Triple

T11186005
Position Surface form Disambiguated ID Type / Status
Subject Vladimir Steklov E264668 entity
Predicate hasEponym P12247 FINISHED
Object Steklov operator
The Steklov operator is a boundary integral operator arising in the study of elliptic partial differential equations and spectral problems, particularly in the context of Steklov eigenvalue problems.
E910282 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 operator | Statement: [Vladimir Steklov, hasEponym, Steklov operator]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Steklov operator
Context triple: [Vladimir Steklov, hasEponym, Steklov operator]
  • 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. Fredholm operator
    A Fredholm operator is a bounded linear operator between Banach (or Hilbert) spaces with finite-dimensional kernel and cokernel and a closed range, characterized by its integer-valued index.
  • C. Hilbert–Schmidt operators
    Hilbert–Schmidt operators are a class of compact operators on Hilbert spaces characterized by having finite Hilbert–Schmidt norm, playing a central role in functional analysis and operator theory.
  • D. Laplace operator
    The Laplace operator is a second-order differential operator widely used in mathematics and physics to describe phenomena such as diffusion, heat flow, and wave propagation.
  • E. Jacobi operator
    The Jacobi operator is a linear differential operator central to the theory of elliptic functions and integrable systems, named after the mathematician Carl Gustav Jacob Jacobi.
  • 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 operator
Triple: [Vladimir Steklov, hasEponym, Steklov operator]
Generated description
The Steklov operator is a boundary integral operator arising in the study of elliptic partial differential equations and spectral problems, particularly in the context of Steklov eigenvalue problems.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Steklov operator
Target entity description: The Steklov operator is a boundary integral operator arising in the study of elliptic partial differential equations and spectral problems, particularly in the context of Steklov eigenvalue problems.
  • 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. Fredholm operator
    A Fredholm operator is a bounded linear operator between Banach (or Hilbert) spaces with finite-dimensional kernel and cokernel and a closed range, characterized by its integer-valued index.
  • C. Hilbert–Schmidt operators
    Hilbert–Schmidt operators are a class of compact operators on Hilbert spaces characterized by having finite Hilbert–Schmidt norm, playing a central role in functional analysis and operator theory.
  • D. Laplace operator
    The Laplace operator is a second-order differential operator widely used in mathematics and physics to describe phenomena such as diffusion, heat flow, and wave propagation.
  • E. Jacobi operator
    The Jacobi operator is a linear differential operator central to the theory of elliptic functions and integrable systems, named after the mathematician Carl Gustav Jacob Jacobi.
  • 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.