Triple

T4416537
Position Surface form Disambiguated ID Type / Status
Subject Marshall Hall E94987 entity
Predicate notableWork P4 FINISHED
Object 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.
E437488 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: Theory of Groups | Statement: [Marshall Hall, notableWork, Theory of Groups]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Theory of Groups
Context triple: [Marshall Hall, notableWork, Theory of Groups]
  • A. Gruppentheorie und Quantenmechanik
    Gruppentheorie und Quantenmechanik is Hermann Weyl’s influential 1928 monograph that systematically applies group theory to the foundations of quantum mechanics, shaping the mathematical formulation of modern physics.
  • B. Abelian groups
    Abelian groups are algebraic structures in which the group operation is commutative, meaning the order of combining elements does not affect the result.
  • C. 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.
  • D. Noether's isomorphism theorems
    Noether's isomorphism theorems are fundamental results in abstract algebra that relate quotient structures and substructures of groups, rings, and modules, providing a unifying framework for understanding homomorphic images and factor structures.
  • E. 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.
  • 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: Theory of Groups
Triple: [Marshall Hall, notableWork, Theory of Groups]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Theory of Groups
Target entity description: 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.
  • A. Gruppentheorie und Quantenmechanik
    Gruppentheorie und Quantenmechanik is Hermann Weyl’s influential 1928 monograph that systematically applies group theory to the foundations of quantum mechanics, shaping the mathematical formulation of modern physics.
  • B. Abelian groups
    Abelian groups are algebraic structures in which the group operation is commutative, meaning the order of combining elements does not affect the result.
  • C. 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.
  • D. Noether's isomorphism theorems
    Noether's isomorphism theorems are fundamental results in abstract algebra that relate quotient structures and substructures of groups, rings, and modules, providing a unifying framework for understanding homomorphic images and factor structures.
  • E. 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.
  • 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_69b3453a36908190b95a79a297ca083c completed March 12, 2026, 10:59 p.m.
NER Named-entity recognition batch_69b3551afb448190a2ce2000193808ac completed March 13, 2026, 12:06 a.m.
NED1 Entity disambiguation (via context triple) batch_69b5f61b56a8819099b5302f1b53f76d completed March 14, 2026, 11:58 p.m.
NEDg Description generation batch_69b5f709063c81909334a5b21da99c22 completed March 15, 2026, 12:02 a.m.
NED2 Entity disambiguation (via description) batch_69b5f7887cb08190bf498eefc3627bfa completed March 15, 2026, 12:04 a.m.
Created at: March 12, 2026, 11:29 p.m.