Triple

T13660530
Position Surface form Disambiguated ID Type / Status
Subject Picard theorem E326981 entity
Predicate hasGeneralization P2372 FINISHED
Object Ahlfors’ theory of covering surfaces
Ahlfors’ theory of covering surfaces is a major extension of classical value-distribution theory in complex analysis that generalizes Picard-type results to the study of branched covering surfaces and their mapping properties.
E1053927 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: Ahlfors’ theory of covering surfaces | Statement: [Picard theorem, hasGeneralization, Ahlfors’ theory of covering surfaces]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Ahlfors’ theory of covering surfaces
Context triple: [Picard theorem, hasGeneralization, Ahlfors’ theory of covering surfaces]
  • A. Ahlfors finiteness theorem
    The Ahlfors finiteness theorem is a fundamental result in the theory of Kleinian groups stating that, under suitable discreteness and analyticity conditions, the quotient of the domain of discontinuity has finite topological type.
  • B. Lectures on Quasiconformal Mappings
    Lectures on Quasiconformal Mappings is a classic mathematical monograph by Lars Ahlfors that systematically develops the theory of quasiconformal mappings in the complex plane and higher dimensions.
  • C. Introduction to the Theory of Algebraic Functions of One Variable
    Introduction to the Theory of Algebraic Functions of One Variable is a classic monograph by Claude Chevalley that provides a rigorous, modern foundation for the theory of algebraic function fields in one variable.
  • D. Lezioni sulla teoria delle superficie
    Lezioni sulla teoria delle superficie is a foundational mathematical treatise on the theory of surfaces written by Italian mathematician Luigi Bianchi.
  • E. Conformal Invariants
    Conformal Invariants is a foundational mathematical work by Lars Ahlfors that systematically develops the theory of quantities preserved under conformal mappings in complex analysis and geometric function 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: Ahlfors’ theory of covering surfaces
Triple: [Picard theorem, hasGeneralization, Ahlfors’ theory of covering surfaces]
Generated description
Ahlfors’ theory of covering surfaces is a major extension of classical value-distribution theory in complex analysis that generalizes Picard-type results to the study of branched covering surfaces and their mapping properties.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Ahlfors’ theory of covering surfaces
Target entity description: Ahlfors’ theory of covering surfaces is a major extension of classical value-distribution theory in complex analysis that generalizes Picard-type results to the study of branched covering surfaces and their mapping properties.
  • A. Ahlfors finiteness theorem
    The Ahlfors finiteness theorem is a fundamental result in the theory of Kleinian groups stating that, under suitable discreteness and analyticity conditions, the quotient of the domain of discontinuity has finite topological type.
  • B. Lectures on Quasiconformal Mappings
    Lectures on Quasiconformal Mappings is a classic mathematical monograph by Lars Ahlfors that systematically develops the theory of quasiconformal mappings in the complex plane and higher dimensions.
  • C. Introduction to the Theory of Algebraic Functions of One Variable
    Introduction to the Theory of Algebraic Functions of One Variable is a classic monograph by Claude Chevalley that provides a rigorous, modern foundation for the theory of algebraic function fields in one variable.
  • D. Lezioni sulla teoria delle superficie
    Lezioni sulla teoria delle superficie is a foundational mathematical treatise on the theory of surfaces written by Italian mathematician Luigi Bianchi.
  • E. Conformal Invariants
    Conformal Invariants is a foundational mathematical work by Lars Ahlfors that systematically develops the theory of quantities preserved under conformal mappings in complex analysis and geometric function 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_69d8076d8270819092afc2f0e9c359a8 completed April 9, 2026, 8:09 p.m.
NER Named-entity recognition batch_69dbc620df208190afaccf3ddd10aa60 completed April 12, 2026, 4:19 p.m.
NED1 Entity disambiguation (via context triple) batch_69f78b08d27c8190badc612c26423c0e completed May 3, 2026, 5:51 p.m.
NEDg Description generation batch_69f78fd0d29481908bd44bda28e3b2c1 completed May 3, 2026, 6:11 p.m.
NED2 Entity disambiguation (via description) batch_69f7908d92e08190918525c59cb37b55 completed May 3, 2026, 6:14 p.m.
Created at: April 9, 2026, 9:52 p.m.