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.