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.