Triple

T15502437
Position Surface form Disambiguated ID Type / Status
Subject Khinchin's law of the iterated logarithm E378993 entity
Predicate refines P6555 FINISHED
Object strong law of large numbers E141078 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: strong law of large numbers | Statement: [Khinchin's law of the iterated logarithm, refines, strong law of large numbers]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: strong law of large numbers
Context triple: [Khinchin's law of the iterated logarithm, refines, strong law of large numbers]
  • A. law of large numbers chosen
    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.
  • B. 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.
  • 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. Borel–Cantelli lemmas
    The Borel–Cantelli lemmas are fundamental results in probability theory that characterize when events occur infinitely often or only finitely often, based on the convergence or divergence of the sum of their probabilities.
  • E. 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.
  • 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_69d85cd53a7c819080f5b9042c4c199e completed April 10, 2026, 2:13 a.m.
NER Named-entity recognition batch_69e03fcc5bb88190b8a9a81419a9a38b completed April 16, 2026, 1:47 a.m.
NED1 Entity disambiguation (via context triple) batch_69ff3669f908819087162b1b8a4e4320 completed May 9, 2026, 1:28 p.m.
Created at: April 10, 2026, 3:54 a.m.