Triple
T2267715
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Harish-Chandra |
E50185
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Harish-Chandra character formula
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.
|
E250730
|
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: Harish-Chandra character formula | Statement: [Harish-Chandra, notableWork, Harish-Chandra character formula]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Harish-Chandra character formula Context triple: [Harish-Chandra, notableWork, Harish-Chandra character formula]
-
A.
Weyl character formula
The Weyl character formula is a fundamental result in representation theory that gives an explicit expression for the characters of irreducible finite-dimensional representations of semisimple Lie algebras and Lie groups.
-
B.
Weil representation
The Weil representation is a fundamental projective unitary representation of symplectic groups (or their metaplectic covers) on spaces of functions, central to number theory, automorphic forms, and the theory of theta functions.
-
C.
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.
-
D.
Harish-Chandra
Harish-Chandra was a pioneering mathematician and physicist best known for his fundamental contributions to representation theory and harmonic analysis on Lie groups.
-
E.
Selberg trace formula
The Selberg trace formula is a fundamental result in analytic number theory and spectral theory that relates lengths of closed geodesics on a Riemannian manifold to the spectrum of its Laplace operator, serving as a non-abelian analogue of the Poisson summation formula.
- 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: Harish-Chandra character formula Triple: [Harish-Chandra, notableWork, Harish-Chandra character formula]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Harish-Chandra character formula Target entity description: 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.
-
A.
Weyl character formula
The Weyl character formula is a fundamental result in representation theory that gives an explicit expression for the characters of irreducible finite-dimensional representations of semisimple Lie algebras and Lie groups.
-
B.
Weil representation
The Weil representation is a fundamental projective unitary representation of symplectic groups (or their metaplectic covers) on spaces of functions, central to number theory, automorphic forms, and the theory of theta functions.
-
C.
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.
-
D.
Harish-Chandra
Harish-Chandra was a pioneering mathematician and physicist best known for his fundamental contributions to representation theory and harmonic analysis on Lie groups.
-
E.
Selberg trace formula
The Selberg trace formula is a fundamental result in analytic number theory and spectral theory that relates lengths of closed geodesics on a Riemannian manifold to the spectrum of its Laplace operator, serving as a non-abelian analogue of the Poisson summation formula.
- 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_69a88b01e0048190ba96431b5f990ba9 |
completed | March 4, 2026, 7:41 p.m. |
| NER | Named-entity recognition | batch_69abc1bbb49c8190822c7d809375e879 |
completed | March 7, 2026, 6:12 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69ae71d492a48190be58396831e87ea0 |
completed | March 9, 2026, 7:08 a.m. |
| NEDg | Description generation | batch_69ae72bdc5dc81908f475353999161e4 |
completed | March 9, 2026, 7:11 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69ae76720e3c8190aeb82dd8779ff715 |
completed | March 9, 2026, 7:27 a.m. |
Created at: March 4, 2026, 7:48 p.m.