Triple

T6282402
Position Surface form Disambiguated ID Type / Status
Subject Lie pseudogroup E140810 entity
Predicate usedFor P98 FINISHED
Object Cartan’s method of moving frames E518475 NE FINISHED

How this triple was built (2 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: [Lie pseudogroup, usedFor, 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: [Lie pseudogroup, usedFor, Cartan’s method of moving frames]
  • A. Cartan connections
    Cartan connections are a geometric framework generalizing affine and Riemannian connections that model curved spaces on homogeneous spaces, developed by Élie Cartan.
  • B. Cartan theorems A and B
    Cartan theorems A and B are fundamental results in complex analytic geometry that characterize coherent analytic sheaves on Stein spaces by guaranteeing the existence of enough global sections and the vanishing of higher cohomology.
  • C. 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.
  • D. Lie sphere geometry
    Lie sphere geometry is a branch of differential geometry that studies the properties and transformations of spheres (and related objects like planes and points) using the methods of Lie groups and projective geometry.
  • E. Méthodes de calcul différentiel absolu et leurs applications
    Méthodes de calcul différentiel absolu et leurs applications is a foundational mathematical work that systematically develops the theory of tensor calculus and its applications, laying groundwork later used in general relativity.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69c008cd17c8819082b82d3fbeb68047 completed March 22, 2026, 3:20 p.m.
NER Named-entity recognition batch_69c063f956c08190ae0f198ccbd68b42 completed March 22, 2026, 9:49 p.m.
NED1 Entity disambiguation (via context triple) batch_69c51962132881909a2eccd1203e03c1 completed March 26, 2026, 11:32 a.m.
Created at: March 22, 2026, 4:26 p.m.