Triple

T21953585
Position Surface form Disambiguated ID Type / Status
Subject Maurer–Cartan form E542126 entity
Predicate satisfies P4233 FINISHED
Object Maurer–Cartan equation — NE NERFINISHED

How this triple was built (3 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: Maurer–Cartan equation | Statement: [Maurer–Cartan form, satisfies, Maurer–Cartan equation]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Maurer–Cartan equation
Context triple: [Maurer–Cartan form, satisfies, Maurer–Cartan equation]
  • A. Maurer–Cartan form
    The Maurer–Cartan form is a canonical Lie algebra-valued 1-form on a Lie group that encodes its infinitesimal structure and underlies many constructions in differential geometry and gauge theory.
  • 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. 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. Cartan magic formula
    The Cartan magic formula is a fundamental identity in differential geometry that expresses the Lie derivative of a differential form in terms of the exterior derivative and interior product.
  • E. Cartan formula
    The Cartan formula is a fundamental identity in differential geometry that expresses the Lie derivative of a differential form in terms of the exterior derivative and interior product.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: Maurer–Cartan equation
Target entity description: The Maurer–Cartan equation is a fundamental differential equation in Lie theory and differential geometry that characterizes the structure of Lie algebras via their associated differential forms on Lie groups.
  • A. Maurer–Cartan form chosen
    The Maurer–Cartan form is a canonical Lie algebra-valued 1-form on a Lie group that encodes its infinitesimal structure and underlies many constructions in differential geometry and gauge theory.
  • 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. 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. Cartan magic formula
    The Cartan magic formula is a fundamental identity in differential geometry that expresses the Lie derivative of a differential form in terms of the exterior derivative and interior product.
  • E. Cartan formula
    The Cartan formula is a fundamental identity in differential geometry that expresses the Lie derivative of a differential form in terms of the exterior derivative and interior product.
  • F. None of above.

Provenance (2 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_69e0c47ef0e48190a50e1bcc43f4b3fd completed April 16, 2026, 11:14 a.m.
NER Named-entity recognition batch_69f1243dfb4081909bc7a722843ffea7 completed April 28, 2026, 9:18 p.m.
Created at: April 16, 2026, 7:59 p.m.