Triple

T6833673
Position Surface form Disambiguated ID Type / Status
Subject Lagrange’s planetary equations E157396 entity
Predicate relatedTo P37 FINISHED
Object Delaunay variables
Delaunay variables are a set of canonical action-angle variables used in celestial mechanics to simplify the analysis of orbital motion and perturbations.
E621101 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: Delaunay variables | Statement: [Lagrange’s planetary equations, relatedTo, Delaunay variables]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Delaunay variables
Context triple: [Lagrange’s planetary equations, relatedTo, Delaunay variables]
  • A. Gale transform
    The Gale transform is a construction in convex geometry and combinatorics that represents a finite point configuration or polytope in a dual space, often used to study their structural and combinatorial properties.
  • B. Lyapunov vector
    A Lyapunov vector is a mathematical construct in dynamical systems theory that characterizes the directions in phase space associated with exponential growth or decay rates quantified by Lyapunov exponents.
  • C. Plücker coordinates
    Plücker coordinates are a system of homogeneous coordinates used in projective geometry to represent lines (and other subspaces) in higher-dimensional spaces.
  • D. Jacobi integral
    The Jacobi integral is a conserved quantity in celestial mechanics and dynamical systems that simplifies the analysis of motion in rotating reference frames, particularly in the restricted three-body problem.
  • E. Longuet-Higgins
    Longuet-Higgins is the surname of a notable British family that includes influential figures in theoretical chemistry, cognitive science, and mathematics.
  • 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: Delaunay variables
Triple: [Lagrange’s planetary equations, relatedTo, Delaunay variables]
Generated description
Delaunay variables are a set of canonical action-angle variables used in celestial mechanics to simplify the analysis of orbital motion and perturbations.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Delaunay variables
Target entity description: Delaunay variables are a set of canonical action-angle variables used in celestial mechanics to simplify the analysis of orbital motion and perturbations.
  • A. Gale transform
    The Gale transform is a construction in convex geometry and combinatorics that represents a finite point configuration or polytope in a dual space, often used to study their structural and combinatorial properties.
  • B. Lyapunov vector
    A Lyapunov vector is a mathematical construct in dynamical systems theory that characterizes the directions in phase space associated with exponential growth or decay rates quantified by Lyapunov exponents.
  • C. Plücker coordinates
    Plücker coordinates are a system of homogeneous coordinates used in projective geometry to represent lines (and other subspaces) in higher-dimensional spaces.
  • D. Jacobi integral
    The Jacobi integral is a conserved quantity in celestial mechanics and dynamical systems that simplifies the analysis of motion in rotating reference frames, particularly in the restricted three-body problem.
  • E. Longuet-Higgins
    Longuet-Higgins is the surname of a notable British family that includes influential figures in theoretical chemistry, cognitive science, and mathematics.
  • 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.