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.