Triple

T2364647
Position Surface form Disambiguated ID Type / Status
Subject Riemann–Liouville integral E47352 entity
Predicate namedAfter P63 FINISHED
Object Joseph Liouville
Joseph Liouville was a 19th-century French mathematician known for foundational contributions to number theory, complex analysis, and the early development of fractional calculus.
 E259776 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: Joseph Liouville | Statement: [Riemann–Liouville integral, namedAfter, Joseph Liouville]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Joseph Liouville
Context triple: [Riemann–Liouville integral, namedAfter, Joseph Liouville]
  • A. Charles Hermite
    Charles Hermite was a 19th-century French mathematician renowned for his work in number theory, algebra, and analysis, including the first proof that e is a transcendental number.
  • B. Jacques Hadamard
    Jacques Hadamard was a prominent French mathematician known for his fundamental contributions to number theory, complex analysis, and partial differential equations, including the prime number theorem and the concept of well-posed problems.
  • C. Maxime Bôcher
    Maxime Bôcher was an American mathematician known for his work in differential equations and analysis, and for his influential role in early 20th-century American mathematics.
  • D. Augustin-Louis Cauchy
    Augustin-Louis Cauchy was a pioneering 19th-century French mathematician whose rigorous foundations for calculus and complex analysis profoundly shaped modern mathematics.
  • E. Adrien-Marie Legendre
    Adrien-Marie Legendre was an influential 18th–19th century French mathematician known for major contributions to number theory, analysis, and mathematical statistics.
  • 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: Joseph Liouville
Triple: [Riemann–Liouville integral, namedAfter, Joseph Liouville]
Generated description
Joseph Liouville was a 19th-century French mathematician known for foundational contributions to number theory, complex analysis, and the early development of fractional calculus.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: Joseph Liouville
Target entity description: Joseph Liouville was a 19th-century French mathematician known for foundational contributions to number theory, complex analysis, and the early development of fractional calculus.
  • A. Charles Hermite
    Charles Hermite was a 19th-century French mathematician renowned for his work in number theory, algebra, and analysis, including the first proof that e is a transcendental number.
  • B. Jacques Hadamard
    Jacques Hadamard was a prominent French mathematician known for his fundamental contributions to number theory, complex analysis, and partial differential equations, including the prime number theorem and the concept of well-posed problems.
  • C. Maxime Bôcher
    Maxime Bôcher was an American mathematician known for his work in differential equations and analysis, and for his influential role in early 20th-century American mathematics.
  • D. Augustin-Louis Cauchy
    Augustin-Louis Cauchy was a pioneering 19th-century French mathematician whose rigorous foundations for calculus and complex analysis profoundly shaped modern mathematics.
  • E. Adrien-Marie Legendre
    Adrien-Marie Legendre was an influential 18th–19th century French mathematician known for major contributions to number theory, analysis, and mathematical statistics.
  • 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_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.
NEDg Description generation batch_69aea91ce164819091aa24b287f9fb8e completed March 9, 2026, 11:03 a.m.
NED2 Entity disambiguation (via description) batch_69aea999b864819084134c670e7c5d9c completed March 9, 2026, 11:06 a.m.
Created at: March 4, 2026, 7:55 p.m.