Triple

T21972928
Position Surface form Disambiguated ID Type / Status
Subject Functional Analysis: Introduction to Further Topics in Analysis E542635 entity
Predicate prequel P1961 FINISHED
Object Fourier Analysis: An Introduction — NE NERFINISHED

How this triple was built (3 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: Fourier Analysis: An Introduction | Statement: [Functional Analysis: Introduction to Further Topics in Analysis, prequel, Fourier Analysis: An Introduction]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Fourier Analysis: An Introduction
Context triple: [Functional Analysis: Introduction to Further Topics in Analysis, prequel, Fourier Analysis: An Introduction]
  • A. The Fourier Transform and Its Applications
    The Fourier Transform and Its Applications is a classic textbook by Ronald N. Bracewell that introduces and develops Fourier analysis techniques for solving problems in engineering, physics, and applied mathematics.
  • B. Functional Analysis: Introduction to Further Topics in Analysis
    "Functional Analysis: Introduction to Further Topics in Analysis" is an advanced graduate-level textbook by Elias Stein that develops modern functional analysis with applications to areas such as operator theory, harmonic analysis, and partial differential equations.
  • C. Fourier analysis
    Fourier analysis is a mathematical method for decomposing functions or signals into sums of sinusoidal components, widely used in fields such as signal processing, physics, and engineering.
  • D. Lectures on Fourier Integrals
    Lectures on Fourier Integrals is a classic mathematical monograph by Salomon Bochner that systematically develops the theory and applications of Fourier integrals and transforms.
  • E. Introduction to Abstract Harmonic Analysis
    Introduction to Abstract Harmonic Analysis is a foundational graduate-level textbook that systematically develops the theory of harmonic analysis on topological groups and related abstract structures.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: Fourier Analysis: An Introduction
Target entity description: "Fourier Analysis: An Introduction" is a foundational mathematics textbook by Elias M. Stein and Rami Shakarchi that presents the core ideas and techniques of Fourier series and Fourier transforms for advanced undergraduates and beginning graduate students.
  • A. The Fourier Transform and Its Applications
    The Fourier Transform and Its Applications is a classic textbook by Ronald N. Bracewell that introduces and develops Fourier analysis techniques for solving problems in engineering, physics, and applied mathematics.
  • B. Functional Analysis: Introduction to Further Topics in Analysis
    "Functional Analysis: Introduction to Further Topics in Analysis" is an advanced graduate-level textbook by Elias Stein that develops modern functional analysis with applications to areas such as operator theory, harmonic analysis, and partial differential equations.
  • C. Fourier analysis
    Fourier analysis is a mathematical method for decomposing functions or signals into sums of sinusoidal components, widely used in fields such as signal processing, physics, and engineering.
  • D. Lectures on Fourier Integrals
    Lectures on Fourier Integrals is a classic mathematical monograph by Salomon Bochner that systematically develops the theory and applications of Fourier integrals and transforms.
  • E. Introduction to Abstract Harmonic Analysis
    Introduction to Abstract Harmonic Analysis is a foundational graduate-level textbook that systematically develops the theory of harmonic analysis on topological groups and related abstract structures.
  • F. None of above. chosen

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_69e0c48070988190909db97667b9a0ac completed April 16, 2026, 11:14 a.m.
NER Named-entity recognition batch_69f124857dcc8190ab474cd8ab9c130a completed April 28, 2026, 9:20 p.m.
Created at: April 16, 2026, 8:02 p.m.