Triple

T10931403
Position Surface form Disambiguated ID Type / Status
Subject Nolan Wallach E258214 entity
Predicate hasWrittenWork P4 FINISHED
Object Real Reductive Groups II
Real Reductive Groups II is a graduate-level mathematics monograph by Nolan Wallach that develops the representation theory and harmonic analysis of real reductive Lie groups in depth.
 E895039 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: Real Reductive Groups II | Statement: [Nolan Wallach, hasWrittenWork, Real Reductive Groups II]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Real Reductive Groups II
Context triple: [Nolan Wallach, hasWrittenWork, Real Reductive Groups II]
  • A. Real Reductive Groups I
    Real Reductive Groups I is a foundational mathematical monograph by Nolan Wallach that develops the representation theory and harmonic analysis of real reductive Lie groups.
  • B. Deligne–Lusztig theory
    Deligne–Lusztig theory is a framework in algebraic geometry and representation theory that constructs and studies representations of finite groups of Lie type using varieties defined over finite fields.
  • C. Adeles and Algebraic Groups
    "Adeles and Algebraic Groups" is a foundational mathematical work by André Weil that develops the theory of adeles and its deep connections with algebraic groups and number theory.
  • D. Algebraic Groups and Class Fields
    "Algebraic Groups and Class Fields" is a influential mathematical monograph that develops the deep connections between algebraic group theory and class field theory within number theory and arithmetic geometry.
  • E. Paley–Wiener theorem for real reductive groups
    The Paley–Wiener theorem for real reductive groups is a fundamental result in harmonic analysis that characterizes the image of compactly supported smooth functions under the group Fourier transform in terms of holomorphic functions with specific growth and support conditions.
  • 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: Real Reductive Groups II
Triple: [Nolan Wallach, hasWrittenWork, Real Reductive Groups II]
Generated description
Real Reductive Groups II is a graduate-level mathematics monograph by Nolan Wallach that develops the representation theory and harmonic analysis of real reductive Lie groups in depth.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: Real Reductive Groups II
Target entity description: Real Reductive Groups II is a graduate-level mathematics monograph by Nolan Wallach that develops the representation theory and harmonic analysis of real reductive Lie groups in depth.
  • A. Real Reductive Groups I
    Real Reductive Groups I is a foundational mathematical monograph by Nolan Wallach that develops the representation theory and harmonic analysis of real reductive Lie groups.
  • B. Deligne–Lusztig theory
    Deligne–Lusztig theory is a framework in algebraic geometry and representation theory that constructs and studies representations of finite groups of Lie type using varieties defined over finite fields.
  • C. Adeles and Algebraic Groups
    "Adeles and Algebraic Groups" is a foundational mathematical work by André Weil that develops the theory of adeles and its deep connections with algebraic groups and number theory.
  • D. Algebraic Groups and Class Fields
    "Algebraic Groups and Class Fields" is a influential mathematical monograph that develops the deep connections between algebraic group theory and class field theory within number theory and arithmetic geometry.
  • E. Paley–Wiener theorem for real reductive groups
    The Paley–Wiener theorem for real reductive groups is a fundamental result in harmonic analysis that characterizes the image of compactly supported smooth functions under the group Fourier transform in terms of holomorphic functions with specific growth and support conditions.
  • 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_69d6aa8769b4819082bfe5e61b9017f0 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d770a062f481908beb76c6dbaeb6a6 completed April 9, 2026, 9:25 a.m.
NED1 Entity disambiguation (via context triple) batch_69e23bdf678881909cae518ecaacf577 completed April 17, 2026, 1:55 p.m.
NEDg Description generation batch_69e24541cbb481908f14a9cb2787c118 completed April 17, 2026, 2:35 p.m.
NED2 Entity disambiguation (via description) batch_69e248f48dc88190af9491e8cdc4a532 completed April 17, 2026, 2:51 p.m.
Created at: April 8, 2026, 9:23 p.m.