Triple

T13458365
Position Surface form Disambiguated ID Type / Status
Subject Paul Painlevé E311292 entity
Predicate notableWork P4 FINISHED
Object Painlevé transcendents
Painlevé transcendents are special functions defined as solutions to certain nonlinear second-order differential equations that cannot be expressed in terms of elementary or classical special functions and play a central role in modern mathematical physics and integrable systems.
E1041302 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: Painlevé transcendents | Statement: [Paul Painlevé, notableWork, Painlevé transcendents]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Painlevé transcendents
Context triple: [Paul Painlevé, notableWork, Painlevé transcendents]
  • A. Fuchsian differential equation
    A Fuchsian differential equation is a type of linear ordinary differential equation characterized by having only regular singular points, extensively studied in complex analysis and the theory of special functions.
  • B. Stokes phenomenon
    The Stokes phenomenon is a concept in asymptotic analysis describing the abrupt change in the behavior of asymptotic expansions of functions as one crosses certain lines, called Stokes lines, in the complex plane.
  • C. Jacobi elliptic functions
    Jacobi elliptic functions are a family of doubly periodic complex functions that generalize trigonometric functions and play a central role in the theory of elliptic integrals and many areas of mathematical physics.
  • D. Painlevé–Kruskal theorem
    The Painlevé–Kruskal theorem is a result in the theory of nonlinear differential equations that characterizes integrability through the analytic structure of their solutions, particularly via the Painlevé property.
  • E. Picard–Vessiot theory
    Picard–Vessiot theory is a branch of differential Galois theory that studies linear differential equations via the symmetries of their solution fields, analogous to classical Galois theory for polynomial equations.
  • 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: Painlevé transcendents
Triple: [Paul Painlevé, notableWork, Painlevé transcendents]
Generated description
Painlevé transcendents are special functions defined as solutions to certain nonlinear second-order differential equations that cannot be expressed in terms of elementary or classical special functions and play a central role in modern mathematical physics and integrable systems.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Painlevé transcendents
Target entity description: Painlevé transcendents are special functions defined as solutions to certain nonlinear second-order differential equations that cannot be expressed in terms of elementary or classical special functions and play a central role in modern mathematical physics and integrable systems.
  • A. Fuchsian differential equation
    A Fuchsian differential equation is a type of linear ordinary differential equation characterized by having only regular singular points, extensively studied in complex analysis and the theory of special functions.
  • B. Stokes phenomenon
    The Stokes phenomenon is a concept in asymptotic analysis describing the abrupt change in the behavior of asymptotic expansions of functions as one crosses certain lines, called Stokes lines, in the complex plane.
  • C. Jacobi elliptic functions
    Jacobi elliptic functions are a family of doubly periodic complex functions that generalize trigonometric functions and play a central role in the theory of elliptic integrals and many areas of mathematical physics.
  • D. Painlevé–Kruskal theorem
    The Painlevé–Kruskal theorem is a result in the theory of nonlinear differential equations that characterizes integrability through the analytic structure of their solutions, particularly via the Painlevé property.
  • E. Picard–Vessiot theory
    Picard–Vessiot theory is a branch of differential Galois theory that studies linear differential equations via the symmetries of their solution fields, analogous to classical Galois theory for polynomial equations.
  • 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_69d806a938b8819097ec43a2229fc7f9 completed April 9, 2026, 8:06 p.m.
NER Named-entity recognition batch_69dbaf0a75008190a508060c85f73604 completed April 12, 2026, 2:41 p.m.
NED1 Entity disambiguation (via context triple) batch_69f739a001d08190ae5664c6670540e7 completed May 3, 2026, 12:03 p.m.
NEDg Description generation batch_69f73b3074bc819081e30b082857c33e completed May 3, 2026, 12:10 p.m.
NED2 Entity disambiguation (via description) batch_69f73ee5839881908ce75c57f1942b57 completed May 3, 2026, 12:26 p.m.
Created at: April 9, 2026, 9:41 p.m.