Triple

T10462105
Position Surface form Disambiguated ID Type / Status
Subject Selberg integral E246700 entity
Predicate relatedTo P37 FINISHED
Object Mehta integral
The Mehta integral is a key multidimensional integral in random matrix theory that evaluates averages over eigenvalue distributions and underpins many results about spectral statistics.
E246700 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: Mehta integral | Statement: [Selberg integral, relatedTo, Mehta integral]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Mehta integral
Context triple: [Selberg integral, relatedTo, Mehta integral]
  • A. Riemann–Liouville integral
    The Riemann–Liouville integral is a fundamental operator in fractional calculus that generalizes the concept of an n-fold repeated integral to non-integer (fractional) orders.
  • B. Riemann–Stieltjes integral
    The Riemann–Stieltjes integral is a generalization of the Riemann integral in which integration is taken with respect to a function of bounded variation rather than just the identity function, allowing more flexible treatment of sums and distributions.
  • C. 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.
  • D. 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.
  • E. Mittag-Leffler function
    The Mittag-Leffler function is a complex function that generalizes the exponential function and plays a central role in fractional calculus and the theory of differential and integral equations.
  • 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: Mehta integral
Triple: [Selberg integral, relatedTo, Mehta integral]
Generated description
The Mehta integral is a key multidimensional integral in random matrix theory that evaluates averages over eigenvalue distributions and underpins many results about spectral statistics.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Mehta integral
Target entity description: The Mehta integral is a key multidimensional integral in random matrix theory that evaluates averages over eigenvalue distributions and underpins many results about spectral statistics.
  • A. Riemann–Liouville integral
    The Riemann–Liouville integral is a fundamental operator in fractional calculus that generalizes the concept of an n-fold repeated integral to non-integer (fractional) orders.
  • B. Riemann–Stieltjes integral
    The Riemann–Stieltjes integral is a generalization of the Riemann integral in which integration is taken with respect to a function of bounded variation rather than just the identity function, allowing more flexible treatment of sums and distributions.
  • C. 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.
  • D. Selberg integral chosen
    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.
  • E. Mittag-Leffler function
    The Mittag-Leffler function is a complex function that generalizes the exponential function and plays a central role in fractional calculus and the theory of differential and integral equations.
  • F. None of above.

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.