Triple
T2364664
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Riemann–Liouville integral |
E47352
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Riemann–Liouville derivative |
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 derivative | Statement: [Riemann–Liouville integral, relatedTo, Riemann–Liouville derivative]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Riemann–Liouville derivative Context triple: [Riemann–Liouville integral, relatedTo, Riemann–Liouville derivative]
-
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.
Radon–Nikodym derivative
The Radon–Nikodym derivative is a function that represents how one measure changes with respect to another absolutely continuous measure, playing a central role in modern probability theory and measure theory.
-
C.
Lie derivative
The Lie derivative is a fundamental differential operator in differential geometry that measures how a tensor field changes along the flow generated by a vector field.
-
D.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
-
E.
d’Alembert’s formula
d’Alembert’s formula is a classical solution method for the one-dimensional wave equation that expresses the displacement of a vibrating string in terms of its initial shape and velocity.
- 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_69aea896e0388190aabff2d70787dc43 |
completed | March 9, 2026, 11:01 a.m. |
Created at: March 4, 2026, 7:55 p.m.