Triple
T20563955
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Borel–Weil theorem |
E504917
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Bott–Borel–Weil theory |
—
|
NE NERFINISHED |
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: Bott–Borel–Weil theory | Statement: [Borel–Weil theorem, relatedTo, Bott–Borel–Weil theory]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Bott–Borel–Weil theory Context triple: [Borel–Weil theorem, relatedTo, Bott–Borel–Weil theory]
-
A.
Borel–Weil–Bott theorem
chosen
The Borel–Weil–Bott theorem is a fundamental result in representation theory and algebraic geometry that constructs all irreducible representations of a compact Lie group (or complex semisimple Lie algebra) as cohomology groups of line bundles over its flag variety.
-
B.
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.
-
C.
Deligne–Lusztig theory
Deligne–Lusztig theory is a framework in algebraic geometry and representation theory that constructs and studies representations of finite groups of Lie type using varieties defined over finite fields.
-
D.
Beilinson–Bernstein localization theorem
The Beilinson–Bernstein localization theorem is a fundamental result in geometric representation theory that realizes representations of semisimple Lie algebras as sheaves of differential operators on flag varieties, establishing an equivalence between algebraic and geometric categories.
-
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 (2 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_69e0b4b6587c8190aee63dc7cff244ea |
completed | April 16, 2026, 10:06 a.m. |
| NER | Named-entity recognition | batch_69e6a7a0a0488190a534050b40ff47da |
completed | April 20, 2026, 10:24 p.m. |
Created at: April 16, 2026, 11:39 a.m.