Triple

T12442823
Position Surface form Disambiguated ID Type / Status
Subject Luigi Bianchi E297317 entity
Predicate hasConceptNamedAfter P3325 FINISHED
Object Bianchi groups
Bianchi groups are a class of Kleinian groups arising as PSL(2) over the ring of integers in imaginary quadratic number fields, central in the study of hyperbolic 3-manifolds and arithmetic groups.
E984867 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: Bianchi groups | Statement: [Luigi Bianchi, hasConceptNamedAfter, Bianchi groups]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Bianchi groups
Context triple: [Luigi Bianchi, hasConceptNamedAfter, Bianchi groups]
  • A. Chevalley groups
    Chevalley groups are a broad class of linear algebraic groups constructed over arbitrary fields that generalize classical Lie groups and play a central role in the classification of finite simple groups.
  • B. Whitehead groups
    Whitehead groups are algebraic K-theory invariants associated with groups that measure the failure of certain projective modules or h-cobordisms to be trivial, playing a central role in high-dimensional topology and geometric group theory.
  • C. Brauer group
    The Brauer group is an algebraic structure that classifies equivalence classes of central simple algebras over a field (or more general schemes), playing a key role in number theory, algebraic geometry, and cohomology.
  • D. Bianchi classification
    Bianchi classification is a scheme in general relativity that categorizes three-dimensional Lie algebras (and corresponding homogeneous cosmological models) into distinct types based on their symmetry properties.
  • E. Cremona group of the projective plane
    The Cremona group of the projective plane is the group of all birational self-maps of the complex projective plane, serving as a fundamental object in algebraic geometry and the study of plane transformations.
  • 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: Bianchi groups
Triple: [Luigi Bianchi, hasConceptNamedAfter, Bianchi groups]
Generated description
Bianchi groups are a class of Kleinian groups arising as PSL(2) over the ring of integers in imaginary quadratic number fields, central in the study of hyperbolic 3-manifolds and arithmetic groups.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Bianchi groups
Target entity description: Bianchi groups are a class of Kleinian groups arising as PSL(2) over the ring of integers in imaginary quadratic number fields, central in the study of hyperbolic 3-manifolds and arithmetic groups.
  • A. Chevalley groups
    Chevalley groups are a broad class of linear algebraic groups constructed over arbitrary fields that generalize classical Lie groups and play a central role in the classification of finite simple groups.
  • B. Whitehead groups
    Whitehead groups are algebraic K-theory invariants associated with groups that measure the failure of certain projective modules or h-cobordisms to be trivial, playing a central role in high-dimensional topology and geometric group theory.
  • C. Brauer group
    The Brauer group is an algebraic structure that classifies equivalence classes of central simple algebras over a field (or more general schemes), playing a key role in number theory, algebraic geometry, and cohomology.
  • D. Bianchi classification
    Bianchi classification is a scheme in general relativity that categorizes three-dimensional Lie algebras (and corresponding homogeneous cosmological models) into distinct types based on their symmetry properties.
  • E. Cremona group of the projective plane
    The Cremona group of the projective plane is the group of all birational self-maps of the complex projective plane, serving as a fundamental object in algebraic geometry and the study of plane transformations.
  • 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_69d6ada166c48190b902972cd2408fa3 completed April 8, 2026, 7:33 p.m.
NER Named-entity recognition batch_69d94d8fd9848190a83410353d88ea8d completed April 10, 2026, 7:20 p.m.
NED1 Entity disambiguation (via context triple) batch_69f63f10926881909ffc641f8d19f93a completed May 2, 2026, 6:14 p.m.
NEDg Description generation batch_69f640874a0481908d9203b48304d866 completed May 2, 2026, 6:20 p.m.
NED2 Entity disambiguation (via description) batch_69f641287f888190bc7000c256c362d3 completed May 2, 2026, 6:23 p.m.
Created at: April 8, 2026, 9:55 p.m.