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.