Triple

T7705193
Position Surface form Disambiguated ID Type / Status
Subject Lindeberg–Feller central limit theorem E174594 entity
Predicate hasVersion P455 FINISHED
Object Lindeberg–Feller theorem for independent but not identically distributed sequences E174594 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: Lindeberg–Feller theorem for independent but not identically distributed sequences | Statement: [Lindeberg–Feller central limit theorem, hasVersion, Lindeberg–Feller theorem for independent but not identically distributed sequences]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Lindeberg–Feller theorem for independent but not identically distributed sequences
Context triple: [Lindeberg–Feller central limit theorem, hasVersion, Lindeberg–Feller theorem for independent but not identically distributed sequences]
  • A. Lindeberg–Feller central limit theorem chosen
    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.
  • B. Limit Laws for Sums of Independent Random Variables
    Limit Laws for Sums of Independent Random Variables is a foundational mathematical work that systematically develops the theory of probability limit theorems, including results such as the law of large numbers and central limit behavior for sums of independent random variables.
  • C. 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.
  • D. 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.
  • E. 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.
  • 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_69c6995b3e8c8190833108f883d5f53c completed March 27, 2026, 2:51 p.m.
NER Named-entity recognition batch_69c7028f17f0819081686ac146750d3a completed March 27, 2026, 10:19 p.m.
NED1 Entity disambiguation (via context triple) batch_69c8b502ebc0819095b0dc7096c2b997 completed March 29, 2026, 5:13 a.m.
Created at: March 27, 2026, 4:03 p.m.