Triple

T19993314
Position Surface form Disambiguated ID Type / Status
Subject Andrew Browder E494115 entity
Predicate notableWork P4 FINISHED
Object Introduction to Function Algebras
Introduction to Function Algebras is a graduate-level mathematics textbook by Andrew Browder that develops the theory of function algebras and their applications in complex analysis and functional analysis.
E1405325 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: Introduction to Function Algebras | Statement: [Andrew Browder, notableWork, Introduction to Function Algebras]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Introduction to Function Algebras
Context triple: [Andrew Browder, notableWork, Introduction to Function Algebras]
  • A. 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.
  • B. Introduction to the Theory of Algebraic Functions of One Variable
    Introduction to the Theory of Algebraic Functions of One Variable is a classic monograph by Claude Chevalley that provides a rigorous, modern foundation for the theory of algebraic function fields in one variable.
  • C. 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.
  • D. Banach algebra
    A Banach algebra is a complete normed vector space equipped with a compatible associative algebra multiplication, allowing analysis and algebra to be combined in a single structure.
  • E. 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.
  • 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: Introduction to Function Algebras
Triple: [Andrew Browder, notableWork, Introduction to Function Algebras]
Generated description
Introduction to Function Algebras is a graduate-level mathematics textbook by Andrew Browder that develops the theory of function algebras and their applications in complex analysis and functional analysis.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Introduction to Function Algebras
Target entity description: Introduction to Function Algebras is a graduate-level mathematics textbook by Andrew Browder that develops the theory of function algebras and their applications in complex analysis and functional analysis.
  • A. 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.
  • B. Introduction to the Theory of Algebraic Functions of One Variable
    Introduction to the Theory of Algebraic Functions of One Variable is a classic monograph by Claude Chevalley that provides a rigorous, modern foundation for the theory of algebraic function fields in one variable.
  • C. 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.
  • D. Banach algebra
    A Banach algebra is a complete normed vector space equipped with a compatible associative algebra multiplication, allowing analysis and algebra to be combined in a single structure.
  • E. 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.
  • 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_69da626a67648190af9653832a3aeced completed April 11, 2026, 3:02 p.m.
NER Named-entity recognition batch_69e65fe2036c8190b9f313215ad44e87 completed April 20, 2026, 5:18 p.m.
NED1 Entity disambiguation (via context triple) batch_6a080503f1bc8190b71f6d7043ac6593 completed May 16, 2026, 5:47 a.m.
NEDg Description generation batch_6a0806563e1c8190b702fcfc009c84d5 completed May 16, 2026, 5:53 a.m.
NED2 Entity disambiguation (via description) batch_6a0806e876c881909f0c30e5dd16ce20 completed May 16, 2026, 5:55 a.m.
Created at: April 11, 2026, 3:31 p.m.