Triple

T11099203
Position Surface form Disambiguated ID Type / Status
Subject Camille Jordan E262458 entity
Predicate knownFor P22 FINISHED
Object Jordan–Chevalley decomposition
The Jordan–Chevalley decomposition is a fundamental result in linear algebra and representation theory that expresses a linear operator (or matrix) as the sum or product of commuting semisimple and nilpotent parts.
E904578 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: Jordan–Chevalley decomposition | Statement: [Camille Jordan, knownFor, Jordan–Chevalley decomposition]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Jordan–Chevalley decomposition
Context triple: [Camille Jordan, knownFor, Jordan–Chevalley decomposition]
  • 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. Chevalley
    Chevalley is a French surname most prominently associated with Claude Chevalley, a influential 20th-century mathematician known for his work in algebra and group theory.
  • C. Schur–Weyl duality
    Schur–Weyl duality is a fundamental result in representation theory that links representations of the symmetric group and the general linear group via their commuting actions on tensor powers of a vector space.
  • D. Gelfand–Kirillov dimension
    The Gelfand–Kirillov dimension is an invariant in noncommutative algebra that measures the growth rate of algebras and modules, serving as an analogue of Krull dimension for noncommutative settings.
  • E. Iwasawa decomposition
    The Iwasawa decomposition is a fundamental factorization in Lie group theory that expresses a semisimple Lie group as a product of a maximal compact subgroup, a maximal abelian subgroup, and a nilpotent subgroup, playing a key role in representation theory and harmonic analysis.
  • 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: Jordan–Chevalley decomposition
Triple: [Camille Jordan, knownFor, Jordan–Chevalley decomposition]
Generated description
The Jordan–Chevalley decomposition is a fundamental result in linear algebra and representation theory that expresses a linear operator (or matrix) as the sum or product of commuting semisimple and nilpotent parts.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Jordan–Chevalley decomposition
Target entity description: The Jordan–Chevalley decomposition is a fundamental result in linear algebra and representation theory that expresses a linear operator (or matrix) as the sum or product of commuting semisimple and nilpotent parts.
  • 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. Chevalley
    Chevalley is a French surname most prominently associated with Claude Chevalley, a influential 20th-century mathematician known for his work in algebra and group theory.
  • C. Schur–Weyl duality
    Schur–Weyl duality is a fundamental result in representation theory that links representations of the symmetric group and the general linear group via their commuting actions on tensor powers of a vector space.
  • D. Gelfand–Kirillov dimension
    The Gelfand–Kirillov dimension is an invariant in noncommutative algebra that measures the growth rate of algebras and modules, serving as an analogue of Krull dimension for noncommutative settings.
  • E. Iwasawa decomposition
    The Iwasawa decomposition is a fundamental factorization in Lie group theory that expresses a semisimple Lie group as a product of a maximal compact subgroup, a maximal abelian subgroup, and a nilpotent subgroup, playing a key role in representation theory and harmonic analysis.
  • 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_69d6aa9a40d88190a373e2c7e48285db completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d79a0c46308190889b94c23ebaca62 completed April 9, 2026, 12:22 p.m.
NED1 Entity disambiguation (via context triple) batch_69e3e7eca9bc8190b43bae081d97d804 completed April 18, 2026, 8:22 p.m.
NEDg Description generation batch_69e3f2cbb4708190a328cff473104d14 completed April 18, 2026, 9:08 p.m.
NED2 Entity disambiguation (via description) batch_69e3f497a01881909d1dae70a02e5f97 completed April 18, 2026, 9:16 p.m.
Created at: April 8, 2026, 9:27 p.m.