Triple

T10992313
Position Surface form Disambiguated ID Type / Status
Subject Hadamard fractional integral E259779 entity
Predicate contrastsWith P278 FINISHED
Object Riemann–Liouville integral on additive domains E47352 NE FINISHED

How this triple was built (2 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: Riemann–Liouville integral on additive domains | Statement: [Hadamard fractional integral, contrastsWith, Riemann–Liouville integral on additive domains]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Riemann–Liouville integral on additive domains
Context triple: [Hadamard fractional integral, contrastsWith, Riemann–Liouville integral on additive domains]
  • A. Riemann–Liouville integral chosen
    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. Hadamard fractional integral
    The Hadamard fractional integral is a generalization of the classical integral that defines fractional-order integration using logarithmic kernels, particularly suited to functions defined on multiplicative (e.g., positive real) domains.
  • C. Henstock–Kurzweil integral
    The Henstock–Kurzweil integral is a highly general integration theory that extends and refines the Riemann integral, capable of integrating a broader class of functions while retaining many of the intuitive properties of Riemann integration.
  • D. 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.
  • E. Weyl fractional integral
    The Weyl fractional integral is a generalization of the classical integral to arbitrary (including non-integer) orders, defined on periodic functions or the whole real line and used in fractional calculus to model memory and hereditary properties in various systems.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69d6aa8a6a548190a750f944ccdc8064 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d795d32f9081909def643571499521 completed April 9, 2026, 12:04 p.m.
NED1 Entity disambiguation (via context triple) batch_69e34504ebec8190a78e4795765b0c24 completed April 18, 2026, 8:47 a.m.
Created at: April 8, 2026, 9:24 p.m.