Triple

T2393112
Position Surface form Disambiguated ID Type / Status
Subject Kolmogorov backward equation E48986 entity
Predicate relatedTo P37 FINISHED
Object Dynkin formula
Dynkin formula is a fundamental result in the theory of Markov processes that expresses the expected value of a function of the process at a stopping time in terms of its generator and an integral over time.
E262081 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: Dynkin formula | Statement: [Kolmogorov backward equation, relatedTo, Dynkin formula]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Dynkin formula
Context triple: [Kolmogorov backward equation, relatedTo, Dynkin formula]
  • 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. 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.
  • C. 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.
  • D. 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.
  • E. 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.
  • 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: Dynkin formula
Triple: [Kolmogorov backward equation, relatedTo, Dynkin formula]
Generated description
Dynkin formula is a fundamental result in the theory of Markov processes that expresses the expected value of a function of the process at a stopping time in terms of its generator and an integral over time.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Dynkin formula
Target entity description: Dynkin formula is a fundamental result in the theory of Markov processes that expresses the expected value of a function of the process at a stopping time in terms of its generator and an integral over time.
  • 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. 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.
  • C. 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.
  • D. 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.
  • E. 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.
  • 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_69a88aa5f63081908d07fd302029fcbd completed March 4, 2026, 7:40 p.m.
NER Named-entity recognition batch_69abc876d48881909e4d6f5ebe430012 completed March 7, 2026, 6:40 a.m.
NED1 Entity disambiguation (via context triple) batch_69aeb3da0978819094584cb23194fb3a completed March 9, 2026, 11:49 a.m.
NEDg Description generation batch_69aeb46f882881909294a3698ead865e completed March 9, 2026, 11:52 a.m.
NED2 Entity disambiguation (via description) batch_69aeb4c715a88190b1009a2cf1d95441 completed March 9, 2026, 11:53 a.m.
Created at: March 4, 2026, 7:57 p.m.