Triple

T15502449
Position Surface form Disambiguated ID Type / Status
Subject Khinchin's law of the iterated logarithm E378993 entity
Predicate isRelatedTo P37 FINISHED
Object Hartman–Wintner law of the iterated logarithm
The Hartman–Wintner law of the iterated logarithm is a fundamental result in probability theory that precisely characterizes the almost-sure fluctuation magnitude of partial sums of independent random variables, refining the classical central limit theorem.
E378993 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: Hartman–Wintner law of the iterated logarithm | Statement: [Khinchin's law of the iterated logarithm, isRelatedTo, Hartman–Wintner law of the iterated logarithm]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Hartman–Wintner law of the iterated logarithm
Context triple: [Khinchin's law of the iterated logarithm, isRelatedTo, Hartman–Wintner law of the iterated logarithm]
  • A. 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.
  • B. 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.
  • C. 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.
  • D. Lyapunov central limit theorem
    The Lyapunov central limit theorem is a version of the central limit theorem that provides sufficient moment conditions under which the normalized sum of independent (not necessarily identically distributed) random variables converges in distribution to a normal law.
  • E. 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.
  • 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: Hartman–Wintner law of the iterated logarithm
Triple: [Khinchin's law of the iterated logarithm, isRelatedTo, Hartman–Wintner law of the iterated logarithm]
Generated description
The Hartman–Wintner law of the iterated logarithm is a fundamental result in probability theory that precisely characterizes the almost-sure fluctuation magnitude of partial sums of independent random variables, refining the classical central limit theorem.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Hartman–Wintner law of the iterated logarithm
Target entity description: The Hartman–Wintner law of the iterated logarithm is a fundamental result in probability theory that precisely characterizes the almost-sure fluctuation magnitude of partial sums of independent random variables, refining the classical central limit theorem.
  • A. 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.
  • B. Khinchin's law of the iterated logarithm chosen
    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.
  • C. 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.
  • D. Lyapunov central limit theorem
    The Lyapunov central limit theorem is a version of the central limit theorem that provides sufficient moment conditions under which the normalized sum of independent (not necessarily identically distributed) random variables converges in distribution to a normal law.
  • E. 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.
  • 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_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_69ff4c345f888190be7a684f3bd86324 completed May 9, 2026, 3:01 p.m.
NEDg Description generation batch_69ff4d4dd8108190aa3271a9feaea5ca completed May 9, 2026, 3:05 p.m.
NED2 Entity disambiguation (via description) batch_69ff4e29e8a48190bf7728cf2d099a7e completed May 9, 2026, 3:09 p.m.
Created at: April 10, 2026, 3:54 a.m.