Triple

T5211818

Position	Surface form	Disambiguated ID	Type / Status
Subject	The Classical Groups: Their Invariants and Representations	`E117650`	entity
Predicate	libraryOfCongressSubject	`P450`	FINISHED
Object	Representations of groups Representations of groups is a branch of mathematics that studies how abstract groups can act as linear transformations on vector spaces, typically via homomorphisms into groups of matrices.	`E503510`	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: Representations of groups | Statement: [The Classical Groups: Their Invariants and Representations, libraryOfCongressSubject, Representations of groups]

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Representations of groups
Context triple: [The Classical Groups: Their Invariants and Representations, libraryOfCongressSubject, Representations of groups]

A. Methods of Representation Theory
Methods of Representation Theory is a foundational multi-volume work in mathematics that systematically develops the theory of group and algebra representations, coauthored by Israel Gelfand and collaborators.
B. Theory of Groups
Theory of Groups is a foundational textbook in abstract algebra that systematically develops the theory of groups and has been widely used for advanced mathematical study and research.
C. Representation Theory and Automorphic Functions
"Representation Theory and Automorphic Functions" is a seminal mathematical work by Israel Gelfand that develops the connections between representation theory of groups and the theory of automorphic forms, with deep applications in number theory and harmonic analysis.
D. The Classical Groups: Their Invariants and Representations
The Classical Groups: Their Invariants and Representations is a foundational mathematical monograph by Hermann Weyl that systematically develops the theory of classical Lie groups, their invariants, and their representation theory.
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. 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: Representations of groups
Triple: [The Classical Groups: Their Invariants and Representations, libraryOfCongressSubject, Representations of groups]

Generated description

Representations of groups is a branch of mathematics that studies how abstract groups can act as linear transformations on vector spaces, typically via homomorphisms into groups of matrices.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Representations of groups
Target entity description: Representations of groups is a branch of mathematics that studies how abstract groups can act as linear transformations on vector spaces, typically via homomorphisms into groups of matrices.

A. Methods of Representation Theory
Methods of Representation Theory is a foundational multi-volume work in mathematics that systematically develops the theory of group and algebra representations, coauthored by Israel Gelfand and collaborators.
B. Theory of Groups
Theory of Groups is a foundational textbook in abstract algebra that systematically develops the theory of groups and has been widely used for advanced mathematical study and research.
C. Representation Theory and Automorphic Functions
"Representation Theory and Automorphic Functions" is a seminal mathematical work by Israel Gelfand that develops the connections between representation theory of groups and the theory of automorphic forms, with deep applications in number theory and harmonic analysis.
D. The Classical Groups: Their Invariants and Representations
The Classical Groups: Their Invariants and Representations is a foundational mathematical monograph by Hermann Weyl that systematically develops the theory of classical Lie groups, their invariants, and their representation theory.
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. 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_69bd4464ba3c8190bc16b2ebbe42ddb0`	completed	March 20, 2026, 12:58 p.m.
NER	Named-entity recognition	`batch_69bd7a7166848190805152142e184529`	completed	March 20, 2026, 4:48 p.m.
NED1	Entity disambiguation (via context triple)	`batch_69beefd9e0b481908db7d6e2907b3b2b`	completed	March 21, 2026, 7:22 p.m.
NEDg	Description generation	`batch_69bef0b1fe9c8190bfc1be621c7c1c76`	completed	March 21, 2026, 7:25 p.m.
NED2	Entity disambiguation (via description)	`batch_69bef16739148190b9700228be7d07f9`	completed	March 21, 2026, 7:28 p.m.

Created at: March 20, 2026, 1:47 p.m.