Triple

T21953203
Position Surface form Disambiguated ID Type / Status
Subject Cartan–Killing form E542117 entity
Predicate isUsedToDefine P773 FINISHED
Object Cartan matrix — NE NERFINISHED

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 matrix | Statement: [Cartan–Killing form, isUsedToDefine, Cartan matrix]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Cartan matrix
Context triple: [Cartan–Killing form, isUsedToDefine, Cartan matrix]
  • A. Cartan decomposition
    Cartan decomposition is a fundamental structural result in Lie theory that expresses a Lie algebra or Lie group as a direct sum or product of subspaces or subgroups with specific symmetry properties, widely used in differential geometry and representation theory.
  • B. Cartan–Killing form
    The Cartan–Killing form is a canonical symmetric bilinear form on a Lie algebra that plays a central role in classifying and studying the structure of Lie algebras and Lie groups.
  • C. Coxeter–Dynkin diagrams chosen
    Coxeter–Dynkin diagrams are graphical representations that encode the structure of reflection groups and root systems, widely used in the classification of regular polytopes, Lie algebras, and symmetries.
  • D. Cartan
    Cartan is a French surname most famously associated with mathematician Élie Cartan and his influential family of mathematicians.
  • E. Cartan subalgebras
    Cartan subalgebras are maximal abelian subalgebras of a Lie algebra consisting of semisimple elements, fundamental for classifying and understanding the structure of Lie algebras.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

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_69f1243d43d8819084e280b129631288 completed April 28, 2026, 9:18 p.m.
Created at: April 16, 2026, 7:59 p.m.