Triple

T11440002
Position Surface form Disambiguated ID Type / Status
Subject Mary Cartwright E271117 entity
Predicate notableWork P4 FINISHED
Object 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.
E926679 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: Cartwright–Littlewood theory on nonlinear differential equations | Statement: [Mary Cartwright, notableWork, Cartwright–Littlewood theory on nonlinear differential equations]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Cartwright–Littlewood theory on nonlinear differential equations
Context triple: [Mary Cartwright, notableWork, Cartwright–Littlewood theory on nonlinear differential equations]
  • A. Inequalities for analytic functions
    "Inequalities for analytic functions" is a mathematical work by Gábor Szegő that develops fundamental bounds and estimates for complex analytic functions, particularly in the context of complex analysis and approximation theory.
  • B. Asymptotic Methods in Analysis
    Asymptotic Methods in Analysis is a classic mathematical monograph by N. G. de Bruijn that systematically develops techniques for approximating functions and integrals in limiting regimes, widely used in analysis and number theory.
  • C. Tauberian theorems
    Tauberian theorems are results in mathematical analysis that connect the behavior of transformed series or integrals (such as those summed by Abel or Cesàro methods) back to the asymptotic behavior or convergence of the original sequences or series.
  • D. Hadamard three-circle theorem
    The Hadamard three-circle theorem is a result in complex analysis that describes how the maximum modulus of a holomorphic function behaves logarithmically between three concentric circles in the complex plane.
  • E. 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.
  • 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: Cartwright–Littlewood theory on nonlinear differential equations
Triple: [Mary Cartwright, notableWork, Cartwright–Littlewood theory on nonlinear differential equations]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Cartwright–Littlewood theory on nonlinear differential equations
Target entity description: 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.
  • A. Inequalities for analytic functions
    "Inequalities for analytic functions" is a mathematical work by Gábor Szegő that develops fundamental bounds and estimates for complex analytic functions, particularly in the context of complex analysis and approximation theory.
  • B. Asymptotic Methods in Analysis
    Asymptotic Methods in Analysis is a classic mathematical monograph by N. G. de Bruijn that systematically develops techniques for approximating functions and integrals in limiting regimes, widely used in analysis and number theory.
  • C. Tauberian theorems
    Tauberian theorems are results in mathematical analysis that connect the behavior of transformed series or integrals (such as those summed by Abel or Cesàro methods) back to the asymptotic behavior or convergence of the original sequences or series.
  • D. Hadamard three-circle theorem
    The Hadamard three-circle theorem is a result in complex analysis that describes how the maximum modulus of a holomorphic function behaves logarithmically between three concentric circles in the complex plane.
  • E. 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.
  • 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_69d6aadeef688190874bcecd88b3dd9b completed April 8, 2026, 7:22 p.m.
NER Named-entity recognition batch_69d80888190c8190b6365550ffe4931c completed April 9, 2026, 8:14 p.m.
NED1 Entity disambiguation (via context triple) batch_69e5d39554c48190969cc0ebd4dbc368 completed April 20, 2026, 7:19 a.m.
NEDg Description generation batch_69e5d91b047c81909ea4c7f114bfbba5 completed April 20, 2026, 7:43 a.m.
NED2 Entity disambiguation (via description) batch_69e5e2de4cd081908d30c44853565029 completed April 20, 2026, 8:25 a.m.
Created at: April 8, 2026, 9:35 p.m.