Triple
T5705548
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Cartan subalgebras |
E125774
|
entity |
| Predicate | usedFor |
P98
|
FINISHED |
| Object | Harish-Chandra theory of representations |
E250730
|
NE FINISHED |
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: Harish-Chandra theory of representations | Statement: [Cartan subalgebras, usedFor, Harish-Chandra theory of representations]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Harish-Chandra theory of representations Context triple: [Cartan subalgebras, usedFor, Harish-Chandra theory of representations]
-
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.
Harish-Chandra isomorphism
The Harish-Chandra isomorphism is a fundamental result in representation theory that identifies the center of the universal enveloping algebra of a semisimple Lie algebra with the algebra of Weyl group–invariant polynomials on a Cartan subalgebra.
-
C.
Plancherel theorem for real reductive groups
The Plancherel theorem for real reductive groups is a fundamental result in representation theory that describes how square-integrable functions on a real reductive Lie group decompose into irreducible unitary representations, generalizing Fourier analysis to this non-abelian setting.
-
D.
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.
-
E.
Harish-Chandra character formula
chosen
The Harish-Chandra character formula is a fundamental result in representation theory that gives an explicit expression for the characters of irreducible admissible representations of real reductive Lie groups.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (3 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_69c0082c96988190b3a6a201edce472a |
completed | March 22, 2026, 3:18 p.m. |
| NER | Named-entity recognition | batch_69c02459cd18819080fda0b481d11f08 |
completed | March 22, 2026, 5:18 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c05a666d788190a0f786d12391a44b |
completed | March 22, 2026, 9:08 p.m. |
Created at: March 22, 2026, 3:45 p.m.