Triple

T20509371
Position Surface form Disambiguated ID Type / Status
Subject Weyl vector E503518 entity
Predicate usedIn P98 FINISHED
Object Borel–Weil–Bott theorem — 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: Borel–Weil–Bott theorem | Statement: [Weyl vector, usedIn, Borel–Weil–Bott theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Borel–Weil–Bott theorem
Context triple: [Weyl vector, usedIn, Borel–Weil–Bott theorem]
  • A. Borel–Weil theorem chosen
    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.
  • B. 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.
  • C. 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.
  • D. 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.
  • E. Oka–Weil theorem
    The Oka–Weil theorem is a fundamental result in several complex variables that extends Runge’s approximation theorem by characterizing when holomorphic functions on certain compact sets in complex manifolds can be uniformly approximated by global holomorphic functions.
  • 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_69e0b4b1e52c8190894281cf7e3283ab completed April 16, 2026, 10:06 a.m.
NER Named-entity recognition batch_69e69dc9de788190882ce471966ef2b4 completed April 20, 2026, 9:42 p.m.
Created at: April 16, 2026, 11:36 a.m.