Triple
T5705403
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Cartan |
E125770
|
entity |
| Predicate | hasRelatedConcept |
P12753
|
FINISHED |
| Object | Cartan–Killing form |
E542117
|
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–Killing form | Statement: [Cartan, hasRelatedConcept, Cartan–Killing form]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Cartan–Killing form Context triple: [Cartan, hasRelatedConcept, Cartan–Killing form]
-
A.
Cartan–Killing form
chosen
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.
-
B.
Kähler form
A Kähler form is a closed, positive-definite (1,1)-form that defines the compatible symplectic and Hermitian structure on a Kähler manifold.
-
C.
Maurer–Cartan form
The Maurer–Cartan form is a canonical Lie algebra-valued 1-form on a Lie group that encodes its infinitesimal structure and underlies many constructions in differential geometry and gauge theory.
-
D.
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.
-
E.
Cartan
Cartan is a French surname most famously associated with mathematician Élie Cartan and his influential family of mathematicians.
- 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_69c0082c96988190b3a6a201edce472a |
completed | March 22, 2026, 3:18 p.m. |
| NER | Named-entity recognition | batch_69c02459cd18819080fda0b481d11f08 |
completed | March 22, 2026, 5:18 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c07de7df8c8190824d24f729eaa04d |
completed | March 22, 2026, 11:40 p.m. |
Created at: March 22, 2026, 3:45 p.m.