Triple

T21047076
Position Surface form Disambiguated ID Type / Status
Subject theory of G-structures E518475 entity
Predicate relatedTo P37 FINISHED
Object Cartan’s method of equivalence
Cartan’s method of equivalence is a geometric technique that uses differential forms and moving frames to determine when two geometric structures are locally the same up to a suitable transformation group.
E518475 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 equivalence | Statement: [theory of G-structures, relatedTo, Cartan’s method of equivalence]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Cartan’s method of equivalence
Context triple: [theory of G-structures, relatedTo, Cartan’s method of equivalence]
  • A. Pfaffian systems
    Pfaffian systems are collections of first-order differential equations expressed in terms of differential 1-forms that define geometric structures and constraints on manifolds in differential geometry and control theory.
  • B. Vessiot theory of differential equations
    The Vessiot theory of differential equations is a geometric framework that studies differential equations via their symmetry and structure using concepts from Lie groups and differential geometry.
  • C. Cartan connections
    Cartan connections are a geometric framework generalizing affine and Riemannian connections that model curved spaces on homogeneous spaces, developed by Élie Cartan.
  • D. theory of G-structures
    The theory of G-structures is a framework in differential geometry that studies geometric structures on manifolds defined by reductions of the frame bundle to a Lie group G, encompassing and unifying many classical geometries such as Riemannian, symplectic, and complex structures.
  • E. Oka–Cartan theory
    Oka–Cartan theory is a foundational area of complex analysis that studies the structure and properties of holomorphic functions and coherent analytic sheaves on complex manifolds, particularly Stein spaces.
  • 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 equivalence
Triple: [theory of G-structures, relatedTo, Cartan’s method of equivalence]
Generated description
Cartan’s method of equivalence is a geometric technique that uses differential forms and moving frames to determine when two geometric structures are locally the same up to a suitable transformation group.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Cartan’s method of equivalence
Target entity description: Cartan’s method of equivalence is a geometric technique that uses differential forms and moving frames to determine when two geometric structures are locally the same up to a suitable transformation group.
  • A. Pfaffian systems
    Pfaffian systems are collections of first-order differential equations expressed in terms of differential 1-forms that define geometric structures and constraints on manifolds in differential geometry and control theory.
  • B. Vessiot theory of differential equations
    The Vessiot theory of differential equations is a geometric framework that studies differential equations via their symmetry and structure using concepts from Lie groups and differential geometry.
  • C. Cartan connections
    Cartan connections are a geometric framework generalizing affine and Riemannian connections that model curved spaces on homogeneous spaces, developed by Élie Cartan.
  • D. theory of G-structures chosen
    The theory of G-structures is a framework in differential geometry that studies geometric structures on manifolds defined by reductions of the frame bundle to a Lie group G, encompassing and unifying many classical geometries such as Riemannian, symplectic, and complex structures.
  • E. Oka–Cartan theory
    Oka–Cartan theory is a foundational area of complex analysis that studies the structure and properties of holomorphic functions and coherent analytic sheaves on complex manifolds, particularly Stein spaces.
  • 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_69e0b50438e08190917e2538bb8bc034 completed April 16, 2026, 10:08 a.m.
NER Named-entity recognition batch_69e6fcf4d26481908b639996500a8319 completed April 21, 2026, 4:28 a.m.
NED1 Entity disambiguation (via context triple) batch_6a09475512b081908ceb38a118b0f026 completed May 17, 2026, 4:43 a.m.
NEDg Description generation batch_6a09489e80288190b401d11ccde39dc1 completed May 17, 2026, 4:48 a.m.
NED2 Entity disambiguation (via description) batch_6a094995d5bc8190b25d328dbf06b8b1 completed May 17, 2026, 4:52 a.m.
Created at: April 16, 2026, 2:34 p.m.