Triple

T17752891
Position Surface form Disambiguated ID Type / Status
Subject Dyson index β E443154 entity
Predicate usedToLabel P127540 FINISHED
Object Laguerre β-ensembles
Laguerre β-ensembles are families of random matrix models generalizing the classical Laguerre (Wishart) ensembles to arbitrary Dyson index β, used to study eigenvalue statistics in mathematical physics and probability theory.
E1286384 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: Laguerre β-ensembles | Statement: [Dyson index β, usedToLabel, Laguerre β-ensembles]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Laguerre β-ensembles
Context triple: [Dyson index β, usedToLabel, Laguerre β-ensembles]
  • A. Gaussian β-ensembles
    Gaussian β-ensembles are families of random matrix models in which eigenvalue statistics depend continuously on a parameter β that governs the strength of eigenvalue repulsion and interpolates between classical matrix ensembles.
  • B. 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.
  • C. 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.
  • D. Gaussian symplectic ensemble
    The Gaussian symplectic ensemble is a random matrix ensemble of self-dual quaternionic Hermitian matrices used in random matrix theory to model systems with time-reversal symmetry and strong spin–orbit coupling.
  • E. 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.
  • 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: Laguerre β-ensembles
Triple: [Dyson index β, usedToLabel, Laguerre β-ensembles]
Generated description
Laguerre β-ensembles are families of random matrix models generalizing the classical Laguerre (Wishart) ensembles to arbitrary Dyson index β, used to study eigenvalue statistics in mathematical physics and probability theory.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Laguerre β-ensembles
Target entity description: Laguerre β-ensembles are families of random matrix models generalizing the classical Laguerre (Wishart) ensembles to arbitrary Dyson index β, used to study eigenvalue statistics in mathematical physics and probability theory.
  • A. Gaussian β-ensembles
    Gaussian β-ensembles are families of random matrix models in which eigenvalue statistics depend continuously on a parameter β that governs the strength of eigenvalue repulsion and interpolates between classical matrix ensembles.
  • B. 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.
  • C. 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.
  • D. Gaussian symplectic ensemble
    The Gaussian symplectic ensemble is a random matrix ensemble of self-dual quaternionic Hermitian matrices used in random matrix theory to model systems with time-reversal symmetry and strong spin–orbit coupling.
  • E. 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.
  • 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_6a02efb4df34819094718758196e8a9f completed May 12, 2026, 9:15 a.m.
NEDg Description generation batch_6a02f13826388190843c9844011b5824 completed May 12, 2026, 9:22 a.m.
NED2 Entity disambiguation (via description) batch_6a02f1a8e3d4819096050f66a4e0563b completed May 12, 2026, 9:23 a.m.
Created at: April 10, 2026, 10:10 a.m.