Triple

T23235104
Position Surface form Disambiguated ID Type / Status
Subject Casimir operator E581262 entity
Predicate relatedTo P37 FINISHED
Object Harish-Chandra isomorphism — 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: Harish-Chandra isomorphism | Statement: [Casimir operator, relatedTo, Harish-Chandra isomorphism]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Harish-Chandra isomorphism
Context triple: [Casimir operator, relatedTo, Harish-Chandra isomorphism]
  • A. Harish-Chandra isomorphism chosen
    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.
  • B. 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.
  • C. Harish-Chandra regularity theorem
    The Harish-Chandra regularity theorem is a fundamental result in representation theory that asserts characters of irreducible admissible representations of real reductive Lie groups are given by real-analytic, locally integrable functions on the group.
  • D. Harish-Chandra theory
    Harish-Chandra theory is a foundational framework in representation theory that analyzes the representations of real and p-adic semisimple Lie groups using tools from harmonic analysis, Lie algebras, and algebraic methods.
  • E. Harish-Chandra projection
    The Harish-Chandra projection is a linear map from a universal enveloping algebra onto the symmetric algebra of a Cartan subalgebra that plays a central role in describing the center via the Harish-Chandra isomorphism.
  • 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_69e2460556f88190be1744a84a84173f completed April 17, 2026, 2:39 p.m.
NER Named-entity recognition batch_69f192e8c7548190b53434eeb2620a6e completed April 29, 2026, 5:11 a.m.
Created at: April 17, 2026, 4:09 p.m.