Triple

T17752838
Position Surface form Disambiguated ID Type / Status
Subject Gaussian orthogonal ensemble E443153 entity
Predicate scalingLimit P9149 FINISHED
Object Airy kernel at the soft edge
The Airy kernel at the soft edge is a universal correlation kernel describing the local eigenvalue statistics near the largest eigenvalues (soft edge) of large random matrices in ensembles such as the Gaussian orthogonal ensemble.
E1284826 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: Airy kernel at the soft edge | Statement: [Gaussian orthogonal ensemble, scalingLimit, Airy kernel at the soft edge]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Airy kernel at the soft edge
Context triple: [Gaussian orthogonal ensemble, scalingLimit, Airy kernel at the soft edge]
  • A. 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.
  • B. Wigner semicircle law
    The Wigner semicircle law is a fundamental result in random matrix theory that describes how the eigenvalues of large random symmetric (or Hermitian) matrices are distributed according to a characteristic semicircular density.
  • C. Selberg integral
    The Selberg integral is a fundamental multidimensional generalization of Euler’s beta integral that plays a central role in random matrix theory, combinatorics, and special functions.
  • D. Wigner matrices
    Wigner matrices are large random symmetric (or Hermitian) matrices with independent, identically distributed entries (up to symmetry) that serve as a fundamental model in random matrix theory for studying eigenvalue statistics and universal spectral behavior.
  • E. 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.
  • 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: Airy kernel at the soft edge
Triple: [Gaussian orthogonal ensemble, scalingLimit, Airy kernel at the soft edge]
Generated description
The Airy kernel at the soft edge is a universal correlation kernel describing the local eigenvalue statistics near the largest eigenvalues (soft edge) of large random matrices in ensembles such as the Gaussian orthogonal ensemble.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Airy kernel at the soft edge
Target entity description: The Airy kernel at the soft edge is a universal correlation kernel describing the local eigenvalue statistics near the largest eigenvalues (soft edge) of large random matrices in ensembles such as the Gaussian orthogonal ensemble.
  • A. 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.
  • B. Wigner semicircle law
    The Wigner semicircle law is a fundamental result in random matrix theory that describes how the eigenvalues of large random symmetric (or Hermitian) matrices are distributed according to a characteristic semicircular density.
  • C. Selberg integral
    The Selberg integral is a fundamental multidimensional generalization of Euler’s beta integral that plays a central role in random matrix theory, combinatorics, and special functions.
  • D. Wigner matrices
    Wigner matrices are large random symmetric (or Hermitian) matrices with independent, identically distributed entries (up to symmetry) that serve as a fundamental model in random matrix theory for studying eigenvalue statistics and universal spectral behavior.
  • E. 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.
  • 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_69d8b9edf16c8190a59ebd245d378f4f completed April 10, 2026, 8:50 a.m.
NER Named-entity recognition batch_69e4841c0540819093a32d759775c61f completed April 19, 2026, 7:28 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0243067e6c8190b94113eb4785faae completed May 11, 2026, 8:58 p.m.
NEDg Description generation batch_6a0244ca6b348190a1c68dc3bf873f1d completed May 11, 2026, 9:06 p.m.
NED2 Entity disambiguation (via description) batch_6a024530b5dc8190a4776863cc01babf completed May 11, 2026, 9:08 p.m.
Created at: April 10, 2026, 10:10 a.m.