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.