Triple

T4552551
Position Surface form Disambiguated ID Type / Status
Subject Gábor Szegő E120398 entity
Predicate notableWork P4 FINISHED
Object Szegő limit theorem
The Szegő limit theorem is a fundamental result in analysis and operator theory that describes the asymptotic behavior of determinants of large Toeplitz matrices in terms of the symbol’s integral.
E451539 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: Szegő limit theorem | Statement: [Gábor Szegő, notableWork, Szegő limit theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Szegő limit theorem
Context triple: [Gábor Szegő, notableWork, Szegő limit theorem]
  • A. 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.
  • B. 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.
  • C. Carathéodory–Fejér interpolation
    Carathéodory–Fejér interpolation is a classical result in complex analysis and approximation theory that concerns constructing analytic functions, typically with bounded or positive real part, that match prescribed initial Taylor coefficients.
  • D. Cauchy–Hadamard theorem
    The Cauchy–Hadamard theorem is a fundamental result in complex analysis that characterizes the radius of convergence of a power series in terms of the growth rate of its coefficients.
  • E. Isserlis’ theorem in probability theory
    Isserlis’ theorem in probability theory is a result that expresses higher-order moments of jointly Gaussian random variables in terms of sums of products of their pairwise covariances.
  • 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: Szegő limit theorem
Triple: [Gábor Szegő, notableWork, Szegő limit theorem]
Generated description
The Szegő limit theorem is a fundamental result in analysis and operator theory that describes the asymptotic behavior of determinants of large Toeplitz matrices in terms of the symbol’s integral.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Szegő limit theorem
Target entity description: The Szegő limit theorem is a fundamental result in analysis and operator theory that describes the asymptotic behavior of determinants of large Toeplitz matrices in terms of the symbol’s integral.
  • A. 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.
  • B. 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.
  • C. Carathéodory–Fejér interpolation
    Carathéodory–Fejér interpolation is a classical result in complex analysis and approximation theory that concerns constructing analytic functions, typically with bounded or positive real part, that match prescribed initial Taylor coefficients.
  • D. Cauchy–Hadamard theorem
    The Cauchy–Hadamard theorem is a fundamental result in complex analysis that characterizes the radius of convergence of a power series in terms of the growth rate of its coefficients.
  • E. Isserlis’ theorem in probability theory
    Isserlis’ theorem in probability theory is a result that expresses higher-order moments of jointly Gaussian random variables in terms of sums of products of their pairwise covariances.
  • 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_69bd4636f1648190a701445c2fcd9c17 completed March 20, 2026, 1:05 p.m.
NER Named-entity recognition batch_69bd581160e08190b715a8ce5c3e6c9b completed March 20, 2026, 2:22 p.m.
NED1 Entity disambiguation (via context triple) batch_69bdb95b01b0819094a600752e41aa09 completed March 20, 2026, 9:17 p.m.
NEDg Description generation batch_69bdbdbf73508190b64a78ff9274ee6d completed March 20, 2026, 9:35 p.m.
NED2 Entity disambiguation (via description) batch_69bdbe1bcd8c819094adea59c91c6f5b completed March 20, 2026, 9:37 p.m.
Created at: March 20, 2026, 1:09 p.m.