Triple

T10462109
Position Surface form Disambiguated ID Type / Status
Subject Selberg integral E246700 entity
Predicate relatedTo P37 FINISHED
Object 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.
E865110 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: Jacobi ensemble | Statement: [Selberg integral, relatedTo, Jacobi ensemble]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Jacobi ensemble
Context triple: [Selberg integral, relatedTo, Jacobi ensemble]
  • A. 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.
  • B. 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.
  • C. 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.
  • D. Wishart distribution
    The Wishart distribution is a fundamental probability distribution over positive-definite matrices that generalizes the chi-squared distribution to multiple dimensions and underpins many multivariate statistical methods.
  • E. 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.
  • 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: Jacobi ensemble
Triple: [Selberg integral, relatedTo, Jacobi ensemble]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Jacobi ensemble
Target entity description: 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.
  • A. 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.
  • B. 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.
  • C. 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.
  • D. Wishart distribution
    The Wishart distribution is a fundamental probability distribution over positive-definite matrices that generalizes the chi-squared distribution to multiple dimensions and underpins many multivariate statistical methods.
  • E. 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.
  • 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_69d381c16c248190a2fe5b471e584e9c completed April 6, 2026, 9:49 a.m.
NER Named-entity recognition batch_69d50884fac48190af22e181b1492557 completed April 7, 2026, 1:37 p.m.
NED1 Entity disambiguation (via context triple) batch_69d89fcc84b48190a39de0d9b9111ebd completed April 10, 2026, 6:59 a.m.
NEDg Description generation batch_69d8a1656b348190ba932d03402d6a4d completed April 10, 2026, 7:06 a.m.
NED2 Entity disambiguation (via description) batch_69d8a2b82bb48190899f37a967fef444 completed April 10, 2026, 7:11 a.m.
Created at: April 6, 2026, 12:19 p.m.