Triple

T2716842
Position Surface form Disambiguated ID Type / Status
Subject Itô’s lemma E59984 entity
Predicate relatesTo P37 FINISHED
Object Stratonovich integral
The Stratonovich integral is a formulation of stochastic integration that preserves the classical chain rule of calculus and is widely used in physics and engineering for modeling systems with noise.
E295051 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: Stratonovich integral | Statement: [Itô’s lemma, relatesTo, Stratonovich integral]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Stratonovich integral
Context triple: [Itô’s lemma, relatesTo, Stratonovich integral]
  • A. Riemann–Stieltjes integral
    The Riemann–Stieltjes integral is a generalization of the Riemann integral in which integration is taken with respect to a function of bounded variation rather than just the identity function, allowing more flexible treatment of sums and distributions.
  • B. Itô calculus
    Itô calculus is a branch of stochastic analysis that extends classical calculus to functions of stochastic processes, particularly Brownian motion, enabling rigorous treatment of stochastic differential equations.
  • C. Henstock–Kurzweil integral
    The Henstock–Kurzweil integral is a highly general integration theory that extends and refines the Riemann integral, capable of integrating a broader class of functions while retaining many of the intuitive properties of Riemann integration.
  • D. Itô’s lemma
    Itô’s lemma is a fundamental result in stochastic calculus that generalizes the chain rule to functions of stochastic processes, especially Brownian motion.
  • E. 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.
  • 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: Stratonovich integral
Triple: [Itô’s lemma, relatesTo, Stratonovich integral]
Generated description
The Stratonovich integral is a formulation of stochastic integration that preserves the classical chain rule of calculus and is widely used in physics and engineering for modeling systems with noise.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Stratonovich integral
Target entity description: The Stratonovich integral is a formulation of stochastic integration that preserves the classical chain rule of calculus and is widely used in physics and engineering for modeling systems with noise.
  • A. Riemann–Stieltjes integral
    The Riemann–Stieltjes integral is a generalization of the Riemann integral in which integration is taken with respect to a function of bounded variation rather than just the identity function, allowing more flexible treatment of sums and distributions.
  • B. Itô calculus
    Itô calculus is a branch of stochastic analysis that extends classical calculus to functions of stochastic processes, particularly Brownian motion, enabling rigorous treatment of stochastic differential equations.
  • C. Henstock–Kurzweil integral
    The Henstock–Kurzweil integral is a highly general integration theory that extends and refines the Riemann integral, capable of integrating a broader class of functions while retaining many of the intuitive properties of Riemann integration.
  • D. Itô’s lemma
    Itô’s lemma is a fundamental result in stochastic calculus that generalizes the chain rule to functions of stochastic processes, especially Brownian motion.
  • E. 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.
  • 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_69ab4ac92a088190bc74bca14038e3de completed March 6, 2026, 9:44 p.m.
NER Named-entity recognition batch_69abda964d4881908179b2a1b16411e4 completed March 7, 2026, 7:58 a.m.
NED1 Entity disambiguation (via context triple) batch_69afbbbe621881909e153290394798d6 completed March 10, 2026, 6:35 a.m.
NEDg Description generation batch_69afbc67c39c8190b5932c0e23595f64 completed March 10, 2026, 6:38 a.m.
NED2 Entity disambiguation (via description) batch_69afbd2d8a2c8190896a9154ebbd8bab completed March 10, 2026, 6:41 a.m.
Created at: March 6, 2026, 9:55 p.m.