Triple

T10641474
Position Surface form Disambiguated ID Type / Status
Subject Plancherel theorem for real reductive groups E250731 entity
Predicate involves P1256 FINISHED
Object Plancherel measure
The Plancherel measure is a canonical measure on the unitary dual of a group that describes how the regular representation decomposes into irreducible unitary representations in harmonic analysis.
E876156 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: Plancherel measure | Statement: [Plancherel theorem for real reductive groups, involves, Plancherel measure]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Plancherel measure
Context triple: [Plancherel theorem for real reductive groups, involves, Plancherel measure]
  • A. Haar measure
    Haar measure is a fundamental concept in harmonic analysis and topological group theory, providing a translation-invariant way to assign measures to subsets of locally compact groups.
  • B. 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.
  • C. Wiener measure
    Wiener measure is the canonical probability measure on the space of continuous paths that models standard Brownian motion in probability theory and stochastic analysis.
  • D. Schwartz–Bruhat space
    The Schwartz–Bruhat space is a function space of rapidly decreasing smooth (or locally constant with compact support, in the non-Archimedean case) test functions on a locally compact abelian group, fundamental in harmonic analysis and number theory.
  • E. Peter–Weyl theorem
    The Peter–Weyl theorem is a fundamental result in representation theory and harmonic analysis that decomposes square-integrable functions on a compact topological group into a direct sum of finite-dimensional irreducible unitary representations.
  • 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: Plancherel measure
Triple: [Plancherel theorem for real reductive groups, involves, Plancherel measure]
Generated description
The Plancherel measure is a canonical measure on the unitary dual of a group that describes how the regular representation decomposes into irreducible unitary representations in harmonic analysis.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Plancherel measure
Target entity description: The Plancherel measure is a canonical measure on the unitary dual of a group that describes how the regular representation decomposes into irreducible unitary representations in harmonic analysis.
  • A. Haar measure
    Haar measure is a fundamental concept in harmonic analysis and topological group theory, providing a translation-invariant way to assign measures to subsets of locally compact groups.
  • B. 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.
  • C. Wiener measure
    Wiener measure is the canonical probability measure on the space of continuous paths that models standard Brownian motion in probability theory and stochastic analysis.
  • D. Schwartz–Bruhat space
    The Schwartz–Bruhat space is a function space of rapidly decreasing smooth (or locally constant with compact support, in the non-Archimedean case) test functions on a locally compact abelian group, fundamental in harmonic analysis and number theory.
  • E. Peter–Weyl theorem
    The Peter–Weyl theorem is a fundamental result in representation theory and harmonic analysis that decomposes square-integrable functions on a compact topological group into a direct sum of finite-dimensional irreducible unitary representations.
  • 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_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_69d96bcd8c0c8190a0fad6a85b5604bb completed April 10, 2026, 9:29 p.m.
NEDg Description generation batch_69d9701de92881908c0b8f05eae97e35 completed April 10, 2026, 9:48 p.m.
NED2 Entity disambiguation (via description) batch_69d970f609108190a499b542f0b10ee9 completed April 10, 2026, 9:51 p.m.
Created at: April 8, 2026, 9:05 p.m.