Triple

T17340993
Position Surface form Disambiguated ID Type / Status
Subject Theory of Linear Operations E421064 entity
Predicate citedBy P771 FINISHED
Object Riesz and Sz.-Nagy: Functional Analysis
"Riesz and Sz.-Nagy: Functional Analysis" is a classic textbook in functional analysis that systematically develops the theory of Hilbert and Banach spaces and linear operators, influential in modern analysis and operator theory.
E1262408 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: Riesz and Sz.-Nagy: Functional Analysis | Statement: [Theory of Linear Operations, citedBy, Riesz and Sz.-Nagy: Functional Analysis]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Riesz and Sz.-Nagy: Functional Analysis
Context triple: [Theory of Linear Operations, citedBy, Riesz and Sz.-Nagy: Functional Analysis]
  • A. Theory of Linear Operations
    Theory of Linear Operations is a foundational 1932 monograph by Stefan Banach that systematically developed functional analysis and the theory of Banach spaces.
  • B. A Hilbert Space Problem Book
    A Hilbert Space Problem Book is a classic problem-oriented textbook by Paul Halmos that presents and explores key concepts in Hilbert space theory through a comprehensive collection of exercises and solutions.
  • C. Introduction to Hilbert Space and the Theory of Spectral Multiplicity
    "Introduction to Hilbert Space and the Theory of Spectral Multiplicity" is a classic mathematical text by Paul Halmos that provides a foundational treatment of Hilbert space theory and the spectral analysis of linear operators.
  • D. Leçons d’analyse fonctionnelle
    Leçons d’analyse fonctionnelle is a foundational textbook in functional analysis that helped shape the modern theory of linear operators and Banach and Hilbert spaces.
  • E. Foundations of Functional Analysis
    Foundations of Functional Analysis is a seminal mathematical text that systematically develops the core concepts and theorems of functional analysis, particularly in the tradition of the Riesz school.
  • 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: Riesz and Sz.-Nagy: Functional Analysis
Triple: [Theory of Linear Operations, citedBy, Riesz and Sz.-Nagy: Functional Analysis]
Generated description
"Riesz and Sz.-Nagy: Functional Analysis" is a classic textbook in functional analysis that systematically develops the theory of Hilbert and Banach spaces and linear operators, influential in modern analysis and operator theory.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Riesz and Sz.-Nagy: Functional Analysis
Target entity description: "Riesz and Sz.-Nagy: Functional Analysis" is a classic textbook in functional analysis that systematically develops the theory of Hilbert and Banach spaces and linear operators, influential in modern analysis and operator theory.
  • A. Theory of Linear Operations
    Theory of Linear Operations is a foundational 1932 monograph by Stefan Banach that systematically developed functional analysis and the theory of Banach spaces.
  • B. A Hilbert Space Problem Book
    A Hilbert Space Problem Book is a classic problem-oriented textbook by Paul Halmos that presents and explores key concepts in Hilbert space theory through a comprehensive collection of exercises and solutions.
  • C. Introduction to Hilbert Space and the Theory of Spectral Multiplicity
    "Introduction to Hilbert Space and the Theory of Spectral Multiplicity" is a classic mathematical text by Paul Halmos that provides a foundational treatment of Hilbert space theory and the spectral analysis of linear operators.
  • D. Leçons d’analyse fonctionnelle
    Leçons d’analyse fonctionnelle is a foundational textbook in functional analysis that helped shape the modern theory of linear operators and Banach and Hilbert spaces.
  • E. Foundations of Functional Analysis
    Foundations of Functional Analysis is a seminal mathematical text that systematically develops the core concepts and theorems of functional analysis, particularly in the tradition of the Riesz school.
  • 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_69d889d3adc881909319f1edb8d2a956 completed April 10, 2026, 5:25 a.m.
NER Named-entity recognition batch_69e43a15f6488190ad7d489e7391ab12 completed April 19, 2026, 2:12 a.m.
NED1 Entity disambiguation (via context triple) batch_6a018c588a7081909ab108cb4adfedfe completed May 11, 2026, 7:59 a.m.
NEDg Description generation batch_6a018e0f09c881909296656b2732bf1e completed May 11, 2026, 8:06 a.m.
NED2 Entity disambiguation (via description) batch_6a018e7b453c81909f75593237bcf9ec completed May 11, 2026, 8:08 a.m.
Created at: April 10, 2026, 5:44 a.m.