Triple

T1094557
Position Surface form Disambiguated ID Type / Status
Subject Élie Cartan E24242 entity
Predicate knownFor P22 FINISHED
Object Cartan’s method of moving frames
Cartan’s method of moving frames is a powerful geometric technique that uses smoothly varying reference frames to analyze the intrinsic properties and invariants of curves, surfaces, and more general manifolds.
E121356 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: Cartan’s method of moving frames | Statement: [Élie Cartan, knownFor, Cartan’s method of moving frames]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Cartan’s method of moving frames
Context triple: [Élie Cartan, knownFor, Cartan’s method of moving frames]
  • A. Carathéodory–Jacobi–Lie theorem
    The Carathéodory–Jacobi–Lie theorem is a fundamental result in symplectic geometry and Hamiltonian mechanics that provides canonical local coordinates adapted to a given set of commuting functions.
  • B. Cartan structure equations
    Cartan structure equations are fundamental differential geometric relations that express curvature and torsion in terms of connection 1-forms on a manifold.
  • C. Erlangen Program
    The Erlangen Program is Felix Klein’s influential 1872 framework that classifies and studies geometries based on their underlying symmetry groups and transformation properties.
  • D. Nash embedding theorem
    The Nash embedding theorem is a fundamental result in differential geometry that shows any Riemannian manifold can be isometrically embedded into some Euclidean space, thereby realizing abstract curved spaces as concrete subsets of standard Euclidean space.
  • E. Janet–Cartan theorem
    The Janet–Cartan theorem is a fundamental result in differential geometry stating that any real-analytic Riemannian manifold can be locally isometrically embedded into a Euclidean space of sufficiently high dimension.
  • 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: Cartan’s method of moving frames
Triple: [Élie Cartan, knownFor, Cartan’s method of moving frames]
Generated description
Cartan’s method of moving frames is a powerful geometric technique that uses smoothly varying reference frames to analyze the intrinsic properties and invariants of curves, surfaces, and more general manifolds.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Cartan’s method of moving frames
Target entity description: Cartan’s method of moving frames is a powerful geometric technique that uses smoothly varying reference frames to analyze the intrinsic properties and invariants of curves, surfaces, and more general manifolds.
  • A. Carathéodory–Jacobi–Lie theorem
    The Carathéodory–Jacobi–Lie theorem is a fundamental result in symplectic geometry and Hamiltonian mechanics that provides canonical local coordinates adapted to a given set of commuting functions.
  • B. Cartan structure equations chosen
    Cartan structure equations are fundamental differential geometric relations that express curvature and torsion in terms of connection 1-forms on a manifold.
  • C. Erlangen Program
    The Erlangen Program is Felix Klein’s influential 1872 framework that classifies and studies geometries based on their underlying symmetry groups and transformation properties.
  • D. Nash embedding theorem
    The Nash embedding theorem is a fundamental result in differential geometry that shows any Riemannian manifold can be isometrically embedded into some Euclidean space, thereby realizing abstract curved spaces as concrete subsets of standard Euclidean space.
  • E. Janet–Cartan theorem
    The Janet–Cartan theorem is a fundamental result in differential geometry stating that any real-analytic Riemannian manifold can be locally isometrically embedded into a Euclidean space of sufficiently high dimension.
  • F. None of above.

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_69a4940542308190ac2a0b1f730b7cfc completed March 1, 2026, 7:31 p.m.
NER Named-entity recognition batch_69a4b99d1e8c81909cf1178d68d38885 completed March 1, 2026, 10:11 p.m.
NED1 Entity disambiguation (via context triple) batch_69ac4c2c6b048190b603e9562dde65d0 completed March 7, 2026, 4:02 p.m.
NEDg Description generation batch_69ac4ca07ce88190bfbf959adc84a74e completed March 7, 2026, 4:04 p.m.
NED2 Entity disambiguation (via description) batch_69ac4d3f62c881908e189bfe8cbbd2ac completed March 7, 2026, 4:07 p.m.
Created at: March 1, 2026, 7:42 p.m.