Triple
T5705551
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Cartan subalgebras |
E125774
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Borel subalgebras |
E542124
|
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: Borel subalgebras | Statement: [Cartan subalgebras, relatedTo, Borel subalgebras]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Borel subalgebras Context triple: [Cartan subalgebras, relatedTo, Borel subalgebras]
-
A.
Borel subalgebras
chosen
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.
-
B.
Cartan subalgebras
Cartan subalgebras are maximal abelian subalgebras of a Lie algebra consisting of semisimple elements, fundamental for classifying and understanding the structure of Lie algebras.
-
C.
Borel–Weil theorem
The Borel–Weil theorem is a fundamental result in representation theory that realizes irreducible representations of compact Lie groups as spaces of holomorphic sections of line bundles over their flag manifolds.
-
D.
Lie algebras
Lie algebras are algebraic structures used to study continuous symmetries, especially those arising from Lie groups, via a linearized, infinitesimal perspective.
-
E.
Kazhdan–Lusztig theory
Kazhdan–Lusztig theory is a framework in representation theory and algebraic geometry that studies Hecke algebras and their bases via Kazhdan–Lusztig polynomials, with deep connections to the representation theory of Lie algebras and geometry of Schubert varieties.
- 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.