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.