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.