Triple

T6606126
Position Surface form Disambiguated ID Type / Status
Subject Maxime Bôcher E149122 entity
Predicate notableWork P4 FINISHED
Object Introduction to the Study of Integral Equations
"Introduction to the Study of Integral Equations" is a foundational mathematical text by Maxime Bôcher that systematically develops the theory and applications of integral equations.
E599703 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: Introduction to the Study of Integral Equations | Statement: [Maxime Bôcher, notableWork, Introduction to the Study of Integral Equations]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Introduction to the Study of Integral Equations
Context triple: [Maxime Bôcher, notableWork, Introduction to the Study of Integral Equations]
  • A. The Fourier Integral and Certain of Its Applications
    The Fourier Integral and Certain of Its Applications is a foundational mathematical work by Norbert Wiener that develops and applies Fourier analysis to problems in harmonic analysis and related areas.
  • B. 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.
  • C. Gelfand–Levitan theory
    Gelfand–Levitan theory is a foundational framework in inverse spectral theory that reconstructs differential operators or potentials from their spectral data using integral equations.
  • D. Methods of Mathematical Physics
    Methods of Mathematical Physics is a classic two-volume textbook by Richard Courant and David Hilbert that rigorously develops the mathematical foundations and techniques used in theoretical physics.
  • E. Hadamard’s example of ill-posed problems
    Hadamard’s example of ill-posed problems is a classical mathematical construction illustrating how small changes in input data can cause large, unstable changes in solutions, thereby violating the standard criteria for well-posedness in analysis and partial differential equations.
  • 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: Introduction to the Study of Integral Equations
Triple: [Maxime Bôcher, notableWork, Introduction to the Study of Integral Equations]
Generated description
"Introduction to the Study of Integral Equations" is a foundational mathematical text by Maxime Bôcher that systematically develops the theory and applications of integral equations.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Introduction to the Study of Integral Equations
Target entity description: "Introduction to the Study of Integral Equations" is a foundational mathematical text by Maxime Bôcher that systematically develops the theory and applications of integral equations.
  • A. The Fourier Integral and Certain of Its Applications
    The Fourier Integral and Certain of Its Applications is a foundational mathematical work by Norbert Wiener that develops and applies Fourier analysis to problems in harmonic analysis and related areas.
  • B. 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.
  • C. Gelfand–Levitan theory
    Gelfand–Levitan theory is a foundational framework in inverse spectral theory that reconstructs differential operators or potentials from their spectral data using integral equations.
  • D. Methods of Mathematical Physics
    Methods of Mathematical Physics is a classic two-volume textbook by Richard Courant and David Hilbert that rigorously develops the mathematical foundations and techniques used in theoretical physics.
  • E. Hadamard’s example of ill-posed problems
    Hadamard’s example of ill-posed problems is a classical mathematical construction illustrating how small changes in input data can cause large, unstable changes in solutions, thereby violating the standard criteria for well-posedness in analysis and partial differential equations.
  • 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_69c687eaa7508190bb58ce2aa02039b3 completed March 27, 2026, 1:36 p.m.
NER Named-entity recognition batch_69c6af143d5c8190b62602602510b1cb completed March 27, 2026, 4:23 p.m.
NED1 Entity disambiguation (via context triple) batch_69c6cbce25b481908d600d38d3c5b871 completed March 27, 2026, 6:26 p.m.
NEDg Description generation batch_69c6cd0a98908190a5725c49bad7589d completed March 27, 2026, 6:31 p.m.
NED2 Entity disambiguation (via description) batch_69c6cdcc10c08190aa98212bd17063a3 completed March 27, 2026, 6:34 p.m.
Created at: March 27, 2026, 1:57 p.m.