Triple

T22668787
Position Surface form Disambiguated ID Type / Status
Subject Chevalley groups E559863 entity
Predicate areSometimesExtendedTo P98303 FINISHED
Object Steinberg groups
Steinberg groups are algebraic groups constructed as universal central extensions of Chevalley groups, playing a key role in the study of algebraic K-theory and group cohomology.
E1548924 NE FINISHED

How this triple was built (5 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: Steinberg groups | Statement: [Chevalley groups, areSometimesExtendedTo, Steinberg groups]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Steinberg groups
Context triple: [Chevalley groups, areSometimesExtendedTo, Steinberg groups]
  • A. 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.
  • B. Steinberg relations
    Steinberg relations are algebraic identities in Milnor K-theory that impose the condition that symbols of pairs of field elements summing to one vanish, playing a central role in defining the structure of these K-groups.
  • C. Selmer group
    A Selmer group is an arithmetic invariant in number theory that encodes obstructions to local-global principles for Galois representations or abelian varieties, playing a central role in studying Diophantine equations and Iwasawa theory.
  • D. 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.
  • E. 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.
  • 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: Steinberg groups
Triple: [Chevalley groups, areSometimesExtendedTo, Steinberg groups]
Generated description
Steinberg groups are algebraic groups constructed as universal central extensions of Chevalley groups, playing a key role in the study of algebraic K-theory and group cohomology.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Steinberg groups
Target entity description: Steinberg groups are algebraic groups constructed as universal central extensions of Chevalley groups, playing a key role in the study of algebraic K-theory and group cohomology.
  • A. 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.
  • B. Steinberg relations
    Steinberg relations are algebraic identities in Milnor K-theory that impose the condition that symbols of pairs of field elements summing to one vanish, playing a central role in defining the structure of these K-groups.
  • C. Selmer group
    A Selmer group is an arithmetic invariant in number theory that encodes obstructions to local-global principles for Galois representations or abelian varieties, playing a central role in studying Diophantine equations and Iwasawa theory.
  • D. 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.
  • E. 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.
  • F. None of above. chosen
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: areSometimesExtendedTo
Context triple: [Chevalley groups, areSometimesExtendedTo, Steinberg groups]
  • A. wasExtendedTo chosen
    Indicates that something previously existing was lengthened, expanded, or prolonged to reach a new limit, scope, or duration.
  • B. extendedInCase
    Indicates that one entity is lengthened, prolonged, or expanded when a particular condition or case applies.
  • C. extendedIn
    Indicates that one entity continues, prolongs, or expands the scope, duration, or range of another entity.
  • D. extendedFrom
    Indicates that one entity is derived by adding to or building upon the scope, content, or structure of another entity.
  • E. extendedTowards
    Indicates that one entity is stretched or directed outward in the direction of another entity or location.
  • F. None of above.

Provenance (6 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_69e2454a158c819093b8e35f5045efb6 completed April 17, 2026, 2:35 p.m.
NER Named-entity recognition batch_69f1781de1d48190947cb1bb9d0890d9 completed April 29, 2026, 3:16 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0b73e98b74819096a28b35a4c5a510 completed May 18, 2026, 8:17 p.m.
NEDg Description generation batch_6a0b75873f2c8190a89772fc560840e1 completed May 18, 2026, 8:24 p.m.
NED2 Entity disambiguation (via description) batch_6a0b7601fda88190bbfa04e7eb240f65 completed May 18, 2026, 8:26 p.m.
PD Predicate disambiguation batch_69ee62a6245881909506ff502da14137 completed April 26, 2026, 7:08 p.m.
Created at: April 17, 2026, 3:09 p.m.