Triple

T8640773

Position	Surface form	Disambiguated ID	Type / Status
Subject	Frigyes Riesz	`E204639`	entity
Predicate	authorOf	`P4244`	FINISHED
Object	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.	`E747352`	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: Foundations of Functional Analysis | Statement: [Frigyes Riesz, authorOf, Foundations of Functional Analysis]

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Foundations of Functional Analysis
Context triple: [Frigyes Riesz, authorOf, Foundations of 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. "Functional Analysis"
Functional Analysis is a branch of mathematical analysis that studies vector spaces with additional structure (such as norms and inner products) and the linear operators acting on them, with deep applications across pure and applied mathematics.
C. Banach spaces
Banach spaces are complete normed vector spaces that provide a fundamental framework for functional analysis and the study of infinite-dimensional linear phenomena.
D. Applied Functional Analysis
Applied Functional Analysis is a foundational textbook by J. Tinsley Oden that introduces and develops the tools of functional analysis with a strong emphasis on applications to differential equations and engineering problems.
E. Hilbert spaces
Hilbert spaces are complete inner product spaces that provide the fundamental framework for modern functional analysis and many areas of mathematical physics.
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: Foundations of Functional Analysis
Triple: [Frigyes Riesz, authorOf, Foundations of Functional Analysis]

Generated description

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.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Foundations of Functional Analysis
Target entity description: 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.

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. "Functional Analysis"
Functional Analysis is a branch of mathematical analysis that studies vector spaces with additional structure (such as norms and inner products) and the linear operators acting on them, with deep applications across pure and applied mathematics.
C. Banach spaces
Banach spaces are complete normed vector spaces that provide a fundamental framework for functional analysis and the study of infinite-dimensional linear phenomena.
D. Applied Functional Analysis
Applied Functional Analysis is a foundational textbook by J. Tinsley Oden that introduces and develops the tools of functional analysis with a strong emphasis on applications to differential equations and engineering problems.
E. Hilbert spaces
Hilbert spaces are complete inner product spaces that provide the fundamental framework for modern functional analysis and many areas of mathematical physics.
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_69ca834ca1c88190a11ffb0200342fac`	completed	March 30, 2026, 2:06 p.m.
NER	Named-entity recognition	`batch_69cc47944d1c819081f448f14d04bf9d`	completed	March 31, 2026, 10:15 p.m.
NED1	Entity disambiguation (via context triple)	`batch_69cebc3b1f508190978df29d995f494c`	completed	April 2, 2026, 6:58 p.m.
NEDg	Description generation	`batch_69cebf12eec081909c40ccced9c1c52b`	completed	April 2, 2026, 7:10 p.m.
NED2	Entity disambiguation (via description)	`batch_69cebf7302b08190bdfc84aac3147954`	completed	April 2, 2026, 7:11 p.m.

Created at: March 30, 2026, 6:28 p.m.