Triple

T12011748
Position Surface form Disambiguated ID Type / Status
Subject Raoul Bott E285919 entity
Predicate knownFor P22 FINISHED
Object Borel–Bott–Weil theorem E504917 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–Bott–Weil theorem | Statement: [Raoul Bott, knownFor, Borel–Bott–Weil theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Borel–Bott–Weil theorem
Context triple: [Raoul Bott, knownFor, Borel–Bott–Weil 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. Harish-Chandra isomorphism
    The Harish-Chandra isomorphism is a fundamental result in representation theory that identifies the center of the universal enveloping algebra of a semisimple Lie algebra with the algebra of Weyl group–invariant polynomials on a Cartan subalgebra.
  • D. Hirzebruch–Riemann–Roch theorem
    The Hirzebruch–Riemann–Roch theorem is a fundamental result in algebraic geometry and topology that expresses the holomorphic Euler characteristic of a complex manifold in terms of characteristic classes, unifying and extending classical Riemann–Roch type formulas.
  • 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 (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_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.
Created at: April 8, 2026, 9:46 p.m.