Triple

T1094558
Position Surface form Disambiguated ID Type / Status
Subject Élie Cartan E24242 entity
Predicate knownFor P22 FINISHED
Object 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.
E125774 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 subalgebras | Statement: [Élie Cartan, knownFor, Cartan subalgebras]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Cartan subalgebras
Context triple: [Élie Cartan, knownFor, Cartan subalgebras]
  • A. Weyl algebra
    The Weyl algebra is a fundamental noncommutative algebra generated by position and momentum operators satisfying canonical commutation relations, central in quantum mechanics and representation theory.
  • B. 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.
  • C. The Classical Groups: Their Invariants and Representations
    The Classical Groups: Their Invariants and Representations is a foundational mathematical monograph by Hermann Weyl that systematically develops the theory of classical Lie groups, their invariants, and their representation theory.
  • D. Weyl group
    A Weyl group is a finite reflection group associated with a root system that encodes the symmetries of Lie algebras and Lie groups in representation theory and geometry.
  • E. 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.
  • 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 subalgebras
Triple: [Élie Cartan, knownFor, Cartan subalgebras]
Generated description
Cartan subalgebras are maximal abelian subalgebras of a Lie algebra consisting of semisimple elements, fundamental for classifying and understanding the structure of Lie algebras.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Cartan subalgebras
Target entity description: Cartan subalgebras are maximal abelian subalgebras of a Lie algebra consisting of semisimple elements, fundamental for classifying and understanding the structure of Lie algebras.
  • A. Weyl algebra
    The Weyl algebra is a fundamental noncommutative algebra generated by position and momentum operators satisfying canonical commutation relations, central in quantum mechanics and representation theory.
  • B. 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.
  • C. The Classical Groups: Their Invariants and Representations
    The Classical Groups: Their Invariants and Representations is a foundational mathematical monograph by Hermann Weyl that systematically develops the theory of classical Lie groups, their invariants, and their representation theory.
  • D. Weyl group
    A Weyl group is a finite reflection group associated with a root system that encodes the symmetries of Lie algebras and Lie groups in representation theory and geometry.
  • E. 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.
  • F. None of above. chosen

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_69a4940542308190ac2a0b1f730b7cfc completed March 1, 2026, 7:31 p.m.
NER Named-entity recognition batch_69a4b99d1e8c81909cf1178d68d38885 completed March 1, 2026, 10:11 p.m.
NED1 Entity disambiguation (via context triple) batch_69ac4c2c6b048190b603e9562dde65d0 completed March 7, 2026, 4:02 p.m.
NEDg Description generation batch_69ac4ca07ce88190bfbf959adc84a74e completed March 7, 2026, 4:04 p.m.
NED2 Entity disambiguation (via description) batch_69ac4d3f62c881908e189bfe8cbbd2ac completed March 7, 2026, 4:07 p.m.
Created at: March 1, 2026, 7:42 p.m.