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.