Triple

T10641481
Position Surface form Disambiguated ID Type / Status
Subject Plancherel theorem for real reductive groups E250731 entity
Predicate involves P1256 FINISHED
Object Harish-Chandra c-function E876151 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 c-function | Statement: [Plancherel theorem for real reductive groups, involves, Harish-Chandra c-function]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Harish-Chandra c-function
Context triple: [Plancherel theorem for real reductive groups, involves, Harish-Chandra c-function]
  • A. Harish-Chandra c-function chosen
    The Harish-Chandra c-function is a key analytic function in representation theory and harmonic analysis on semisimple Lie groups, encoding the Plancherel measure and asymptotic behavior of spherical functions.
  • 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 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.
  • D. 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.
  • E. 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.
  • 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_69d6aa5a4c4881908f39be6efe5981e5 completed April 8, 2026, 7:19 p.m.
NER Named-entity recognition batch_69d6dfcd19648190882380d2c90be486 completed April 8, 2026, 11:07 p.m.
NED1 Entity disambiguation (via context triple) batch_69d97a4555e48190be39c0a7698b4282 completed April 10, 2026, 10:31 p.m.
Created at: April 8, 2026, 9:05 p.m.