Triple

T2325347
Position Surface form Disambiguated ID Type / Status
Subject Markov process E48274 entity
Predicate relatedTo P37 FINISHED
Object Chapman–Kolmogorov equation
The Chapman–Kolmogorov equation is a fundamental relation in the theory of stochastic processes that expresses how transition probabilities of a Markov process over longer time intervals can be obtained by integrating over intermediate states.
E254907 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: Chapman–Kolmogorov equation | Statement: [Markov process, relatedTo, Chapman–Kolmogorov equation]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Chapman–Kolmogorov equation
Context triple: [Markov process, relatedTo, Chapman–Kolmogorov equation]
  • A. Kolmogorov backward equation
    The Kolmogorov backward equation is a fundamental partial differential equation in stochastic processes that characterizes the time evolution of expected values of functionals of Markov processes, complementary to the Fokker–Planck (forward) equation.
  • 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. 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.
  • 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. 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.
  • 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: Chapman–Kolmogorov equation
Triple: [Markov process, relatedTo, Chapman–Kolmogorov equation]
Generated description
The Chapman–Kolmogorov equation is a fundamental relation in the theory of stochastic processes that expresses how transition probabilities of a Markov process over longer time intervals can be obtained by integrating over intermediate states.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Chapman–Kolmogorov equation
Target entity description: The Chapman–Kolmogorov equation is a fundamental relation in the theory of stochastic processes that expresses how transition probabilities of a Markov process over longer time intervals can be obtained by integrating over intermediate states.
  • A. Kolmogorov backward equation
    The Kolmogorov backward equation is a fundamental partial differential equation in stochastic processes that characterizes the time evolution of expected values of functionals of Markov processes, complementary to the Fokker–Planck (forward) equation.
  • 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. 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.
  • 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. 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.
  • 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_69a88aa308a88190b0b86c011fda7fce completed March 4, 2026, 7:40 p.m.
NER Named-entity recognition batch_69abc649af4481908fdc0bc7f4777b71 completed March 7, 2026, 6:31 a.m.
NED1 Entity disambiguation (via context triple) batch_69ae896de2c48190ada0814d3a4f8497 completed March 9, 2026, 8:48 a.m.
NEDg Description generation batch_69ae89e2efd48190a2f0a4702dcbc081 completed March 9, 2026, 8:50 a.m.
NED2 Entity disambiguation (via description) batch_69ae8a7726dc8190a18f7f1e1609253a completed March 9, 2026, 8:53 a.m.
Created at: March 4, 2026, 7:50 p.m.