Triple

T20563954
Position Surface form Disambiguated ID Type / Status
Subject Borel–Weil theorem E504917 entity
Predicate relatedTo P37 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: [Borel–Weil theorem, relatedTo, Borel–Weil–Bott theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Borel–Weil–Bott theorem
Context triple: [Borel–Weil theorem, relatedTo, Borel–Weil–Bott theorem]
  • 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. 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.
  • D. 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.
  • 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.
  • 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.