Triple
T13660515
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Picard theorem |
E326981
|
entity |
| Predicate | usedIn |
P98
|
FINISHED |
| Object |
Nevanlinna theory
Nevanlinna theory is a branch of complex analysis that studies the value distribution of meromorphic functions, quantifying how often they take or omit certain values.
|
E1053926
|
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: Nevanlinna theory | Statement: [Picard theorem, usedIn, Nevanlinna theory]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Nevanlinna theory Context triple: [Picard theorem, usedIn, Nevanlinna theory]
-
A.
Picard theorem
Picard theorem is a fundamental result in complex analysis stating that entire non-constant functions take on all possible complex values, with at most one exception.
-
B.
Dynamics in One Complex Variable
Dynamics in One Complex Variable is a foundational graduate-level textbook by John Milnor that introduces and develops the theory of complex dynamical systems, particularly the iteration of rational maps on the Riemann sphere.
-
C.
Théorie des fonctions analytiques
Théorie des fonctions analytiques is a foundational mathematical treatise by Joseph-Louis Lagrange that systematically develops calculus using power series and analytic functions instead of geometric or infinitesimal arguments.
-
D.
Cartwright–Littlewood theory on nonlinear differential equations
Cartwright–Littlewood theory on nonlinear differential equations is a foundational body of work in dynamical systems that rigorously analyzed the complex, often chaotic behavior of solutions to nonlinear differential equations, particularly in the context of forced oscillations.
-
E.
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.
- 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: Nevanlinna theory Triple: [Picard theorem, usedIn, Nevanlinna theory]
Generated description
Nevanlinna theory is a branch of complex analysis that studies the value distribution of meromorphic functions, quantifying how often they take or omit certain values.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Nevanlinna theory Target entity description: Nevanlinna theory is a branch of complex analysis that studies the value distribution of meromorphic functions, quantifying how often they take or omit certain values.
-
A.
Picard theorem
Picard theorem is a fundamental result in complex analysis stating that entire non-constant functions take on all possible complex values, with at most one exception.
-
B.
Dynamics in One Complex Variable
Dynamics in One Complex Variable is a foundational graduate-level textbook by John Milnor that introduces and develops the theory of complex dynamical systems, particularly the iteration of rational maps on the Riemann sphere.
-
C.
Théorie des fonctions analytiques
Théorie des fonctions analytiques is a foundational mathematical treatise by Joseph-Louis Lagrange that systematically develops calculus using power series and analytic functions instead of geometric or infinitesimal arguments.
-
D.
Cartwright–Littlewood theory on nonlinear differential equations
Cartwright–Littlewood theory on nonlinear differential equations is a foundational body of work in dynamical systems that rigorously analyzed the complex, often chaotic behavior of solutions to nonlinear differential equations, particularly in the context of forced oscillations.
-
E.
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.
- 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.