Triple

T10931406
Position Surface form Disambiguated ID Type / Status
Subject Nolan Wallach E258214 entity
Predicate hasWrittenWork P4 FINISHED
Object Lie Groups: History, Frontiers and Applications (contributions)
"Lie Groups: History, Frontiers and Applications (contributions)" is a scholarly work featuring contributions by mathematician Nolan Wallach on the theory and applications of Lie groups.
E893440 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: Lie Groups: History, Frontiers and Applications (contributions) | Statement: [Nolan Wallach, hasWrittenWork, Lie Groups: History, Frontiers and Applications (contributions)]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Lie Groups: History, Frontiers and Applications (contributions)
Context triple: [Nolan Wallach, hasWrittenWork, Lie Groups: History, Frontiers and Applications (contributions)]
  • A. Lie theory
    Lie theory is a branch of mathematics that studies continuous symmetry through Lie groups and Lie algebras, with deep applications in geometry, analysis, and theoretical physics.
  • B. 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.
  • C. Lie algebras
    Lie algebras are algebraic structures used to study continuous symmetries, especially those arising from Lie groups, via a linearized, infinitesimal perspective.
  • D. Lie group
    A Lie group is a mathematical structure that is both a smooth manifold and a group, where the group operations are differentiable and used to study continuous symmetries.
  • E. L’intégration dans les groupes topologiques et ses applications
    L’intégration dans les groupes topologiques et ses applications is a foundational mathematical monograph by André Weil that develops the theory of integration on topological groups and explores its far-reaching applications in analysis and number theory.
  • 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: Lie Groups: History, Frontiers and Applications (contributions)
Triple: [Nolan Wallach, hasWrittenWork, Lie Groups: History, Frontiers and Applications (contributions)]
Generated description
"Lie Groups: History, Frontiers and Applications (contributions)" is a scholarly work featuring contributions by mathematician Nolan Wallach on the theory and applications of Lie groups.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Lie Groups: History, Frontiers and Applications (contributions)
Target entity description: "Lie Groups: History, Frontiers and Applications (contributions)" is a scholarly work featuring contributions by mathematician Nolan Wallach on the theory and applications of Lie groups.
  • A. Lie theory
    Lie theory is a branch of mathematics that studies continuous symmetry through Lie groups and Lie algebras, with deep applications in geometry, analysis, and theoretical physics.
  • B. 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.
  • C. Lie algebras
    Lie algebras are algebraic structures used to study continuous symmetries, especially those arising from Lie groups, via a linearized, infinitesimal perspective.
  • D. Lie group
    A Lie group is a mathematical structure that is both a smooth manifold and a group, where the group operations are differentiable and used to study continuous symmetries.
  • E. L’intégration dans les groupes topologiques et ses applications
    L’intégration dans les groupes topologiques et ses applications is a foundational mathematical monograph by André Weil that develops the theory of integration on topological groups and explores its far-reaching applications in analysis and number theory.
  • 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_69d6aa8769b4819082bfe5e61b9017f0 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d770a062f481908beb76c6dbaeb6a6 completed April 9, 2026, 9:25 a.m.
NED1 Entity disambiguation (via context triple) batch_69e2175711d4819088f93bdf64ba4d3f completed April 17, 2026, 11:19 a.m.
NEDg Description generation batch_69e21e54e22881908726f088643edfd2 completed April 17, 2026, 11:49 a.m.
NED2 Entity disambiguation (via description) batch_69e21f1134d0819082fcc735da61d347 completed April 17, 2026, 11:52 a.m.
Created at: April 8, 2026, 9:23 p.m.