Triple

T17549836
Position Surface form Disambiguated ID Type / Status
Subject Wirtinger E427428 entity
Predicate hasEponym P12247 FINISHED
Object Wirtinger inequality
The Wirtinger inequality is a fundamental result in mathematical analysis that provides a sharp bound relating the L² norms of a periodic function and its derivative, often used in Fourier analysis and the study of Sobolev spaces.
E156195 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: Wirtinger inequality | Statement: [Wirtinger, hasEponym, Wirtinger inequality]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Wirtinger inequality
Context triple: [Wirtinger, hasEponym, Wirtinger inequality]
  • A. Friedrichs inequality
    Friedrichs inequality is a fundamental result in functional analysis and partial differential equations that provides bounds on the norms of functions in terms of their derivatives, playing a key role in the theory of Sobolev spaces and boundary value problems.
  • B. Poincaré inequality
    The Poincaré inequality is a fundamental result in functional analysis and partial differential equations that bounds the average oscillation of a function by the size of its gradient, playing a key role in Sobolev space theory and the study of elliptic problems.
  • C. Korn inequality
    Korn inequality is a fundamental result in functional analysis and the mathematical theory of elasticity that provides bounds relating the full gradient of a vector field to its symmetric part, ensuring control of deformations by their strains.
  • D. Sobolev inequality
    The Sobolev inequality is a fundamental result in functional analysis and partial differential equations that bounds the size of a function in certain Lebesgue spaces by the size of its derivatives, enabling key embedding and regularity properties.
  • E. 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.
  • 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: Wirtinger inequality
Triple: [Wirtinger, hasEponym, Wirtinger inequality]
Generated description
The Wirtinger inequality is a fundamental result in mathematical analysis that provides a sharp bound relating the L² norms of a periodic function and its derivative, often used in Fourier analysis and the study of Sobolev spaces.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Wirtinger inequality
Target entity description: The Wirtinger inequality is a fundamental result in mathematical analysis that provides a sharp bound relating the L² norms of a periodic function and its derivative, often used in Fourier analysis and the study of Sobolev spaces.
  • A. Friedrichs inequality
    Friedrichs inequality is a fundamental result in functional analysis and partial differential equations that provides bounds on the norms of functions in terms of their derivatives, playing a key role in the theory of Sobolev spaces and boundary value problems.
  • B. Poincaré inequality chosen
    The Poincaré inequality is a fundamental result in functional analysis and partial differential equations that bounds the average oscillation of a function by the size of its gradient, playing a key role in Sobolev space theory and the study of elliptic problems.
  • C. Korn inequality
    Korn inequality is a fundamental result in functional analysis and the mathematical theory of elasticity that provides bounds relating the full gradient of a vector field to its symmetric part, ensuring control of deformations by their strains.
  • D. Sobolev inequality
    The Sobolev inequality is a fundamental result in functional analysis and partial differential equations that bounds the size of a function in certain Lebesgue spaces by the size of its derivatives, enabling key embedding and regularity properties.
  • E. 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.
  • F. None of above.

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_69d889df6dc081908f67dbadc03c07ee completed April 10, 2026, 5:25 a.m.
NER Named-entity recognition batch_69e45463ddf88190a2c29f3246adcb6e completed April 19, 2026, 4:04 a.m.
NED1 Entity disambiguation (via context triple) batch_6a01d290edbc8190a7b2cb0835456890 completed May 11, 2026, 12:58 p.m.
NEDg Description generation batch_6a01d597c96c8190a5eca56a748da50c completed May 11, 2026, 1:11 p.m.
NED2 Entity disambiguation (via description) batch_6a01d639c220819088dd3389d1ab60ca completed May 11, 2026, 1:14 p.m.
Created at: April 10, 2026, 5:50 a.m.