Triple

T5225668
Position Surface form Disambiguated ID Type / Status
Subject Gösta Mittag-Leffler E117978 entity
Predicate hasConceptNamedAfter P3325 FINISHED
Object 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.
E503871 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: Mittag-Leffler function | Statement: [Gösta Mittag-Leffler, hasConceptNamedAfter, Mittag-Leffler function]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Mittag-Leffler function
Context triple: [Gösta Mittag-Leffler, hasConceptNamedAfter, Mittag-Leffler function]
  • A. Mittag-Leffler theorem
    The Mittag-Leffler theorem is a fundamental result in complex analysis that characterizes meromorphic functions by allowing the construction of such functions with prescribed principal parts at given poles.
  • B. 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.
  • 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. Weierstrass factorization theorem
    The Weierstrass factorization theorem is a fundamental result in complex analysis that expresses any entire function as an infinite product determined by its zeros, generalizing the factorization of polynomials.
  • E. Gamma function
    The Gamma function is a fundamental extension of the factorial function to complex and real non-integer arguments, widely used in analysis, probability, and mathematical physics.
  • 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: Mittag-Leffler function
Triple: [Gösta Mittag-Leffler, hasConceptNamedAfter, Mittag-Leffler function]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Mittag-Leffler function
Target entity description: 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.
  • A. Mittag-Leffler theorem
    The Mittag-Leffler theorem is a fundamental result in complex analysis that characterizes meromorphic functions by allowing the construction of such functions with prescribed principal parts at given poles.
  • B. 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.
  • 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. Weierstrass factorization theorem
    The Weierstrass factorization theorem is a fundamental result in complex analysis that expresses any entire function as an infinite product determined by its zeros, generalizing the factorization of polynomials.
  • E. Gamma function
    The Gamma function is a fundamental extension of the factorial function to complex and real non-integer arguments, widely used in analysis, probability, and mathematical physics.
  • 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_69bd4465e03081909bfcfd7113062590 completed March 20, 2026, 12:58 p.m.
NER Named-entity recognition batch_69bd7adc9be081909903b9f844c3d146 completed March 20, 2026, 4:50 p.m.
NED1 Entity disambiguation (via context triple) batch_69beeffc51888190938dc157b14c4b6c completed March 21, 2026, 7:22 p.m.
NEDg Description generation batch_69bef0b2b6448190be1c465738be741b completed March 21, 2026, 7:25 p.m.
NED2 Entity disambiguation (via description) batch_69bef121817c8190aebd27ee34c0a419 completed March 21, 2026, 7:27 p.m.
Created at: March 20, 2026, 1:48 p.m.