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.