Triple

T3771953
Position Surface form Disambiguated ID Type / Status
Subject Martin David Kruskal E83217 entity
Predicate notableWork P4 FINISHED
Object 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.
E387067 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–Kruskal theorem | Statement: [Martin David Kruskal, notableWork, Painlevé–Kruskal theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Painlevé–Kruskal theorem
Context triple: [Martin David Kruskal, notableWork, Painlevé–Kruskal theorem]
  • A. Cauchy–Kovalevskaya theorem
    The Cauchy–Kovalevskaya theorem is a fundamental result in partial differential equations that guarantees the existence and uniqueness of analytic solutions to certain initial value problems under appropriate analyticity conditions.
  • B. Israel–Carter–Robinson uniqueness theorems
    The Israel–Carter–Robinson uniqueness theorems are a set of results in general relativity showing that stationary, asymptotically flat black holes in four-dimensional spacetime are completely characterized by just their mass, charge, and angular momentum.
  • C. Hilbert’s twenty-second problem
    Hilbert’s twenty-second problem is one of David Hilbert’s famous list of 23 problems, concerning the uniformization of analytic relations and the representation of multi-valued analytic functions by single-valued ones on suitable Riemann surfaces.
  • D. Interaction of solitons in a collisionless plasma and the recurrence of initial states
    "Interaction of solitons in a collisionless plasma and the recurrence of initial states" is a landmark 1965 paper by Norman J. Zabusky and Martin Kruskal that introduced the concept of solitons and demonstrated their particle-like interactions and recurrence behavior in nonlinear wave systems.
  • E. Kolmogorov spectrum of turbulence
    The Kolmogorov spectrum of turbulence is a fundamental theory in fluid dynamics that predicts how kinetic energy is distributed across different scales in fully developed turbulent flow, most famously yielding the −5/3 power law for the inertial subrange.
  • 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–Kruskal theorem
Triple: [Martin David Kruskal, notableWork, Painlevé–Kruskal theorem]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Painlevé–Kruskal theorem
Target entity description: 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.
  • A. Cauchy–Kovalevskaya theorem
    The Cauchy–Kovalevskaya theorem is a fundamental result in partial differential equations that guarantees the existence and uniqueness of analytic solutions to certain initial value problems under appropriate analyticity conditions.
  • B. Israel–Carter–Robinson uniqueness theorems
    The Israel–Carter–Robinson uniqueness theorems are a set of results in general relativity showing that stationary, asymptotically flat black holes in four-dimensional spacetime are completely characterized by just their mass, charge, and angular momentum.
  • C. Szekeres–Lindström theorem
    The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
  • D. Hilbert’s twenty-second problem
    Hilbert’s twenty-second problem is one of David Hilbert’s famous list of 23 problems, concerning the uniformization of analytic relations and the representation of multi-valued analytic functions by single-valued ones on suitable Riemann surfaces.
  • E. Interaction of solitons in a collisionless plasma and the recurrence of initial states
    "Interaction of solitons in a collisionless plasma and the recurrence of initial states" is a landmark 1965 paper by Norman J. Zabusky and Martin Kruskal that introduced the concept of solitons and demonstrated their particle-like interactions and recurrence behavior in nonlinear wave systems.
  • 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_69ad8b235e608190b5a2b1d1bfcef50b completed March 8, 2026, 2:43 p.m.
NER Named-entity recognition batch_69adcc3219b881908a2f82126f9a679d completed March 8, 2026, 7:21 p.m.
NED1 Entity disambiguation (via context triple) batch_69b4e52bb2d08190b457dd517ff366d7 completed March 14, 2026, 4:33 a.m.
NEDg Description generation batch_69b4e99c942c819094e2228bd3dc3b30 completed March 14, 2026, 4:52 a.m.
NED2 Entity disambiguation (via description) batch_69b4ea201fe8819098ac5459c39b258c completed March 14, 2026, 4:54 a.m.
Created at: March 8, 2026, 3:36 p.m.