Triple

T13070791
Position Surface form Disambiguated ID Type / Status
Subject Paul Lévy E329449 entity
Predicate knownFor P22 FINISHED
Object Lévy–Itô decomposition
The Lévy–Itô decomposition is a fundamental result in probability theory that expresses any Lévy process as the sum of a Brownian motion with drift and a jump process constructed from a Poisson random measure.
E1020435 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–Itô decomposition | Statement: [Paul Lévy, knownFor, Lévy–Itô decomposition]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Lévy–Itô decomposition
Context triple: [Paul Lévy, knownFor, Lévy–Itô decomposition]
  • A. Doob–Meyer decomposition
    The Doob–Meyer decomposition is a fundamental result in stochastic process theory that uniquely expresses a submartingale as the sum of a martingale and a predictable, increasing process.
  • B. Itô processes
    Itô processes are a class of stochastic processes, typically modeled as solutions to stochastic differential equations, that form the fundamental objects of study in Itô calculus and modern stochastic analysis.
  • C. Lévy alpha-stable distribution
    The Lévy alpha-stable distribution is a family of heavy-tailed probability distributions characterized by a stability parameter α, generalizing the normal and Cauchy distributions and often used to model impulsive or anomalous random phenomena.
  • D. Clark–Ocone formula
    The Clark–Ocone formula is a key result in stochastic calculus and Malliavin calculus that provides an explicit integral representation of square-integrable random variables with respect to Brownian motion.
  • E. Khinchin–Pollaczek formula
    The Khinchin–Pollaczek formula is a result in probability theory and queueing theory that provides an explicit expression for the stationary waiting-time distribution in certain single-server queues.
  • 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–Itô decomposition
Triple: [Paul Lévy, knownFor, Lévy–Itô decomposition]
Generated description
The Lévy–Itô decomposition is a fundamental result in probability theory that expresses any Lévy process as the sum of a Brownian motion with drift and a jump process constructed from a Poisson random measure.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Lévy–Itô decomposition
Target entity description: The Lévy–Itô decomposition is a fundamental result in probability theory that expresses any Lévy process as the sum of a Brownian motion with drift and a jump process constructed from a Poisson random measure.
  • A. Doob–Meyer decomposition
    The Doob–Meyer decomposition is a fundamental result in stochastic process theory that uniquely expresses a submartingale as the sum of a martingale and a predictable, increasing process.
  • B. Itô processes
    Itô processes are a class of stochastic processes, typically modeled as solutions to stochastic differential equations, that form the fundamental objects of study in Itô calculus and modern stochastic analysis.
  • C. Lévy alpha-stable distribution
    The Lévy alpha-stable distribution is a family of heavy-tailed probability distributions characterized by a stability parameter α, generalizing the normal and Cauchy distributions and often used to model impulsive or anomalous random phenomena.
  • D. Clark–Ocone formula
    The Clark–Ocone formula is a key result in stochastic calculus and Malliavin calculus that provides an explicit integral representation of square-integrable random variables with respect to Brownian motion.
  • E. Khinchin–Pollaczek formula
    The Khinchin–Pollaczek formula is a result in probability theory and queueing theory that provides an explicit expression for the stationary waiting-time distribution in certain single-server queues.
  • 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.