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.