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.