Triple

T3365580
Position Surface form Disambiguated ID Type / Status
Subject Kiyoshi Itô E70827 entity
Predicate knownFor P22 FINISHED
Object Itô integral
The Itô integral is a fundamental stochastic integral used in probability theory and mathematical finance to rigorously define integration with respect to Brownian motion and more general semimartingales.
E351145 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: Itô integral | Statement: [Kiyoshi Itô, knownFor, Itô integral]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Itô integral
Context triple: [Kiyoshi Itô, knownFor, Itô integral]
  • A. 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.
  • 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. 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.
  • D. 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.
  • E. 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.
  • 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: Itô integral
Triple: [Kiyoshi Itô, knownFor, Itô integral]
Generated description
The Itô integral is a fundamental stochastic integral used in probability theory and mathematical finance to rigorously define integration with respect to Brownian motion and more general semimartingales.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Itô integral
Target entity description: The Itô integral is a fundamental stochastic integral used in probability theory and mathematical finance to rigorously define integration with respect to Brownian motion and more general semimartingales.
  • A. 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.
  • 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. 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.
  • D. 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.
  • E. 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.
  • 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_69ad85a729d48190afd789cd8417f289 completed March 8, 2026, 2:20 p.m.
NER Named-entity recognition batch_69adb28643f48190b78b0222f8323344 completed March 8, 2026, 5:31 p.m.
NED1 Entity disambiguation (via context triple) batch_69b3254daf8c8190b2141682503c111e completed March 12, 2026, 8:42 p.m.
NEDg Description generation batch_69b326f94db481908560b64f701dd433 completed March 12, 2026, 8:50 p.m.
NED2 Entity disambiguation (via description) batch_69b3276b55a0819094face2e56001921 completed March 12, 2026, 8:51 p.m.
Created at: March 8, 2026, 3:13 p.m.