Triple

T10641504
Position Surface form Disambiguated ID Type / Status
Subject Plancherel theorem for real reductive groups E250731 entity
Predicate requires P100 FINISHED
Object Cartan decomposition E125775 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 decomposition | Statement: [Plancherel theorem for real reductive groups, requires, Cartan decomposition]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Cartan decomposition
Context triple: [Plancherel theorem for real reductive groups, requires, Cartan decomposition]
  • 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 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.
  • C. 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.
  • D. Cartan
    Cartan is a French surname most famously associated with mathematician Élie Cartan and his influential family of mathematicians.
  • 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.
  • 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_69d6aa5a4c4881908f39be6efe5981e5 completed April 8, 2026, 7:19 p.m.
NER Named-entity recognition batch_69d6dfcd19648190882380d2c90be486 completed April 8, 2026, 11:07 p.m.
NED1 Entity disambiguation (via context triple) batch_69d96bcd8c0c8190a0fad6a85b5604bb completed April 10, 2026, 9:29 p.m.
Created at: April 8, 2026, 9:05 p.m.