Triple

T1057172
Position Surface form Disambiguated ID Type / Status
Subject local existence and uniqueness theorem E22820 entity
Predicate historicallyAssociatedWith P2830 FINISHED
Object Rudolf Lipschitz
Rudolf Lipschitz was a 19th-century German mathematician known for foundational work in analysis and differential equations, including the Lipschitz continuity condition that underpins key existence and uniqueness results.
 E138509 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: Rudolf Lipschitz | Statement: [local existence and uniqueness theorem, historicallyAssociatedWith, Rudolf Lipschitz]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Rudolf Lipschitz
Context triple: [local existence and uniqueness theorem, historicallyAssociatedWith, Rudolf Lipschitz]
  • A. Leopold Kronecker
    Leopold Kronecker was a 19th-century German mathematician known for his work in number theory, algebra, and logic, and for his influential finitist and constructivist views on mathematics.
  • B. Kurt Hensel
    Kurt Hensel was a German mathematician best known for introducing p-adic numbers, which became fundamental in number theory and algebraic geometry.
  • C. Felix Klein
    Felix Klein was a German mathematician renowned for his work in group theory, non-Euclidean geometry, and the Erlangen Program, which redefined the foundations of geometry.
  • D. Lazarus Fuchs
    Lazarus Fuchs was a 19th-century German mathematician known for his foundational work in complex analysis and the theory of differential equations, particularly Fuchsian groups and Fuchsian differential equations.
  • E. Wilhelm Wirtinger
    Wilhelm Wirtinger was an Austrian mathematician known for his contributions to complex analysis, algebraic geometry, and knot theory.
  • 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: Rudolf Lipschitz
Triple: [local existence and uniqueness theorem, historicallyAssociatedWith, Rudolf Lipschitz]
Generated description
Rudolf Lipschitz was a 19th-century German mathematician known for foundational work in analysis and differential equations, including the Lipschitz continuity condition that underpins key existence and uniqueness results.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: Rudolf Lipschitz
Target entity description: Rudolf Lipschitz was a 19th-century German mathematician known for foundational work in analysis and differential equations, including the Lipschitz continuity condition that underpins key existence and uniqueness results.
  • A. Leopold Kronecker
    Leopold Kronecker was a 19th-century German mathematician known for his work in number theory, algebra, and logic, and for his influential finitist and constructivist views on mathematics.
  • B. Kurt Hensel
    Kurt Hensel was a German mathematician best known for introducing p-adic numbers, which became fundamental in number theory and algebraic geometry.
  • C. Felix Klein
    Felix Klein was a German mathematician renowned for his work in group theory, non-Euclidean geometry, and the Erlangen Program, which redefined the foundations of geometry.
  • D. Lazarus Fuchs
    Lazarus Fuchs was a 19th-century German mathematician known for his foundational work in complex analysis and the theory of differential equations, particularly Fuchsian groups and Fuchsian differential equations.
  • E. Wilhelm Wirtinger
    Wilhelm Wirtinger was an Austrian mathematician known for his contributions to complex analysis, algebraic geometry, and knot theory.
  • 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_69a493dada0481909c43649f9843ea91 completed March 1, 2026, 7:30 p.m.
NER Named-entity recognition batch_69a4b8da80dc8190b79beaf509910725 completed March 1, 2026, 10:08 p.m.
NED1 Entity disambiguation (via context triple) batch_69ac7f2b76308190a843ccad1ef95f07 completed March 7, 2026, 7:40 p.m.
NEDg Description generation batch_69ac7fba00f0819086a0fffa090c5809 completed March 7, 2026, 7:42 p.m.
NED2 Entity disambiguation (via description) batch_69ac807ead9c819088f7195aec87a538 completed March 7, 2026, 7:46 p.m.
Created at: March 1, 2026, 7:42 p.m.