Triple

T2364655
Position Surface form Disambiguated ID Type / Status
Subject Riemann–Liouville integral E47352 entity
Predicate hasVariant P455 FINISHED
Object right-sided Riemann–Liouville integral 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: right-sided Riemann–Liouville integral | Statement: [Riemann–Liouville integral, hasVariant, right-sided Riemann–Liouville integral]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: right-sided Riemann–Liouville integral
Context triple: [Riemann–Liouville integral, hasVariant, right-sided Riemann–Liouville integral]
  • 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. 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.
  • 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. Caputo derivative
    The Caputo derivative is a commonly used definition of a fractional derivative that modifies the Riemann–Liouville approach to allow for more physically meaningful initial conditions in differential equations.
  • 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_69a88a1a4a6081908645b0f2914521ab completed March 4, 2026, 7:38 p.m.
NER Named-entity recognition batch_69abc7486cb48190acef1891cc87bdb1 completed March 7, 2026, 6:35 a.m.
NED1 Entity disambiguation (via context triple) batch_69aeb3c5c4b881909ad3223206fb2940 completed March 9, 2026, 11:49 a.m.
Created at: March 4, 2026, 7:55 p.m.