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.