of skewness and kurtosis.
- 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: Tracy–Widom distribution Triple: [random matrix theory, hasKeyConcept, Tracy–Widom distribution]
Generated description
The Tracy–Widom distribution is a probability distribution that describes the fluctuations of the largest eigenvalue in many classes of large random matrices and appears widely in random matrix theory and related probabilistic limit theorems.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Tracy–Widom distribution Target entity description: The Tracy–Widom distribution is a probability distribution that describes the fluctuations of the largest eigenvalue in many classes of large random matrices and appears widely in random matrix theory and related probabilistic limit theorems.
-
A.
Wigner surmise
The Wigner surmise is an approximate formula in random matrix theory that describes the statistical distribution of spacings between neighboring energy levels in complex quantum systems.
-
B.
Gaussian unitary ensemble
The Gaussian unitary ensemble is a fundamental random matrix ensemble of complex Hermitian matrices with statistically independent, Gaussian-distributed entries, central to quantum chaos and random matrix theory.
-
C.
Jacobi ensemble
The Jacobi ensemble is a family of random matrix models whose eigenvalue distributions are supported on a finite interval and are closely connected to classical orthogonal polynomials and beta-type probability measures.
-
D.
Gaussian orthogonal ensemble
The Gaussian orthogonal ensemble is a fundamental random matrix ensemble of real symmetric matrices with Gaussian-distributed entries, central to the study of eigenvalue statistics and universality in random matrix theory.
-
E.
Tukey's lambda distribution
Tukey's lambda distribution is a flexible family of probability distributions used primarily for exploratory data analysis and modeling diverse shapes of data, including varying degrees of skewness and kurtosis.
- 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.