Triple

T243806
Position Surface form Disambiguated ID Type / Status
Subject central limit theorem E4991 entity
Predicate relatedTo P37 FINISHED
Object Berry–Esseen theorem
The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
E32545 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: Berry–Esseen theorem | Statement: [central limit theorem, relatedTo, Berry–Esseen theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Berry–Esseen theorem
Context triple: [central limit theorem, relatedTo, Berry–Esseen theorem]
  • A. central limit theorem
    The central limit theorem is a fundamental result in probability theory stating that the sum (or average) of many independent, identically distributed random variables tends to follow a normal distribution, regardless of the original variables’ distribution, under mild conditions.
  • B. Minkowski inequality
    The Minkowski inequality is a fundamental result in functional analysis and measure theory that generalizes the triangle inequality to L^p spaces, providing a key tool for studying norms and integrable functions.
  • C. Gauss–Markov theorem
    The Gauss–Markov theorem is a fundamental result in statistics stating that, under certain conditions, the ordinary least squares estimator is the best linear unbiased estimator (BLUE) of the coefficients in a linear regression model.
  • D. Gaussian law of error
    The Gaussian law of error is a fundamental statistical principle stating that measurement errors tend to follow a normal (bell-shaped) distribution, forming the basis of much of probability theory and statistical inference.
  • E. Girsanov theorem
    Girsanov theorem is a fundamental result in stochastic calculus that describes how the dynamics of stochastic processes, particularly Brownian motion, change under an equivalent change of probability measure.
  • 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: Berry–Esseen theorem
Triple: [central limit theorem, relatedTo, Berry–Esseen theorem]
Generated description
The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Berry–Esseen theorem
Target entity description: The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
  • A. central limit theorem
    The central limit theorem is a fundamental result in probability theory stating that the sum (or average) of many independent, identically distributed random variables tends to follow a normal distribution, regardless of the original variables’ distribution, under mild conditions.
  • B. Minkowski inequality
    The Minkowski inequality is a fundamental result in functional analysis and measure theory that generalizes the triangle inequality to L^p spaces, providing a key tool for studying norms and integrable functions.
  • C. Gauss–Markov theorem
    The Gauss–Markov theorem is a fundamental result in statistics stating that, under certain conditions, the ordinary least squares estimator is the best linear unbiased estimator (BLUE) of the coefficients in a linear regression model.
  • D. Gaussian law of error
    The Gaussian law of error is a fundamental statistical principle stating that measurement errors tend to follow a normal (bell-shaped) distribution, forming the basis of much of probability theory and statistical inference.
  • E. Girsanov theorem
    Girsanov theorem is a fundamental result in stochastic calculus that describes how the dynamics of stochastic processes, particularly Brownian motion, change under an equivalent change of probability measure.
  • 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_69a257c3d0708190b0871c4269d273e6 completed Feb. 28, 2026, 2:49 a.m.
NER Named-entity recognition batch_69a25cef84ac81908fcc175b7f89653b completed Feb. 28, 2026, 3:11 a.m.
NED1 Entity disambiguation (via context triple) batch_69a3736ff4388190b6b43a149d0003c5 completed Feb. 28, 2026, 11 p.m.
NEDg Description generation batch_69a3745c4cb481908fb0ba52119fabbb completed Feb. 28, 2026, 11:03 p.m.
NED2 Entity disambiguation (via description) batch_69a374e12e9c819090217b5197c90ccf completed Feb. 28, 2026, 11:06 p.m.
Created at: Feb. 28, 2026, 2:53 a.m.