Triple
T5212022
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Weyl character formula |
E117655
|
entity |
| Predicate | usesConcept |
P531
|
FINISHED |
| Object | Cartan subalgebra |
E125774
|
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 subalgebra | Statement: [Weyl character formula, usesConcept, Cartan subalgebra]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Cartan subalgebra Context triple: [Weyl character formula, usesConcept, Cartan subalgebra]
-
A.
Cartan subalgebras
chosen
Cartan subalgebras are maximal abelian subalgebras of a Lie algebra consisting of semisimple elements, fundamental for classifying and understanding the structure of Lie algebras.
-
B.
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.
-
C.
Cartan
Cartan is a French surname most famously associated with mathematician Élie Cartan and his influential family of mathematicians.
-
D.
Harish-Chandra isomorphism
The Harish-Chandra isomorphism is a fundamental result in representation theory that identifies the center of the universal enveloping algebra of a semisimple Lie algebra with the algebra of Weyl group–invariant polynomials on a Cartan subalgebra.
-
E.
affine Lie algebras
Affine Lie algebras are infinite-dimensional extensions of finite-dimensional simple Lie algebras that play a central role in representation theory, conformal field theory, and the study of exactly solvable models in mathematical physics.
- 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_69bd4464ba3c8190bc16b2ebbe42ddb0 |
completed | March 20, 2026, 12:58 p.m. |
| NER | Named-entity recognition | batch_69bd7a7166848190805152142e184529 |
completed | March 20, 2026, 4:48 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69beefdee940819098e397ab50f57411 |
completed | March 21, 2026, 7:22 p.m. |
Created at: March 20, 2026, 1:47 p.m.