Triple

T15961333
Position Surface form Disambiguated ID Type / Status
Subject Korteweg–De Vries equation E387064 entity
Predicate isRelatedTo P37 FINISHED
Object Kadomtsev–Petviashvili equation
The Kadomtsev–Petviashvili equation is a fundamental nonlinear partial differential equation in mathematical physics that generalizes the Korteweg–De Vries equation to two spatial dimensions to describe the evolution of weakly dispersive, weakly nonlinear waves.
E1187023 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: Kadomtsev–Petviashvili equation | Statement: [Korteweg–De Vries equation, isRelatedTo, Kadomtsev–Petviashvili equation]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Kadomtsev–Petviashvili equation
Context triple: [Korteweg–De Vries equation, isRelatedTo, Kadomtsev–Petviashvili equation]
  • A. Korteweg–De Vries equation
    The Korteweg–De Vries equation is a fundamental nonlinear partial differential equation that models shallow water waves and solitons, playing a central role in the theory of integrable systems.
  • B. 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.
  • C. Gross–Pitaevskii equation
    The Gross–Pitaevskii equation is a nonlinear Schrödinger-type equation that describes the macroscopic wavefunction and dynamics of weakly interacting Bose gases at ultra-cold temperatures.
  • D. Zur Theorie der nichtlinearen Wellen
    "Zur Theorie der nichtlinearen Wellen" is Klaus Hasselmann's doctoral thesis, a foundational work on the behavior and mathematical description of nonlinear waves in physics.
  • E. Kardar–Parisi–Zhang equation
    The Kardar–Parisi–Zhang equation is a fundamental stochastic partial differential equation that models the dynamic scaling and roughening of growing interfaces in nonequilibrium statistical physics.
  • 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: Kadomtsev–Petviashvili equation
Triple: [Korteweg–De Vries equation, isRelatedTo, Kadomtsev–Petviashvili equation]
Generated description
The Kadomtsev–Petviashvili equation is a fundamental nonlinear partial differential equation in mathematical physics that generalizes the Korteweg–De Vries equation to two spatial dimensions to describe the evolution of weakly dispersive, weakly nonlinear waves.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Kadomtsev–Petviashvili equation
Target entity description: The Kadomtsev–Petviashvili equation is a fundamental nonlinear partial differential equation in mathematical physics that generalizes the Korteweg–De Vries equation to two spatial dimensions to describe the evolution of weakly dispersive, weakly nonlinear waves.
  • A. Korteweg–De Vries equation
    The Korteweg–De Vries equation is a fundamental nonlinear partial differential equation that models shallow water waves and solitons, playing a central role in the theory of integrable systems.
  • B. 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.
  • C. Gross–Pitaevskii equation
    The Gross–Pitaevskii equation is a nonlinear Schrödinger-type equation that describes the macroscopic wavefunction and dynamics of weakly interacting Bose gases at ultra-cold temperatures.
  • D. Zur Theorie der nichtlinearen Wellen
    "Zur Theorie der nichtlinearen Wellen" is Klaus Hasselmann's doctoral thesis, a foundational work on the behavior and mathematical description of nonlinear waves in physics.
  • E. Kardar–Parisi–Zhang equation
    The Kardar–Parisi–Zhang equation is a fundamental stochastic partial differential equation that models the dynamic scaling and roughening of growing interfaces in nonequilibrium statistical physics.
  • 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_69d86da882448190a82ea962fe343b79 completed April 10, 2026, 3:25 a.m.
NER Named-entity recognition batch_69e156ff4cdc81908db31394eaa191bc completed April 16, 2026, 9:39 p.m.
NED1 Entity disambiguation (via context triple) batch_69ffbe827d248190adbfd41f55638ebd completed May 9, 2026, 11:08 p.m.
NEDg Description generation batch_69ffbffcbd748190a666eca28cf44ad5 completed May 9, 2026, 11:15 p.m.
NED2 Entity disambiguation (via description) batch_69ffc09df25481908674f306b0f96f95 completed May 9, 2026, 11:17 p.m.
Created at: April 10, 2026, 4:53 a.m.