Triple
T7161972
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Vito Volterra |
E166967
|
entity |
| Predicate | knownFor |
P22
|
FINISHED |
| Object |
Volterra integral equations
Volterra integral equations are a class of integral equations, often used in physics and biology, where the integration limits involve a variable upper bound, modeling systems with memory or hereditary effects.
|
E645176
|
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: Volterra integral equations | Statement: [Vito Volterra, knownFor, Volterra integral equations]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Volterra integral equations Context triple: [Vito Volterra, knownFor, Volterra integral equations]
-
A.
Introduction to the Study of Integral Equations
"Introduction to the Study of Integral Equations" is a foundational mathematical text by Maxime Bôcher that systematically develops the theory and applications of integral equations.
-
B.
Wiener–Hopf equations
Wiener–Hopf equations are integral equations that arise in problems of filtering, prediction, and diffraction, forming the mathematical foundation for optimal linear filters such as the Wiener filter.
-
C.
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.
-
D.
Gelfand–Levitan theory
Gelfand–Levitan theory is a foundational framework in inverse spectral theory that reconstructs differential operators or potentials from their spectral data using integral equations.
-
E.
Green's functions
Green's functions are mathematical tools used in physics and engineering to solve inhomogeneous differential equations and describe the propagation of fields or particles in space and time.
- 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: Volterra integral equations Triple: [Vito Volterra, knownFor, Volterra integral equations]
Generated description
Volterra integral equations are a class of integral equations, often used in physics and biology, where the integration limits involve a variable upper bound, modeling systems with memory or hereditary effects.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Volterra integral equations Target entity description: Volterra integral equations are a class of integral equations, often used in physics and biology, where the integration limits involve a variable upper bound, modeling systems with memory or hereditary effects.
-
A.
Introduction to the Study of Integral Equations
"Introduction to the Study of Integral Equations" is a foundational mathematical text by Maxime Bôcher that systematically develops the theory and applications of integral equations.
-
B.
Wiener–Hopf equations
Wiener–Hopf equations are integral equations that arise in problems of filtering, prediction, and diffraction, forming the mathematical foundation for optimal linear filters such as the Wiener filter.
-
C.
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.
-
D.
Gelfand–Levitan theory
Gelfand–Levitan theory is a foundational framework in inverse spectral theory that reconstructs differential operators or potentials from their spectral data using integral equations.
-
E.
Green's functions
Green's functions are mathematical tools used in physics and engineering to solve inhomogeneous differential equations and describe the propagation of fields or particles in space and time.
- 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_69c68887a5cc8190bec0ea96227164f7 |
completed | March 27, 2026, 1:39 p.m. |
| NER | Named-entity recognition | batch_69c6e82e4b248190ad3c3863cb93971e |
completed | March 27, 2026, 8:27 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c7adc4b7648190969fab0351f9fd22 |
completed | March 28, 2026, 10:30 a.m. |
| NEDg | Description generation | batch_69c7ae44e0d48190818b193e03aba6a4 |
completed | March 28, 2026, 10:32 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69c7aeb68c3481909c6dff8ee51349ab |
completed | March 28, 2026, 10:34 a.m. |
Created at: March 27, 2026, 2:47 p.m.