Triple
T10641426
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Harish-Chandra character formula |
E250730
|
entity |
| Predicate | uses |
P98
|
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: [Harish-Chandra character formula, uses, Cartan subalgebra]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Cartan subalgebra Context triple: [Harish-Chandra character formula, uses, 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.
Borel subalgebras
Borel subalgebras are maximal solvable subalgebras of a Lie algebra that play a central role in the classification and representation theory of Lie algebras and algebraic groups.
-
D.
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.
-
E.
Heisenberg Lie algebra
The Heisenberg Lie algebra is a fundamental nilpotent Lie algebra generated by position and momentum operators with a central element, encoding the canonical commutation relations that underlie quantum mechanics and harmonic analysis.
- 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_69d97a4555e48190be39c0a7698b4282 |
completed | April 10, 2026, 10:31 p.m. |
Created at: April 8, 2026, 9:05 p.m.