Triple

T2252108
Position Surface form Disambiguated ID Type / Status
Subject Atle Selberg E49639 entity
Predicate knownFor P22 FINISHED
Object 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.
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: Selberg integral | Statement: [Atle Selberg, knownFor, Selberg integral]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Selberg integral
Context triple: [Atle Selberg, knownFor, Selberg integral]
  • A. Riemann–Siegel formula
    The Riemann–Siegel formula is an asymptotic expression that efficiently approximates the Riemann zeta function on the critical line, playing a key role in the numerical study of its zeros.
  • B. Riemann zeta function
    The Riemann zeta function is a complex-valued function central to analytic number theory, whose properties—especially the distribution of its zeros—are deeply connected to the distribution of prime numbers.
  • C. Hardy Z-function
    The Hardy Z-function is a real-valued function derived from the Riemann zeta function on the critical line, used extensively in the study of the distribution of its zeros and the Riemann Hypothesis.
  • D. Rogers–Ramanujan-type identities
    Rogers–Ramanujan-type identities are a class of deep q-series and partition identities generalizing the classical Rogers–Ramanujan identities, with rich connections to combinatorics, number theory, and modular forms.
  • 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: Selberg integral
Triple: [Atle Selberg, knownFor, Selberg integral]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Selberg integral
Target entity description: 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.
  • A. Riemann–Siegel formula
    The Riemann–Siegel formula is an asymptotic expression that efficiently approximates the Riemann zeta function on the critical line, playing a key role in the numerical study of its zeros.
  • B. Riemann zeta function
    The Riemann zeta function is a complex-valued function central to analytic number theory, whose properties—especially the distribution of its zeros—are deeply connected to the distribution of prime numbers.
  • C. Hardy Z-function
    The Hardy Z-function is a real-valued function derived from the Riemann zeta function on the critical line, used extensively in the study of the distribution of its zeros and the Riemann Hypothesis.
  • D. Rogers–Ramanujan-type identities
    Rogers–Ramanujan-type identities are a class of deep q-series and partition identities generalizing the classical Rogers–Ramanujan identities, with rich connections to combinatorics, number theory, and modular forms.
  • 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_69a88aaa9250819095e127d0d77e8a32 completed March 4, 2026, 7:40 p.m.
NER Named-entity recognition batch_69abc11eb2708190bc5a3d152a3bb133 completed March 7, 2026, 6:09 a.m.
NED1 Entity disambiguation (via context triple) batch_69ae6b1bc424819087b2ce9a6256a180 completed March 9, 2026, 6:39 a.m.
NEDg Description generation batch_69ae6be0d108819085cf8c531d08db65 completed March 9, 2026, 6:42 a.m.
NED2 Entity disambiguation (via description) batch_69ae6c0fc220819090b254cc20b1bc26 completed March 9, 2026, 6:43 a.m.
Created at: March 4, 2026, 7:47 p.m.