Triple

T22423506
Position Surface form Disambiguated ID Type / Status
Subject Erdős–Rényi law of large numbers E554306 entity
Predicate relatedTo P37 FINISHED
Object Kolmogorov strong law of large numbers
The Kolmogorov strong law of large numbers is a fundamental theorem in probability theory stating that the sample average of independent, identically distributed random variables converges almost surely to their expected value under suitable conditions.
E1536263 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 strong law of large numbers | Statement: [Erdős–Rényi law of large numbers, relatedTo, Kolmogorov strong law of large numbers]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Kolmogorov strong law of large numbers
Context triple: [Erdős–Rényi law of large numbers, relatedTo, Kolmogorov strong law of large numbers]
  • 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. Gnedenko–Kolmogorov limit theorem
    The Gnedenko–Kolmogorov limit theorem is a fundamental result in probability theory that characterizes the limiting distributions of properly normalized sums of independent random variables, generalizing the classical central limit theorem to stable laws.
  • D. 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.
  • E. Erdős–Rényi law of large numbers
    The Erdős–Rényi law of large numbers is a refinement of the classical law of large numbers that provides precise asymptotic behavior and convergence rates for sums of independent random variables, developed by mathematicians Pál Erdős and Alfréd Rényi.
  • 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 strong law of large numbers
Triple: [Erdős–Rényi law of large numbers, relatedTo, Kolmogorov strong law of large numbers]
Generated description
The Kolmogorov strong law of large numbers is a fundamental theorem in probability theory stating that the sample average of independent, identically distributed random variables converges almost surely to their expected value under suitable conditions.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Kolmogorov strong law of large numbers
Target entity description: The Kolmogorov strong law of large numbers is a fundamental theorem in probability theory stating that the sample average of independent, identically distributed random variables converges almost surely to their expected value under suitable conditions.
  • 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. Gnedenko–Kolmogorov limit theorem
    The Gnedenko–Kolmogorov limit theorem is a fundamental result in probability theory that characterizes the limiting distributions of properly normalized sums of independent random variables, generalizing the classical central limit theorem to stable laws.
  • D. 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.
  • E. Erdős–Rényi law of large numbers
    The Erdős–Rényi law of large numbers is a refinement of the classical law of large numbers that provides precise asymptotic behavior and convergence rates for sums of independent random variables, developed by mathematicians Pál Erdős and Alfréd Rényi.
  • 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_69e11e4f2d0c819091aa3558ea2ee630 completed April 16, 2026, 5:37 p.m.
NER Named-entity recognition batch_69f15a2af620819083338127e78137dc completed April 29, 2026, 1:08 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0af0f06cec8190a911ab9a867c0596 completed May 18, 2026, 10:58 a.m.
NEDg Description generation batch_6a0af2c6151881908f85a7c3c751cea9 completed May 18, 2026, 11:06 a.m.
NED2 Entity disambiguation (via description) batch_6a0b08e411048190a368214c57c35d5e completed May 18, 2026, 12:41 p.m.
Created at: April 16, 2026, 8:47 p.m.