Triple

T378951
Position Surface form Disambiguated ID Type / Status
Subject Fokker–Planck equation E8633 entity
Predicate relatedTo P37 FINISHED
Object 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.
E48273 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: Ornstein–Uhlenbeck process | Statement: [Fokker–Planck equation, relatedTo, Ornstein–Uhlenbeck process]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Ornstein–Uhlenbeck process
Context triple: [Fokker–Planck equation, relatedTo, Ornstein–Uhlenbeck process]
  • A. 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.
  • B. Fokker–Planck equation
    The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
  • C. Brownian motion
    Brownian motion is the random, jittery movement of microscopic particles suspended in a fluid, whose explanation provided key evidence for the existence of atoms and the molecular nature of matter.
  • D. 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.
  • E. Euler–Maruyama method
    The Euler–Maruyama method is a basic time-stepping scheme for numerically approximating solutions to stochastic differential equations, widely used in simulations of systems with noise such as Langevin dynamics.
  • 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: Ornstein–Uhlenbeck process
Triple: [Fokker–Planck equation, relatedTo, Ornstein–Uhlenbeck process]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Ornstein–Uhlenbeck process
Target entity description: 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.
  • A. 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.
  • B. Fokker–Planck equation
    The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
  • C. Brownian motion
    Brownian motion is the random, jittery movement of microscopic particles suspended in a fluid, whose explanation provided key evidence for the existence of atoms and the molecular nature of matter.
  • D. 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.
  • E. Euler–Maruyama method
    The Euler–Maruyama method is a basic time-stepping scheme for numerically approximating solutions to stochastic differential equations, widely used in simulations of systems with noise such as Langevin dynamics.
  • 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_69a2e7f47dd08190a4e294ccbbe46cd4 completed Feb. 28, 2026, 1:04 p.m.
NER Named-entity recognition batch_69a2ec2974988190a1d6316cbb5159c8 completed Feb. 28, 2026, 1:22 p.m.
NED1 Entity disambiguation (via context triple) batch_69a3fafe091881908fdf8ddbb6b8a7e6 completed March 1, 2026, 8:38 a.m.
NEDg Description generation batch_69a3fba8a31881909a32dca83c07e197 completed March 1, 2026, 8:41 a.m.
NED2 Entity disambiguation (via description) batch_69a3fc96cbd88190b05e70c73cbb45c0 completed March 1, 2026, 8:45 a.m.
Created at: Feb. 28, 2026, 1:08 p.m.