Triple

T18479437
Position Surface form Disambiguated ID Type / Status
Subject Tauberian theorems E451517 entity
Predicate relatedConcept P37 FINISHED
Object Hardy–Littlewood–Karamata theory of regular variation
The Hardy–Littlewood–Karamata theory of regular variation is a framework in analysis that characterizes functions with power-like asymptotic behavior and underpins many Tauberian theorems and limit results.
E451517 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: Hardy–Littlewood–Karamata theory of regular variation | Statement: [Tauberian theorems, relatedConcept, Hardy–Littlewood–Karamata theory of regular variation]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Hardy–Littlewood–Karamata theory of regular variation
Context triple: [Tauberian theorems, relatedConcept, Hardy–Littlewood–Karamata theory of regular variation]
  • A. Gnedenko’s theorem in extreme value theory
    Gnedenko’s theorem in extreme value theory is a fundamental result that characterizes all possible non-degenerate limit distributions for properly normalized maxima of independent, identically distributed random variables, forming the basis of modern extreme value analysis.
  • B. Kolmogorov's law of the iterated logarithm
    Kolmogorov's law of the iterated logarithm is a fundamental result in probability theory that precisely characterizes the almost-sure fluctuations of partial sums of independent random variables between the law of large numbers and the central limit theorem.
  • C. Tauberian theorems
    Tauberian theorems are results in mathematical analysis that connect the behavior of transformed series or integrals (such as those summed by Abel or Cesàro methods) back to the asymptotic behavior or convergence of the original sequences or series.
  • D. Khinchin's law of the iterated logarithm
    Khinchin's law of the iterated logarithm is a fundamental result in probability theory that precisely characterizes the almost-sure fluctuations of partial sums of independent random variables on the scale of the square root of twice the product of their variance and the iterated logarithm of the sample size.
  • E. Harmonic Analysis and the Theory of Probability
    Harmonic Analysis and the Theory of Probability is a seminal mathematical monograph that connects Fourier-analytic methods with probabilistic concepts, helping to lay the foundations of modern probability theory.
  • 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: Hardy–Littlewood–Karamata theory of regular variation
Triple: [Tauberian theorems, relatedConcept, Hardy–Littlewood–Karamata theory of regular variation]
Generated description
The Hardy–Littlewood–Karamata theory of regular variation is a framework in analysis that characterizes functions with power-like asymptotic behavior and underpins many Tauberian theorems and limit results.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Hardy–Littlewood–Karamata theory of regular variation
Target entity description: The Hardy–Littlewood–Karamata theory of regular variation is a framework in analysis that characterizes functions with power-like asymptotic behavior and underpins many Tauberian theorems and limit results.
  • A. Gnedenko’s theorem in extreme value theory
    Gnedenko’s theorem in extreme value theory is a fundamental result that characterizes all possible non-degenerate limit distributions for properly normalized maxima of independent, identically distributed random variables, forming the basis of modern extreme value analysis.
  • B. Kolmogorov's law of the iterated logarithm
    Kolmogorov's law of the iterated logarithm is a fundamental result in probability theory that precisely characterizes the almost-sure fluctuations of partial sums of independent random variables between the law of large numbers and the central limit theorem.
  • C. Tauberian theorems chosen
    Tauberian theorems are results in mathematical analysis that connect the behavior of transformed series or integrals (such as those summed by Abel or Cesàro methods) back to the asymptotic behavior or convergence of the original sequences or series.
  • D. Khinchin's law of the iterated logarithm
    Khinchin's law of the iterated logarithm is a fundamental result in probability theory that precisely characterizes the almost-sure fluctuations of partial sums of independent random variables on the scale of the square root of twice the product of their variance and the iterated logarithm of the sample size.
  • E. Harmonic Analysis and the Theory of Probability
    Harmonic Analysis and the Theory of Probability is a seminal mathematical monograph that connects Fourier-analytic methods with probabilistic concepts, helping to lay the foundations of modern probability theory.
  • 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_69d8d38465a0819099b9b42d2a662ac1 completed April 10, 2026, 10:40 a.m.
NER Named-entity recognition batch_69e53065e8388190bb216dae89f8cf75 completed April 19, 2026, 7:43 p.m.
NED1 Entity disambiguation (via context triple) batch_6a043f2f64848190808075254008e6e1 completed May 13, 2026, 9:06 a.m.
NEDg Description generation batch_6a043fb7db388190bb50cfade4f025f9 completed May 13, 2026, 9:09 a.m.
NED2 Entity disambiguation (via description) batch_6a044063c6048190b65620af8ceed897 completed May 13, 2026, 9:12 a.m.
Created at: April 10, 2026, 11:35 a.m.