Triple
T11961991
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Brownian filtration |
E284689
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
Markov property of Brownian motion
The Markov property of Brownian motion is the characteristic that, given its present value, the future evolution of the process is independent of its past, making Brownian motion a Markov process.
|
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: Markov property of Brownian motion | Statement: [Brownian filtration, relatedTo, Markov property of Brownian motion]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Markov property of Brownian motion Context triple: [Brownian filtration, relatedTo, Markov property of Brownian motion]
-
A.
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.
-
B.
Brownian filtration
Brownian filtration is the natural increasing family of σ-algebras generated by a Brownian motion, encoding all information revealed by the process up to each time.
-
C.
Dyson Brownian motion
Dyson Brownian motion is a stochastic process describing the time evolution of eigenvalues of random matrices as if they were interacting particles undergoing Brownian motion, fundamental in random matrix theory.
-
D.
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.
-
E.
Random Walk and the Theory of Brownian Motion
"Random Walk and the Theory of Brownian Motion" is a mathematical work by Mark Kac that rigorously develops the connection between discrete random walks and continuous Brownian motion within probability theory.
- 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: Markov property of Brownian motion Triple: [Brownian filtration, relatedTo, Markov property of Brownian motion]
Generated description
The Markov property of Brownian motion is the characteristic that, given its present value, the future evolution of the process is independent of its past, making Brownian motion a Markov process.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Markov property of Brownian motion Target entity description: The Markov property of Brownian motion is the characteristic that, given its present value, the future evolution of the process is independent of its past, making Brownian motion a Markov process.
-
A.
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.
-
B.
Brownian filtration
Brownian filtration is the natural increasing family of σ-algebras generated by a Brownian motion, encoding all information revealed by the process up to each time.
-
C.
Dyson Brownian motion
Dyson Brownian motion is a stochastic process describing the time evolution of eigenvalues of random matrices as if they were interacting particles undergoing Brownian motion, fundamental in random matrix theory.
-
D.
Chapman–Kolmogorov equation
chosen
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.
-
E.
Random Walk and the Theory of Brownian Motion
"Random Walk and the Theory of Brownian Motion" is a mathematical work by Mark Kac that rigorously develops the connection between discrete random walks and continuous Brownian motion within probability theory.
- F. None of above.
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_69d6ab2eaeb881909f7914758f859413 |
completed | April 8, 2026, 7:23 p.m. |
| NER | Named-entity recognition | batch_69d9037848f481908276716675464464 |
completed | April 10, 2026, 2:04 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f4592fa9a48190a0450e3d0c57c4d3 |
completed | May 1, 2026, 7:41 a.m. |
| NEDg | Description generation | batch_69f4645ef63881909b46937f73d637a3 |
completed | May 1, 2026, 8:29 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69f465be4db08190882898a17d077019 |
completed | May 1, 2026, 8:35 a.m. |
Created at: April 8, 2026, 9:45 p.m.