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.