Triple
T12011746
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Raoul Bott |
E285919
|
entity |
| Predicate | knownFor |
P22
|
FINISHED |
| Object |
Bott–Samelson theorem
The Bott–Samelson theorem is a fundamental result in algebraic topology and geometry that provides a resolution of singularities for Schubert varieties via Bott–Samelson varieties, illuminating the topology and cohomology of flag manifolds.
|
E960592
|
NE FINISHED |
How this triple was built (4 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–Samelson theorem | Statement: [Raoul Bott, knownFor, Bott–Samelson theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Bott–Samelson theorem Context triple: [Raoul Bott, knownFor, Bott–Samelson theorem]
-
A.
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.
-
B.
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.
-
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.
Bernstein–Gelfand–Gelfand resolution
The Bernstein–Gelfand–Gelfand resolution is a fundamental construction in representation theory that provides an explicit, exact sequence resolving finite-dimensional representations of semisimple Lie algebras using complexes of Verma modules.
-
E.
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.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Bott–Samelson theorem Triple: [Raoul Bott, knownFor, Bott–Samelson theorem]
Generated description
The Bott–Samelson theorem is a fundamental result in algebraic topology and geometry that provides a resolution of singularities for Schubert varieties via Bott–Samelson varieties, illuminating the topology and cohomology of flag manifolds.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Bott–Samelson theorem Target entity description: The Bott–Samelson theorem is a fundamental result in algebraic topology and geometry that provides a resolution of singularities for Schubert varieties via Bott–Samelson varieties, illuminating the topology and cohomology of flag manifolds.
-
A.
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.
-
B.
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.
-
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.
Bernstein–Gelfand–Gelfand resolution
The Bernstein–Gelfand–Gelfand resolution is a fundamental construction in representation theory that provides an explicit, exact sequence resolving finite-dimensional representations of semisimple Lie algebras using complexes of Verma modules.
-
E.
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.
- F. None of above. chosen
Provenance (5 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_69d6ab45a368819084fce08bf0dc3705 |
completed | April 8, 2026, 7:23 p.m. |
| NER | Named-entity recognition | batch_69d903d7777481908cd5a001f75e2ee3 |
completed | April 10, 2026, 2:06 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f48b363c6481908c8414c1eecc14f5 |
completed | May 1, 2026, 11:15 a.m. |
| NEDg | Description generation | batch_69f48fc6da4c81908442f18cb4a65b27 |
completed | May 1, 2026, 11:34 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69f495cc50908190aab4f8ca64c66ef3 |
completed | May 1, 2026, noon |
Created at: April 8, 2026, 9:46 p.m.