Triple

T14704229
Position Surface form Disambiguated ID Type / Status
Subject Émile Borel E345382 entity
Predicate notableWork P4 FINISHED
Object Borel’s strong law of large numbers formulation E1041768 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: Borel’s strong law of large numbers formulation | Statement: [Émile Borel, notableWork, Borel’s strong law of large numbers formulation]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Borel’s strong law of large numbers formulation
Context triple: [Émile Borel, notableWork, Borel’s strong law of large numbers formulation]
  • A. Borel–Cantelli lemmas chosen
    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.
  • 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. 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.
  • D. Kolmogorov zero–one law
    The Kolmogorov zero–one law is a fundamental result in probability theory stating that certain events determined by the tail behavior of independent random variables must have probability either zero or one.
  • E. 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.
  • 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_69d822e4a8c08190a155df736bb7bc13 completed April 9, 2026, 10:06 p.m.
NER Named-entity recognition batch_69deb6071e5c8190bb5509c859135c2d completed April 14, 2026, 9:47 p.m.
NED1 Entity disambiguation (via context triple) batch_69fdf087ce8c819081a7186df67bcf1f completed May 8, 2026, 2:17 p.m.
Created at: April 10, 2026, 1:28 a.m.