Triple

T14840799
Position Surface form Disambiguated ID Type / Status
Subject François Bruhat E348956 entity
Predicate notableConcept P201 FINISHED
Object Iwahori–Bruhat decomposition E1121929 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: Iwahori–Bruhat decomposition | Statement: [François Bruhat, notableConcept, Iwahori–Bruhat decomposition]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Iwahori–Bruhat decomposition
Context triple: [François Bruhat, notableConcept, Iwahori–Bruhat decomposition]
  • A. Bruhat decomposition chosen
    Bruhat decomposition is a fundamental result in algebraic group theory that expresses a group as a union of double cosets indexed by elements of its Weyl group, revealing a deep combinatorial structure.
  • 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. Iwasawa decomposition
    The Iwasawa decomposition is a fundamental factorization in Lie group theory that expresses a semisimple Lie group as a product of a maximal compact subgroup, a maximal abelian subgroup, and a nilpotent subgroup, playing a key role in representation theory and harmonic analysis.
  • 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. 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.
  • 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_69d822ec69008190a9232caa68836872 completed April 9, 2026, 10:06 p.m.
NER Named-entity recognition batch_69ded28e40f08190b309d8ac6404d2fc completed April 14, 2026, 11:49 p.m.
NED1 Entity disambiguation (via context triple) batch_69fe64fe89e88190912cd205feef85d3 completed May 8, 2026, 10:34 p.m.
Created at: April 10, 2026, 1:53 a.m.