Triple

T10992194
Position Surface form Disambiguated ID Type / Status
Subject Caputo derivative E259777 entity
Predicate modifies P1121 FINISHED
Object Riemann–Liouville derivative
The Riemann–Liouville derivative is a fundamental definition of fractional-order differentiation in fractional calculus, generalizing the classical derivative to non-integer orders via integral transforms.
E899968 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: Riemann–Liouville derivative | Statement: [Caputo derivative, modifies, Riemann–Liouville derivative]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Riemann–Liouville derivative
Context triple: [Caputo derivative, modifies, Riemann–Liouville derivative]
  • 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. Grünwald–Letnikov derivative
    The Grünwald–Letnikov derivative is a fundamental definition of fractional differentiation based on limit processes and finite differences, widely used as a foundation for fractional calculus.
  • C. 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.
  • D. 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.
  • 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. 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: Riemann–Liouville derivative
Triple: [Caputo derivative, modifies, Riemann–Liouville derivative]
Generated description
The Riemann–Liouville derivative is a fundamental definition of fractional-order differentiation in fractional calculus, generalizing the classical derivative to non-integer orders via integral transforms.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Riemann–Liouville derivative
Target entity description: The Riemann–Liouville derivative is a fundamental definition of fractional-order differentiation in fractional calculus, generalizing the classical derivative to non-integer orders via integral transforms.
  • 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. Grünwald–Letnikov derivative
    The Grünwald–Letnikov derivative is a fundamental definition of fractional differentiation based on limit processes and finite differences, widely used as a foundation for fractional calculus.
  • C. 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.
  • D. 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.
  • 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. 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_69d6aa8a6a548190a750f944ccdc8064 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d795d1e918819090c71f5a077fa15a completed April 9, 2026, 12:04 p.m.
NED1 Entity disambiguation (via context triple) batch_69e374639f1481908ea372b81a834f6f completed April 18, 2026, 12:09 p.m.
NEDg Description generation batch_69e37ab6ca788190ac41f9494ad9a47f completed April 18, 2026, 12:36 p.m.
NED2 Entity disambiguation (via description) batch_69e37c9439fc8190a69cfb1a13da4c19 completed April 18, 2026, 12:44 p.m.
Created at: April 8, 2026, 9:24 p.m.