Triple

T13561578
Position Surface form Disambiguated ID Type / Status
Subject Vladimir Arnold E323919 entity
Predicate notableWork P4 FINISHED
Object Lectures on Partial Differential Equations
"Lectures on Partial Differential Equations" is a concise, influential textbook by Vladimir Arnold that presents the theory of partial differential equations with a strong geometric and intuitive emphasis.
E1046818 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: Lectures on Partial Differential Equations | Statement: [Vladimir Arnold, notableWork, Lectures on Partial Differential Equations]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Lectures on Partial Differential Equations
Context triple: [Vladimir Arnold, notableWork, Lectures on Partial Differential Equations]
  • A. "Partial Differential Equations"
    "Partial Differential Equations" is a foundational mathematical text that systematically develops the theory and methods for analyzing equations involving multivariable functions and their partial derivatives.
  • B. Lectures on Cauchy’s problem in linear partial differential equations
    "Lectures on Cauchy’s Problem in Linear Partial Differential Equations" is a classic mathematical treatise by Jacques Hadamard that systematically develops the theory of existence, uniqueness, and well-posedness for solutions to linear partial differential equations.
  • C. Agmon–Douglis–Nirenberg estimates
    Agmon–Douglis–Nirenberg estimates are fundamental a priori estimates in the theory of linear elliptic partial differential equations and systems, providing precise control of solution regularity in terms of data norms.
  • D. Lectures on Fourier Integrals
    Lectures on Fourier Integrals is a classic mathematical monograph by Salomon Bochner that systematically develops the theory and applications of Fourier integrals and transforms.
  • E. 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.
  • 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: Lectures on Partial Differential Equations
Triple: [Vladimir Arnold, notableWork, Lectures on Partial Differential Equations]
Generated description
"Lectures on Partial Differential Equations" is a concise, influential textbook by Vladimir Arnold that presents the theory of partial differential equations with a strong geometric and intuitive emphasis.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Lectures on Partial Differential Equations
Target entity description: "Lectures on Partial Differential Equations" is a concise, influential textbook by Vladimir Arnold that presents the theory of partial differential equations with a strong geometric and intuitive emphasis.
  • A. "Partial Differential Equations"
    "Partial Differential Equations" is a foundational mathematical text that systematically develops the theory and methods for analyzing equations involving multivariable functions and their partial derivatives.
  • B. Lectures on Cauchy’s problem in linear partial differential equations
    "Lectures on Cauchy’s Problem in Linear Partial Differential Equations" is a classic mathematical treatise by Jacques Hadamard that systematically develops the theory of existence, uniqueness, and well-posedness for solutions to linear partial differential equations.
  • C. Agmon–Douglis–Nirenberg estimates
    Agmon–Douglis–Nirenberg estimates are fundamental a priori estimates in the theory of linear elliptic partial differential equations and systems, providing precise control of solution regularity in terms of data norms.
  • D. Lectures on Fourier Integrals
    Lectures on Fourier Integrals is a classic mathematical monograph by Salomon Bochner that systematically develops the theory and applications of Fourier integrals and transforms.
  • E. 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.
  • 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_69d8076830b48190910a902bae5888e2 completed April 9, 2026, 8:09 p.m.
NER Named-entity recognition batch_69dbaff5219081909cf60423e79d278f completed April 12, 2026, 2:45 p.m.
NED1 Entity disambiguation (via context triple) batch_69f75dad601481908de5f266f01f3f49 completed May 3, 2026, 2:37 p.m.
NEDg Description generation batch_69f75f563cfc81909cde4c403ac10a58 completed May 3, 2026, 2:44 p.m.
NED2 Entity disambiguation (via description) batch_69f75fcbf9548190abd74bf4f4ae2e11 completed May 3, 2026, 2:46 p.m.
Created at: April 9, 2026, 9:47 p.m.