Triple
T5709653
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Elias Stein |
E125871
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
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.
|
E542635
|
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: Functional Analysis: Introduction to Further Topics in Analysis | Statement: [Elias Stein, notableWork, Functional Analysis: Introduction to Further Topics in Analysis]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Functional Analysis: Introduction to Further Topics in Analysis Context triple: [Elias Stein, notableWork, Functional Analysis: Introduction to Further Topics in Analysis]
-
A.
"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.
-
B.
Problems and Theorems in Analysis (with George Pólya)
"Problems and Theorems in Analysis (with George Pólya)" is a classic two-volume collection of challenging problems and results in mathematical analysis that has become a standard reference and training resource for advanced students and researchers.
-
C.
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.
-
D.
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.
-
E.
Sobolev spaces
Sobolev spaces are function spaces that incorporate both functions and their weak derivatives, providing a fundamental framework for studying partial differential equations and variational problems.
- 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: Functional Analysis: Introduction to Further Topics in Analysis Triple: [Elias Stein, notableWork, Functional Analysis: Introduction to Further Topics in Analysis]
Generated description
"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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Functional Analysis: Introduction to Further Topics in Analysis Target entity description: "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.
-
A.
"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.
-
B.
Problems and Theorems in Analysis (with George Pólya)
"Problems and Theorems in Analysis (with George Pólya)" is a classic two-volume collection of challenging problems and results in mathematical analysis that has become a standard reference and training resource for advanced students and researchers.
-
C.
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.
-
D.
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.
-
E.
Sobolev spaces
Sobolev spaces are function spaces that incorporate both functions and their weak derivatives, providing a fundamental framework for studying partial differential equations and variational problems.
- 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_69c0082d6fe48190b777fb383769e5c8 |
completed | March 22, 2026, 3:18 p.m. |
| NER | Named-entity recognition | batch_69c0248c3dac8190824fca9ddde89665 |
completed | March 22, 2026, 5:19 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c05a6f5ac08190b5acbccea756d2de |
completed | March 22, 2026, 9:09 p.m. |
| NEDg | Description generation | batch_69c062029e3c8190ade3f0836d6b3842 |
completed | March 22, 2026, 9:41 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69c06268eb0c8190959ba762c2d9b47d |
completed | March 22, 2026, 9:43 p.m. |
Created at: March 22, 2026, 3:46 p.m.