Triple

T2267714
Position Surface form Disambiguated ID Type / Status
Subject Harish-Chandra E50185 entity
Predicate notableWork P4 FINISHED
Object 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.
E250729 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 isomorphism | Statement: [Harish-Chandra, notableWork, Harish-Chandra isomorphism]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Harish-Chandra isomorphism
Context triple: [Harish-Chandra, notableWork, Harish-Chandra isomorphism]
  • A. 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.
  • B. 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.
  • 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. Conway–Norton collaboration
    The Conway–Norton collaboration was a joint mathematical effort, led by John Conway and Simon Norton, that played a key role in developing the theory of monstrous moonshine and the construction of the Monster group.
  • 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 isomorphism
Triple: [Harish-Chandra, notableWork, Harish-Chandra isomorphism]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Harish-Chandra isomorphism
Target entity description: 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.
  • A. 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.
  • B. 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.
  • 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. Conway–Norton collaboration
    The Conway–Norton collaboration was a joint mathematical effort, led by John Conway and Simon Norton, that played a key role in developing the theory of monstrous moonshine and the construction of the Monster group.
  • 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.