Triple
T11186002
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Vladimir Steklov |
E264668
|
entity |
| Predicate | notableFor |
P22
|
FINISHED |
| Object |
Steklov eigenvalue problem
The Steklov eigenvalue problem is a type of spectral boundary value problem in which eigenvalues appear in the boundary conditions of a partial differential equation, playing a key role in mathematical physics and geometric analysis.
|
E910281
|
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: Steklov eigenvalue problem | Statement: [Vladimir Steklov, notableFor, Steklov eigenvalue problem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Steklov eigenvalue problem Context triple: [Vladimir Steklov, notableFor, Steklov eigenvalue problem]
-
A.
Sturm–Liouville problem
The Sturm–Liouville problem is a class of second-order linear differential equations with boundary conditions that yield real eigenvalues and orthogonal eigenfunctions forming a basis for function expansions in mathematical physics and engineering.
-
B.
Dirichlet problem
The Dirichlet problem is a fundamental boundary value problem in potential theory and partial differential equations, asking for a function that solves a specified PDE inside a domain while taking prescribed values on the domain’s boundary.
-
C.
Morawetz inequalities
Morawetz inequalities are fundamental energy and decay estimates in the study of partial differential equations, especially wave and dispersive equations, that provide control over the long-time behavior of solutions.
-
D.
Neumann boundary conditions in potential theory
Neumann boundary conditions in potential theory specify that the normal derivative of a potential function on a boundary is prescribed, modeling situations where flux across the boundary is controlled rather than the potential itself.
-
E.
Noether boundary value problems
Noether boundary value problems are a class of boundary value problems in the theory of partial differential equations characterized by conditions ensuring well-posedness and finite-dimensional solution spaces, developed by mathematician Fritz Noether.
- 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: Steklov eigenvalue problem Triple: [Vladimir Steklov, notableFor, Steklov eigenvalue problem]
Generated description
The Steklov eigenvalue problem is a type of spectral boundary value problem in which eigenvalues appear in the boundary conditions of a partial differential equation, playing a key role in mathematical physics and geometric analysis.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Steklov eigenvalue problem Target entity description: The Steklov eigenvalue problem is a type of spectral boundary value problem in which eigenvalues appear in the boundary conditions of a partial differential equation, playing a key role in mathematical physics and geometric analysis.
-
A.
Sturm–Liouville problem
The Sturm–Liouville problem is a class of second-order linear differential equations with boundary conditions that yield real eigenvalues and orthogonal eigenfunctions forming a basis for function expansions in mathematical physics and engineering.
-
B.
Dirichlet problem
The Dirichlet problem is a fundamental boundary value problem in potential theory and partial differential equations, asking for a function that solves a specified PDE inside a domain while taking prescribed values on the domain’s boundary.
-
C.
Morawetz inequalities
Morawetz inequalities are fundamental energy and decay estimates in the study of partial differential equations, especially wave and dispersive equations, that provide control over the long-time behavior of solutions.
-
D.
Neumann boundary conditions in potential theory
Neumann boundary conditions in potential theory specify that the normal derivative of a potential function on a boundary is prescribed, modeling situations where flux across the boundary is controlled rather than the potential itself.
-
E.
Noether boundary value problems
Noether boundary value problems are a class of boundary value problems in the theory of partial differential equations characterized by conditions ensuring well-posedness and finite-dimensional solution spaces, developed by mathematician Fritz Noether.
- 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_69d6aa9eb9248190b20211772621b4bc |
completed | April 8, 2026, 7:21 p.m. |
| NER | Named-entity recognition | batch_69d7e8abbeac8190ad6e419258999f4e |
completed | April 9, 2026, 5:58 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69e483d0f4548190b97c7725a9f7c0e6 |
completed | April 19, 2026, 7:27 a.m. |
| NEDg | Description generation | batch_69e48717c35481908fb05597084167e7 |
completed | April 19, 2026, 7:41 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69e48875faa88190af33654e6d9a708b |
completed | April 19, 2026, 7:47 a.m. |
Created at: April 8, 2026, 9:29 p.m.