Triple

T10991788
Position Surface form Disambiguated ID Type / Status
Subject uniformization theorem E259768 entity
Predicate historicallyAssociatedWith P2830 FINISHED
Object Paul Koebe
Paul Koebe was a German mathematician known for his foundational contributions to complex analysis, particularly in the development of uniformization and conformal mapping theory.
E898492 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: Paul Koebe | Statement: [uniformization theorem, historicallyAssociatedWith, Paul Koebe]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Paul Koebe
Context triple: [uniformization theorem, historicallyAssociatedWith, Paul Koebe]
  • A. Kurt Hensel
    Kurt Hensel was a German mathematician best known for introducing p-adic numbers, which became fundamental in number theory and algebraic geometry.
  • B. Hermann Amandus Schwarz
    Hermann Amandus Schwarz was a German mathematician known for his fundamental contributions to complex analysis and for co-formulating the Cauchy–Schwarz inequality.
  • C. 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.
  • D. Wilhelm Blaschke
    Wilhelm Blaschke was a prominent Austrian mathematician known for his influential work in differential and integral geometry and for mentoring several leading 20th-century geometers.
  • E. Max Dehn
    Max Dehn was a German mathematician known for his foundational work in topology and group theory, including the introduction of Dehn surgery and the study of decision problems in group 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: Paul Koebe
Triple: [uniformization theorem, historicallyAssociatedWith, Paul Koebe]
Generated description
Paul Koebe was a German mathematician known for his foundational contributions to complex analysis, particularly in the development of uniformization and conformal mapping theory.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Paul Koebe
Target entity description: Paul Koebe was a German mathematician known for his foundational contributions to complex analysis, particularly in the development of uniformization and conformal mapping theory.
  • A. Kurt Hensel
    Kurt Hensel was a German mathematician best known for introducing p-adic numbers, which became fundamental in number theory and algebraic geometry.
  • B. Hermann Amandus Schwarz
    Hermann Amandus Schwarz was a German mathematician known for his fundamental contributions to complex analysis and for co-formulating the Cauchy–Schwarz inequality.
  • C. 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.
  • D. Wilhelm Blaschke
    Wilhelm Blaschke was a prominent Austrian mathematician known for his influential work in differential and integral geometry and for mentoring several leading 20th-century geometers.
  • E. Max Dehn
    Max Dehn was a German mathematician known for his foundational work in topology and group theory, including the introduction of Dehn surgery and the study of decision problems in group 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_69d6aa8a6a548190a750f944ccdc8064 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d795d1e918819090c71f5a077fa15a completed April 9, 2026, 12:04 p.m.
NED1 Entity disambiguation (via context triple) batch_69e34504ebec8190a78e4795765b0c24 completed April 18, 2026, 8:47 a.m.
NEDg Description generation batch_69e3556fd3548190a33f04604be947cf completed April 18, 2026, 9:57 a.m.
NED2 Entity disambiguation (via description) batch_69e3593b0f8481909ed7a90f8bb9839d completed April 18, 2026, 10:13 a.m.
Created at: April 8, 2026, 9:24 p.m.