Triple

T1535807
Position Surface form Disambiguated ID Type / Status
Subject Berry–Esseen theorem E32545 entity
Predicate hasGeneralizations P2372 FINISHED
Object Berry–Esseen bounds for dependent variables E32545 NE FINISHED

How this triple was built (2 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 bounds for dependent variables | Statement: [Berry–Esseen theorem, hasGeneralizations, Berry–Esseen bounds for dependent variables]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Berry–Esseen bounds for dependent variables
Context triple: [Berry–Esseen theorem, hasGeneralizations, Berry–Esseen bounds for dependent variables]
  • A. Berry–Esseen theorem chosen
    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. 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.
  • C. Statistical Independence in Probability, Analysis and Number Theory
    "Statistical Independence in Probability, Analysis and Number Theory" is a mathematical monograph by Mark Kac that explores the concept of independence across probability theory, real analysis, and number theory.
  • D. Khinchin–Kahane type inequalities
    Khinchin–Kahane type inequalities are fundamental results in probability and functional analysis that bound moments or norms of random series (often with Rademacher or Gaussian coefficients) in terms of each other, providing powerful tools for studying the geometry of Banach spaces and random processes.
  • E. Edgeworth expansion
    Edgeworth expansion is an asymptotic series that refines the central limit theorem by providing higher-order approximations to the distribution of normalized sums of random variables.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69aa61dc6ab881908b22aa7a5295bf21 completed March 6, 2026, 5:10 a.m.
NED1 Entity disambiguation (via context triple) batch_69ad30942dc481908de85bd2ca30c0bd completed March 8, 2026, 8:17 a.m.
Created at: March 4, 2026, 7:26 p.m.