Triple

T4552550
Position Surface form Disambiguated ID Type / Status
Subject Gábor Szegő E120398 entity
Predicate notableWork P4 FINISHED
Object Inequalities for analytic functions
"Inequalities for analytic functions" is a mathematical work by Gábor Szegő that develops fundamental bounds and estimates for complex analytic functions, particularly in the context of complex analysis and approximation theory.
 E451538 NE FINISHED

Named-entity recognition

Before disambiguation, gpt-5-mini classified whether the object phrase is a named entity — the step behind the object's NE type shown above.

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: Inequalities for analytic functions | Statement: [Gábor Szegő, notableWork, Inequalities for analytic functions]

Disambiguation candidates (2 decisions)

The exact options the model was shown at each disambiguation step, with the option it chose highlighted — the evidence behind this triple's disambiguated ids.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Inequalities for analytic functions
Context triple: [Gábor Szegő, notableWork, Inequalities for analytic functions]
  • A. Bernstein inequalities
    Bernstein inequalities are fundamental results in approximation theory and probability that provide bounds on the derivatives or deviations of functions and random variables under certain smoothness or moment conditions.
  • B. Hadamard three-circle theorem
    The Hadamard three-circle theorem is a result in complex analysis that describes how the maximum modulus of a holomorphic function behaves logarithmically between three concentric circles in the complex plane.
  • C. Théorie des fonctions analytiques
    Théorie des fonctions analytiques is a foundational mathematical treatise by Joseph-Louis Lagrange that systematically develops calculus using power series and analytic functions instead of geometric or infinitesimal arguments.
  • D. Khinchin–Kahane type inequalities
    Khinchin–Kahane type inequalities are fundamental results in probability and functional analysis that bound moments or norms of random series (often with Rademacher or Gaussian coefficients) in terms of each other, providing powerful tools for studying the geometry of Banach spaces and random processes.
  • E. Schwarz lemma
    Schwarz lemma is a fundamental result in complex analysis that constrains holomorphic self-maps of the unit disk, particularly bounding their magnitude and derivative at the origin.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: Inequalities for analytic functions
Target entity description: "Inequalities for analytic functions" is a mathematical work by Gábor Szegő that develops fundamental bounds and estimates for complex analytic functions, particularly in the context of complex analysis and approximation theory.
  • A. Bernstein inequalities
    Bernstein inequalities are fundamental results in approximation theory and probability that provide bounds on the derivatives or deviations of functions and random variables under certain smoothness or moment conditions.
  • B. Hadamard three-circle theorem
    The Hadamard three-circle theorem is a result in complex analysis that describes how the maximum modulus of a holomorphic function behaves logarithmically between three concentric circles in the complex plane.
  • C. Théorie des fonctions analytiques
    Théorie des fonctions analytiques is a foundational mathematical treatise by Joseph-Louis Lagrange that systematically develops calculus using power series and analytic functions instead of geometric or infinitesimal arguments.
  • D. Khinchin–Kahane type inequalities
    Khinchin–Kahane type inequalities are fundamental results in probability and functional analysis that bound moments or norms of random series (often with Rademacher or Gaussian coefficients) in terms of each other, providing powerful tools for studying the geometry of Banach spaces and random processes.
  • E. Schwarz lemma
    Schwarz lemma is a fundamental result in complex analysis that constrains holomorphic self-maps of the unit disk, particularly bounding their magnitude and derivative at the origin.
  • F. None of above. chosen

How the object was described

The object's one-sentence description was generated by prompting gpt-5.1 with the object name and this triple as context.

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: Inequalities for analytic functions
Triple: [Gábor Szegő, notableWork, Inequalities for analytic functions]
Generated description
"Inequalities for analytic functions" is a mathematical work by Gábor Szegő that develops fundamental bounds and estimates for complex analytic functions, particularly in the context of complex analysis and approximation theory.

Provenance (5 batches)

Stage Batch ID Job type Status
creating batch_69bd4636f1648190a701445c2fcd9c17 elicitation completed
NER batch_69bd581160e08190b715a8ce5c3e6c9b ner completed
NED1 batch_69bdb95b01b0819094a600752e41aa09 ned_source_triple completed
NED2 batch_69bdbe1bcd8c819094adea59c91c6f5b ned_description completed
NEDg batch_69bdbdbf73508190b64a78ff9274ee6d nedg completed
Created at: March 20, 2026, 1:09 p.m.