Triple

T18151188
Position Surface form Disambiguated ID Type / Status
Subject Jacob T. Schwartz E434504 entity
Predicate notableWork P4 FINISHED
Object Linear Operators (with Nelson Dunford)
"Linear Operators" (with Nelson Dunford) is a landmark three-volume treatise on functional analysis and operator theory that became a foundational reference in modern analysis and related areas of mathematics.
E1309720 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: Linear Operators (with Nelson Dunford) | Statement: [Jacob T. Schwartz, notableWork, Linear Operators (with Nelson Dunford)]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Linear Operators (with Nelson Dunford)
Context triple: [Jacob T. Schwartz, notableWork, Linear Operators (with Nelson Dunford)]
  • 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. 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.
  • C. Hilbert–Schmidt operators
    Hilbert–Schmidt operators are a class of compact operators on Hilbert spaces characterized by having finite Hilbert–Schmidt norm, playing a central role in functional analysis and operator theory.
  • D. 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.
  • 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: Linear Operators (with Nelson Dunford)
Triple: [Jacob T. Schwartz, notableWork, Linear Operators (with Nelson Dunford)]
Generated description
"Linear Operators" (with Nelson Dunford) is a landmark three-volume treatise on functional analysis and operator theory that became a foundational reference in modern analysis and related areas of mathematics.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Linear Operators (with Nelson Dunford)
Target entity description: "Linear Operators" (with Nelson Dunford) is a landmark three-volume treatise on functional analysis and operator theory that became a foundational reference in modern analysis and related areas of mathematics.
  • 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. 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.
  • C. Hilbert–Schmidt operators
    Hilbert–Schmidt operators are a class of compact operators on Hilbert spaces characterized by having finite Hilbert–Schmidt norm, playing a central role in functional analysis and operator theory.
  • D. 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.
  • 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_69d8b90aac308190801e2c57d8c5bfe5 completed April 10, 2026, 8:47 a.m.
NER Named-entity recognition batch_69e4de38d4e08190bc4d430b70b7e288 completed April 19, 2026, 1:52 p.m.
NED1 Entity disambiguation (via context triple) batch_6a038fb93f8481908ea190ce4ec54455 completed May 12, 2026, 8:38 p.m.
NEDg Description generation batch_6a03911462d0819080d6a59fe3b120a1 completed May 12, 2026, 8:44 p.m.
NED2 Entity disambiguation (via description) batch_6a0392a51df48190aab14218f28f129d completed May 12, 2026, 8:50 p.m.
Created at: April 10, 2026, 10:29 a.m.