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.