Triple
T20509430
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Peter–Weyl theorem |
E503519
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Tannaka–Krein duality |
—
|
NE NERFINISHED |
How this triple was built (2 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: Tannaka–Krein duality | Statement: [Peter–Weyl theorem, relatedTo, Tannaka–Krein duality]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Tannaka–Krein duality Context triple: [Peter–Weyl theorem, relatedTo, Tannaka–Krein duality]
-
A.
Tannakian categories
chosen
Tannakian categories are rigid, abelian, tensor categories that generalize the representation theory of affine group schemes and provide a categorical framework for Galois-type dualities.
-
B.
Schur–Weyl duality
Schur–Weyl duality is a fundamental result in representation theory that links representations of the symmetric group and the general linear group via their commuting actions on tensor powers of a vector space.
-
C.
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.
-
D.
Dixmier mapping in representation theory
The Dixmier mapping in representation theory is a correspondence introduced by Jacques Dixmier that relates primitive ideals in the universal enveloping algebra of a Lie algebra to coadjoint orbits, playing a key role in understanding the orbit method and the structure of representations.
-
E.
Atiyah–Segal axioms
The Atiyah–Segal axioms are a set of mathematical conditions that rigorously define topological quantum field theories as functorial assignments from geometric data to algebraic structures.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (2 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_69e0b4b1e52c8190894281cf7e3283ab |
completed | April 16, 2026, 10:06 a.m. |
| NER | Named-entity recognition | batch_69e69dc9de788190882ce471966ef2b4 |
completed | April 20, 2026, 9:42 p.m. |
Created at: April 16, 2026, 11:36 a.m.