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.