Triple

T5705556
Position Surface form Disambiguated ID Type / Status
Subject Cartan subalgebras E125774 entity
Predicate relatedTo P37 FINISHED
Object Cartan matrix E412212 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 matrix | Statement: [Cartan subalgebras, relatedTo, Cartan matrix]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Cartan matrix
Context triple: [Cartan subalgebras, relatedTo, 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. 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.
  • C. Cartan
    Cartan is a French surname most famously associated with mathematician Élie Cartan and his influential family of mathematicians.
  • D. 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.
  • E. Weyl character formula
    The Weyl character formula is a fundamental result in representation theory that gives an explicit expression for the characters of irreducible finite-dimensional representations of semisimple Lie algebras and Lie groups.
  • 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_69c0082c96988190b3a6a201edce472a completed March 22, 2026, 3:18 p.m.
NER Named-entity recognition batch_69c02459cd18819080fda0b481d11f08 completed March 22, 2026, 5:18 p.m.
NED1 Entity disambiguation (via context triple) batch_69c05a666d788190a0f786d12391a44b completed March 22, 2026, 9:08 p.m.
Created at: March 22, 2026, 3:45 p.m.