Triple

T18479245
Position Surface form Disambiguated ID Type / Status
Subject theory of divergent series E451513 entity
Predicate hasHistoricalFigure P643 FINISHED
Object Ernst Cesàro
Ernst Cesàro was a Belgian mathematician known for his influential work in summability theory and the study of divergent series.
E1325979 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: Ernst Cesàro | Statement: [theory of divergent series, hasHistoricalFigure, Ernst Cesàro]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Ernst Cesàro
Context triple: [theory of divergent series, hasHistoricalFigure, Ernst Cesàro]
  • A. Ulisse Dini
    Ulisse Dini was an Italian mathematician known for his contributions to real analysis and the theory of functions, including Dini's theorem on uniform convergence.
  • B. Enrico Betti
    Enrico Betti was a 19th-century Italian mathematician best known for his foundational work in topology, particularly the introduction of Betti numbers.
  • C. Guido Fubini
    Guido Fubini was an Italian mathematician best known for his foundational work in analysis and for formulating Fubini's theorem on the interchange of order of integration.
  • D. Giuseppe Peano
    Giuseppe Peano was an Italian mathematician and logician best known for his foundational work in mathematical logic, the formalization of arithmetic (including the Peano axioms), and contributions to the development of modern symbolic notation.
  • E. Eugenio Beltrami
    Eugenio Beltrami was a 19th-century Italian mathematician best known for providing the first rigorous models of non-Euclidean geometry, helping to establish its consistency and significance in modern mathematics.
  • 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: Ernst Cesàro
Triple: [theory of divergent series, hasHistoricalFigure, Ernst Cesàro]
Generated description
Ernst Cesàro was a Belgian mathematician known for his influential work in summability theory and the study of divergent series.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Ernst Cesàro
Target entity description: Ernst Cesàro was a Belgian mathematician known for his influential work in summability theory and the study of divergent series.
  • A. Ulisse Dini
    Ulisse Dini was an Italian mathematician known for his contributions to real analysis and the theory of functions, including Dini's theorem on uniform convergence.
  • B. Enrico Betti
    Enrico Betti was a 19th-century Italian mathematician best known for his foundational work in topology, particularly the introduction of Betti numbers.
  • C. Guido Fubini
    Guido Fubini was an Italian mathematician best known for his foundational work in analysis and for formulating Fubini's theorem on the interchange of order of integration.
  • D. Giuseppe Peano
    Giuseppe Peano was an Italian mathematician and logician best known for his foundational work in mathematical logic, the formalization of arithmetic (including the Peano axioms), and contributions to the development of modern symbolic notation.
  • E. Eugenio Beltrami
    Eugenio Beltrami was a 19th-century Italian mathematician best known for providing the first rigorous models of non-Euclidean geometry, helping to establish its consistency and significance in modern mathematics.
  • 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_69d8d38465a0819099b9b42d2a662ac1 completed April 10, 2026, 10:40 a.m.
NER Named-entity recognition batch_69e53065e8388190bb216dae89f8cf75 completed April 19, 2026, 7:43 p.m.
NED1 Entity disambiguation (via context triple) batch_6a043f2f64848190808075254008e6e1 completed May 13, 2026, 9:06 a.m.
NEDg Description generation batch_6a043fb7db388190bb50cfade4f025f9 completed May 13, 2026, 9:09 a.m.
NED2 Entity disambiguation (via description) batch_6a044063c6048190b65620af8ceed897 completed May 13, 2026, 9:12 a.m.
Created at: April 10, 2026, 11:35 a.m.