Triple

T6833659
Position Surface form Disambiguated ID Type / Status
Subject Lagrange’s planetary equations E157396 entity
Predicate basedOn P98 FINISHED
Object Lagrange’s variation of parameters method
Lagrange’s variation of parameters method is a classical analytical technique in celestial mechanics and differential equations that determines how orbital or system parameters evolve over time under perturbing forces.
E621100 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: Lagrange’s variation of parameters method | Statement: [Lagrange’s planetary equations, basedOn, Lagrange’s variation of parameters method]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Lagrange’s variation of parameters method
Context triple: [Lagrange’s planetary equations, basedOn, Lagrange’s variation of parameters method]
  • A. Linear Differential Equations and Their Applications
    "Linear Differential Equations and Their Applications" is a classic mathematical text by Maxime Bôcher that systematically develops the theory of linear differential equations and demonstrates their use in solving applied problems.
  • B. Bogoliubov–Mitropolsky asymptotic methods in nonlinear oscillations
    "Bogoliubov–Mitropolsky Asymptotic Methods in Nonlinear Oscillations" is a classic mathematical monograph that develops systematic asymptotic techniques for analyzing and approximating solutions of nonlinear oscillatory systems.
  • C. Cauchy–Euler equation
    The Cauchy–Euler equation is a type of linear ordinary differential equation with variable coefficients that often appears in problems with power-law or scale-invariant behavior.
  • D. Laplace method
    The Laplace method is an asymptotic technique in mathematical analysis used to approximate integrals, especially those dominated by contributions near a maximum point of the integrand.
  • E. d’Alembert’s formula
    d’Alembert’s formula is a classical solution method for the one-dimensional wave equation that expresses the displacement of a vibrating string in terms of its initial shape and velocity.
  • 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: Lagrange’s variation of parameters method
Triple: [Lagrange’s planetary equations, basedOn, Lagrange’s variation of parameters method]
Generated description
Lagrange’s variation of parameters method is a classical analytical technique in celestial mechanics and differential equations that determines how orbital or system parameters evolve over time under perturbing forces.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Lagrange’s variation of parameters method
Target entity description: Lagrange’s variation of parameters method is a classical analytical technique in celestial mechanics and differential equations that determines how orbital or system parameters evolve over time under perturbing forces.
  • A. Linear Differential Equations and Their Applications
    "Linear Differential Equations and Their Applications" is a classic mathematical text by Maxime Bôcher that systematically develops the theory of linear differential equations and demonstrates their use in solving applied problems.
  • B. Bogoliubov–Mitropolsky asymptotic methods in nonlinear oscillations
    "Bogoliubov–Mitropolsky Asymptotic Methods in Nonlinear Oscillations" is a classic mathematical monograph that develops systematic asymptotic techniques for analyzing and approximating solutions of nonlinear oscillatory systems.
  • C. Cauchy–Euler equation
    The Cauchy–Euler equation is a type of linear ordinary differential equation with variable coefficients that often appears in problems with power-law or scale-invariant behavior.
  • D. Laplace method
    The Laplace method is an asymptotic technique in mathematical analysis used to approximate integrals, especially those dominated by contributions near a maximum point of the integrand.
  • E. d’Alembert’s formula
    d’Alembert’s formula is a classical solution method for the one-dimensional wave equation that expresses the displacement of a vibrating string in terms of its initial shape and velocity.
  • 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_69c6882c53608190b99aebef079b23bd completed March 27, 2026, 1:37 p.m.
NER Named-entity recognition batch_69c6d67936288190829fedc3729aadd8 completed March 27, 2026, 7:11 p.m.
NED1 Entity disambiguation (via context triple) batch_69c723fd50c88190af005fd58ca0aee6 completed March 28, 2026, 12:42 a.m.
NEDg Description generation batch_69c7247806808190ac60c134cec612c8 completed March 28, 2026, 12:44 a.m.
NED2 Entity disambiguation (via description) batch_69c7253b94f081909e7cee870a12af6b completed March 28, 2026, 12:47 a.m.
Created at: March 27, 2026, 2:18 p.m.