Triple

T5705600
Position Surface form Disambiguated ID Type / Status
Subject Cartan decomposition E125775 entity
Predicate involves P1256 FINISHED
Object Cartan involution
A Cartan involution is a specific type of involutive automorphism of a Lie algebra or Lie group that enables the decomposition of the structure into compact and non-compact parts, playing a central role in the classification of semisimple Lie algebras.
E125775 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 involution | Statement: [Cartan decomposition, involves, Cartan involution]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Cartan involution
Context triple: [Cartan decomposition, involves, Cartan involution]
  • 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. 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. 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.
  • 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 involution
Triple: [Cartan decomposition, involves, Cartan involution]
Generated description
A Cartan involution is a specific type of involutive automorphism of a Lie algebra or Lie group that enables the decomposition of the structure into compact and non-compact parts, playing a central role in the classification of semisimple Lie algebras.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Cartan involution
Target entity description: A Cartan involution is a specific type of involutive automorphism of a Lie algebra or Lie group that enables the decomposition of the structure into compact and non-compact parts, playing a central role in the classification of semisimple Lie algebras.
  • A. Cartan decomposition chosen
    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. 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. 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.
  • 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_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_69c07de7df8c8190824d24f729eaa04d completed March 22, 2026, 11:40 p.m.
NEDg Description generation batch_69c08b820a048190b3874522d568d485 completed March 23, 2026, 12:38 a.m.
NED2 Entity disambiguation (via description) batch_69c08be237a88190ace6e3d4ab97bf17 completed March 23, 2026, 12:40 a.m.
Created at: March 22, 2026, 3:45 p.m.