Triple

T1535799
Position Surface form Disambiguated ID Type / Status
Subject Berry–Esseen theorem E32545 entity
Predicate relatedTo P37 FINISHED
Object Lindeberg–Feller central limit theorem
The Lindeberg–Feller central limit theorem is a general form of the central limit theorem that provides conditions under which sums of independent, not necessarily identically distributed random variables converge in distribution to a normal law.
E174594 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: Lindeberg–Feller central limit theorem | Statement: [Berry–Esseen theorem, relatedTo, Lindeberg–Feller central limit theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Lindeberg–Feller central limit theorem
Context triple: [Berry–Esseen theorem, relatedTo, Lindeberg–Feller central limit theorem]
  • A. 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.
  • B. 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.
  • C. Kronecker’s lemma
    Kronecker’s lemma is a result in real analysis and summability theory that links the convergence of series with weighted averages of their partial sums, often used in the study of Fourier series and ergodic theorems.
  • D. law of large numbers
    The law of large numbers is a fundamental theorem in probability theory stating that as the number of independent trials increases, the sample average converges to the expected value.
  • E. Riemann–Lebesgue lemma
    The Riemann–Lebesgue lemma is a fundamental result in Fourier analysis stating that the Fourier coefficients (or transform) of an integrable function vanish at infinity.
  • 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: Lindeberg–Feller central limit theorem
Triple: [Berry–Esseen theorem, relatedTo, Lindeberg–Feller central limit theorem]
Generated description
The Lindeberg–Feller central limit theorem is a general form of the central limit theorem that provides conditions under which sums of independent, not necessarily identically distributed random variables converge in distribution to a normal law.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Lindeberg–Feller central limit theorem
Target entity description: The Lindeberg–Feller central limit theorem is a general form of the central limit theorem that provides conditions under which sums of independent, not necessarily identically distributed random variables converge in distribution to a normal law.
  • A. 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.
  • B. 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.
  • C. Kronecker’s lemma
    Kronecker’s lemma is a result in real analysis and summability theory that links the convergence of series with weighted averages of their partial sums, often used in the study of Fourier series and ergodic theorems.
  • D. law of large numbers
    The law of large numbers is a fundamental theorem in probability theory stating that as the number of independent trials increases, the sample average converges to the expected value.
  • E. Riemann–Lebesgue lemma
    The Riemann–Lebesgue lemma is a fundamental result in Fourier analysis stating that the Fourier coefficients (or transform) of an integrable function vanish at infinity.
  • 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_69a885ea86308190998f6bc14bb91f8e completed March 4, 2026, 7:20 p.m.
NER Named-entity recognition batch_69a90829e60081909d3f9f79585e080e completed March 5, 2026, 4:35 a.m.
NED1 Entity disambiguation (via context triple) batch_69ad295da0988190b1dc171bcdfe4d71 completed March 8, 2026, 7:46 a.m.
NEDg Description generation batch_69ad29dc9fd08190b67527f0662c92dc completed March 8, 2026, 7:48 a.m.
NED2 Entity disambiguation (via description) batch_69ad2a4d71a88190b67ed21beebbb479 completed March 8, 2026, 7:50 a.m.
Created at: March 4, 2026, 7:26 p.m.