Triple

T14430235
Position Surface form Disambiguated ID Type / Status
Subject Kurt Friedrichs E357805 entity
Predicate notableWork P4 FINISHED
Object Friedrichs mollifier
Friedrichs mollifier is a smooth approximation tool in analysis used to regularize functions by convolving them with a specially constructed smooth, compactly supported kernel.
E1100055 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: Friedrichs mollifier | Statement: [Kurt Friedrichs, notableWork, Friedrichs mollifier]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Friedrichs mollifier
Context triple: [Kurt Friedrichs, notableWork, Friedrichs mollifier]
  • A. Du Bois-Reymond function
    The Du Bois-Reymond function is a classic example of a continuous but nowhere differentiable function, illustrating pathological behavior in real analysis.
  • B. Grünwald–Letnikov derivative
    The Grünwald–Letnikov derivative is a fundamental definition of fractional differentiation based on limit processes and finite differences, widely used as a foundation for fractional calculus.
  • C. Rellich–Kondrachov compactness theorem
    The Rellich–Kondrachov compactness theorem is a fundamental result in functional analysis and the theory of Sobolev spaces that guarantees the compactness of certain embedding operators, playing a key role in the study of partial differential equations.
  • D. 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.
  • E. Sobolev spaces
    Sobolev spaces are function spaces that incorporate both functions and their weak derivatives, providing a fundamental framework for studying partial differential equations and variational problems.
  • 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: Friedrichs mollifier
Triple: [Kurt Friedrichs, notableWork, Friedrichs mollifier]
Generated description
Friedrichs mollifier is a smooth approximation tool in analysis used to regularize functions by convolving them with a specially constructed smooth, compactly supported kernel.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Friedrichs mollifier
Target entity description: Friedrichs mollifier is a smooth approximation tool in analysis used to regularize functions by convolving them with a specially constructed smooth, compactly supported kernel.
  • A. Du Bois-Reymond function
    The Du Bois-Reymond function is a classic example of a continuous but nowhere differentiable function, illustrating pathological behavior in real analysis.
  • B. Grünwald–Letnikov derivative
    The Grünwald–Letnikov derivative is a fundamental definition of fractional differentiation based on limit processes and finite differences, widely used as a foundation for fractional calculus.
  • C. Rellich–Kondrachov compactness theorem
    The Rellich–Kondrachov compactness theorem is a fundamental result in functional analysis and the theory of Sobolev spaces that guarantees the compactness of certain embedding operators, playing a key role in the study of partial differential equations.
  • D. 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.
  • E. Sobolev spaces
    Sobolev spaces are function spaces that incorporate both functions and their weak derivatives, providing a fundamental framework for studying partial differential equations and variational problems.
  • 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_69d8279402a88190821ffa39ae15bccf completed April 9, 2026, 10:26 p.m.
NER Named-entity recognition batch_69de914570f08190b1c7c1c57a0cb476 completed April 14, 2026, 7:11 p.m.
NED1 Entity disambiguation (via context triple) batch_69fd5bd1c4d0819085edb9ed22128b68 completed May 8, 2026, 3:43 a.m.
NEDg Description generation batch_69fd5d42e1b48190b41ecafcf9ca9a3b completed May 8, 2026, 3:49 a.m.
NED2 Entity disambiguation (via description) batch_69fd5e1ca1e081908441508d651ecc63 completed May 8, 2026, 3:53 a.m.
Created at: April 10, 2026, 1:18 a.m.