Triple

T13070795
Position Surface form Disambiguated ID Type / Status
Subject Paul Lévy E329449 entity
Predicate knownFor P22 FINISHED
Object Lévy’s continuity theorem
Lévy’s continuity theorem is a fundamental result in probability theory that characterizes convergence in distribution of random variables via pointwise convergence of their characteristic functions.
E1020437 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: Lévy’s continuity theorem | Statement: [Paul Lévy, knownFor, Lévy’s continuity theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Lévy’s continuity theorem
Context triple: [Paul Lévy, knownFor, Lévy’s continuity theorem]
  • A. 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.
  • B. Cramér–Wold theorem
    The Cramér–Wold theorem is a fundamental result in probability theory stating that a multivariate distribution is uniquely determined by the distributions of all its one-dimensional linear projections.
  • C. Bochner theorem on characteristic functions
    The Bochner theorem on characteristic functions is a fundamental result in probability theory and harmonic analysis that characterizes which functions are Fourier transforms of probability measures by requiring them to be positive-definite, continuous, and normalized at zero.
  • D. 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.
  • E. Khinchin–Kolmogorov theorem
    The Khinchin–Kolmogorov theorem is a fundamental result in probability theory that provides conditions under which series of independent random variables converge almost surely.
  • 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: Lévy’s continuity theorem
Triple: [Paul Lévy, knownFor, Lévy’s continuity theorem]
Generated description
Lévy’s continuity theorem is a fundamental result in probability theory that characterizes convergence in distribution of random variables via pointwise convergence of their characteristic functions.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Lévy’s continuity theorem
Target entity description: Lévy’s continuity theorem is a fundamental result in probability theory that characterizes convergence in distribution of random variables via pointwise convergence of their characteristic functions.
  • A. 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.
  • B. Cramér–Wold theorem
    The Cramér–Wold theorem is a fundamental result in probability theory stating that a multivariate distribution is uniquely determined by the distributions of all its one-dimensional linear projections.
  • C. Bochner theorem on characteristic functions
    The Bochner theorem on characteristic functions is a fundamental result in probability theory and harmonic analysis that characterizes which functions are Fourier transforms of probability measures by requiring them to be positive-definite, continuous, and normalized at zero.
  • D. 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.
  • E. Khinchin–Kolmogorov theorem
    The Khinchin–Kolmogorov theorem is a fundamental result in probability theory that provides conditions under which series of independent random variables converge almost surely.
  • 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_69d80771749c81909a6d9197b9504872 completed April 9, 2026, 8:09 p.m.
NER Named-entity recognition batch_69d980ee6130819095d835e7ff6a8c5b completed April 10, 2026, 10:59 p.m.
NED1 Entity disambiguation (via context triple) batch_69f6d60510dc81909e0cba8b63a50d9c completed May 3, 2026, 4:58 a.m.
NEDg Description generation batch_69f6dbb4b8848190825102be81ff693a completed May 3, 2026, 5:23 a.m.
NED2 Entity disambiguation (via description) batch_69f6dc705f28819087e5d374f83d3acc completed May 3, 2026, 5:26 a.m.
Created at: April 9, 2026, 9 p.m.