Triple

T10462106
Position Surface form Disambiguated ID Type / Status
Subject Selberg integral E246700 entity
Predicate relatedTo P37 FINISHED
Object Dyson integral
The Dyson integral is a multidimensional integral arising in random matrix theory and statistical physics that evaluates averages over eigenvalue distributions with logarithmic interactions.
E865109 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: Dyson integral | Statement: [Selberg integral, relatedTo, Dyson integral]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Dyson integral
Context triple: [Selberg integral, relatedTo, Dyson integral]
  • A. Dyson’s formula
    Dyson’s formula is a key expression in quantum field theory that provides the perturbative expansion of time-ordered exponentials, forming the basis of the Dyson series used to compute interaction effects.
  • B. Poisson integral
    The Poisson integral is a fundamental formula in harmonic analysis that reconstructs harmonic functions inside a disk (or half-plane) from their boundary values using the Poisson kernel.
  • C. Dyson index β
    The Dyson index β is a parameter in random matrix theory that classifies ensembles by their underlying symmetry, typically taking values 1, 2, or 4 for orthogonal, unitary, and symplectic ensembles, respectively.
  • D. Dyson series
    The Dyson series is a perturbative expansion in quantum field theory that expresses time-ordered exponentials and scattering amplitudes as an infinite series of integrals, each term corresponding to a Feynman diagram.
  • E. Fresnel integrals
    Fresnel integrals are special functions in mathematics that describe the complex oscillatory behavior of wave diffraction and interference, particularly in optics.
  • 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: Dyson integral
Triple: [Selberg integral, relatedTo, Dyson integral]
Generated description
The Dyson integral is a multidimensional integral arising in random matrix theory and statistical physics that evaluates averages over eigenvalue distributions with logarithmic interactions.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Dyson integral
Target entity description: The Dyson integral is a multidimensional integral arising in random matrix theory and statistical physics that evaluates averages over eigenvalue distributions with logarithmic interactions.
  • A. Dyson’s formula
    Dyson’s formula is a key expression in quantum field theory that provides the perturbative expansion of time-ordered exponentials, forming the basis of the Dyson series used to compute interaction effects.
  • B. Poisson integral
    The Poisson integral is a fundamental formula in harmonic analysis that reconstructs harmonic functions inside a disk (or half-plane) from their boundary values using the Poisson kernel.
  • C. Dyson index β
    The Dyson index β is a parameter in random matrix theory that classifies ensembles by their underlying symmetry, typically taking values 1, 2, or 4 for orthogonal, unitary, and symplectic ensembles, respectively.
  • D. Dyson series
    The Dyson series is a perturbative expansion in quantum field theory that expresses time-ordered exponentials and scattering amplitudes as an infinite series of integrals, each term corresponding to a Feynman diagram.
  • E. Fresnel integrals
    Fresnel integrals are special functions in mathematics that describe the complex oscillatory behavior of wave diffraction and interference, particularly in optics.
  • 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.