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.