Triple

T478456
Position Surface form Disambiguated ID Type / Status
Subject Itô calculus E9112 entity
Predicate appliesTo P1129 FINISHED
Object 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.
E60316 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 processes | Statement: [Itô calculus, appliesTo, Itô processes]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Itô processes
Context triple: [Itô calculus, appliesTo, Itô processes]
  • A. 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.
  • B. Ornstein–Uhlenbeck process
    The Ornstein–Uhlenbeck process is a continuous-time stochastic process that models mean-reverting random motion, widely used in physics and quantitative finance to describe systems fluctuating around a long-term equilibrium.
  • 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. Feynman–Kac formula
    The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
  • E. 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.
  • 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 processes
Triple: [Itô calculus, appliesTo, Itô processes]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Itô processes
Target entity description: 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.
  • A. 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.
  • B. Ornstein–Uhlenbeck process
    The Ornstein–Uhlenbeck process is a continuous-time stochastic process that models mean-reverting random motion, widely used in physics and quantitative finance to describe systems fluctuating around a long-term equilibrium.
  • 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. Feynman–Kac formula
    The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
  • E. 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.
  • 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_69a2e7ff81708190b0507a24a997232c completed Feb. 28, 2026, 1:05 p.m.
NER Named-entity recognition batch_69a2f056459881909749764cc4a7f9e8 completed Feb. 28, 2026, 1:40 p.m.
NED1 Entity disambiguation (via context triple) batch_69a4711cd9ac8190bc95a6560950525b completed March 1, 2026, 5:02 p.m.
NEDg Description generation batch_69a47180628c8190b801210ec5edf071 completed March 1, 2026, 5:04 p.m.
NED2 Entity disambiguation (via description) batch_69a4721291a08190bc0b6f3aaadf8b71 completed March 1, 2026, 5:06 p.m.
Created at: Feb. 28, 2026, 1:12 p.m.