Triple

T15502447
Position Surface form Disambiguated ID Type / Status
Subject Khinchin's law of the iterated logarithm E378993 entity
Predicate isSpecialCaseOf P2372 FINISHED
Object 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.
E1161638 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: Kolmogorov's law of the iterated logarithm | Statement: [Khinchin's law of the iterated logarithm, isSpecialCaseOf, Kolmogorov's law of the iterated logarithm]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Kolmogorov's law of the iterated logarithm
Context triple: [Khinchin's law of the iterated logarithm, isSpecialCaseOf, Kolmogorov's law of the iterated logarithm]
  • A. 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.
  • B. Kolmogorov zero–one law
    The Kolmogorov zero–one law is a fundamental result in probability theory stating that certain events determined by the tail behavior of independent random variables must have probability either zero or one.
  • C. Donsker's invariance principle
    Donsker's invariance principle is a fundamental result in probability theory stating that suitably normalized random walks converge in distribution to Brownian motion, providing a functional central limit theorem.
  • D. Khinchin–Kolmogorov theorem
    The Khinchin–Kolmogorov theorem is a fundamental result in probability theory that provides conditions under which series of independent random variables converge almost surely.
  • E. Borel–Cantelli lemmas
    The Borel–Cantelli lemmas are fundamental results in probability theory that characterize when events occur infinitely often or only finitely often, based on the convergence or divergence of the sum of their probabilities.
  • 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: Kolmogorov's law of the iterated logarithm
Triple: [Khinchin's law of the iterated logarithm, isSpecialCaseOf, Kolmogorov's law of the iterated logarithm]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Kolmogorov's law of the iterated logarithm
Target entity description: 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.
  • A. 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.
  • B. Kolmogorov zero–one law
    The Kolmogorov zero–one law is a fundamental result in probability theory stating that certain events determined by the tail behavior of independent random variables must have probability either zero or one.
  • C. Donsker's invariance principle
    Donsker's invariance principle is a fundamental result in probability theory stating that suitably normalized random walks converge in distribution to Brownian motion, providing a functional central limit theorem.
  • D. Khinchin–Kolmogorov theorem
    The Khinchin–Kolmogorov theorem is a fundamental result in probability theory that provides conditions under which series of independent random variables converge almost surely.
  • E. Borel–Cantelli lemmas
    The Borel–Cantelli lemmas are fundamental results in probability theory that characterize when events occur infinitely often or only finitely often, based on the convergence or divergence of the sum of their probabilities.
  • 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_69d85cd53a7c819080f5b9042c4c199e completed April 10, 2026, 2:13 a.m.
NER Named-entity recognition batch_69e03fcc5bb88190b8a9a81419a9a38b completed April 16, 2026, 1:47 a.m.
NED1 Entity disambiguation (via context triple) batch_69ff3d4a9bf88190b7c6b4874abe165f completed May 9, 2026, 1:57 p.m.
NEDg Description generation batch_69ff3e77330881909f13327aa2616203 completed May 9, 2026, 2:02 p.m.
NED2 Entity disambiguation (via description) batch_69ff3eed56b881908363380284e9d81b completed May 9, 2026, 2:04 p.m.
Created at: April 10, 2026, 3:54 a.m.