Triple

T23185671
Position Surface form Disambiguated ID Type / Status
Subject Bessel E579586 entity
Predicate hasDerivativeConcept P56157 FINISHED
Object Bessel process
The Bessel process is a family of stochastic processes describing the radial part of Brownian motion in Euclidean space, widely used in probability theory and mathematical finance.
E1572538 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: Bessel process | Statement: [Bessel, hasDerivativeConcept, Bessel process]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Bessel process
Context triple: [Bessel, hasDerivativeConcept, Bessel process]
  • A. Itô processes
    Itô processes are a class of stochastic processes, typically modeled as solutions to stochastic differential equations, that form the fundamental objects of study in Itô calculus and modern stochastic analysis.
  • B. 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.
  • C. G-Brownian motion
    G-Brownian motion is a generalization of classical Brownian motion developed within the framework of sublinear expectations to model uncertainty in volatility.
  • D. Lévy processes
    Lévy processes are a class of stochastic processes with stationary, independent increments that generalize random walks and Brownian motion, widely used to model jump-like and continuous-time random phenomena in probability theory and finance.
  • E. 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.
  • 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: Bessel process
Triple: [Bessel, hasDerivativeConcept, Bessel process]
Generated description
The Bessel process is a family of stochastic processes describing the radial part of Brownian motion in Euclidean space, widely used in probability theory and mathematical finance.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Bessel process
Target entity description: The Bessel process is a family of stochastic processes describing the radial part of Brownian motion in Euclidean space, widely used in probability theory and mathematical finance.
  • A. Itô processes
    Itô processes are a class of stochastic processes, typically modeled as solutions to stochastic differential equations, that form the fundamental objects of study in Itô calculus and modern stochastic analysis.
  • B. 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.
  • C. G-Brownian motion
    G-Brownian motion is a generalization of classical Brownian motion developed within the framework of sublinear expectations to model uncertainty in volatility.
  • D. Lévy processes
    Lévy processes are a class of stochastic processes with stationary, independent increments that generalize random walks and Brownian motion, widely used to model jump-like and continuous-time random phenomena in probability theory and finance.
  • E. 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.
  • 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_69e245ff8000819090d12008805315b7 completed April 17, 2026, 2:38 p.m.
NER Named-entity recognition batch_69f18f7230208190820acf52f537b3ff completed April 29, 2026, 4:56 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0c30b5db0c8190b59b51b14f9a09b4 completed May 19, 2026, 9:43 a.m.
NEDg Description generation batch_6a0c314598d081908816ff2bee9b192a completed May 19, 2026, 9:45 a.m.
NED2 Entity disambiguation (via description) batch_6a0c3245c9808190ab5212a14aa2e42e completed May 19, 2026, 9:49 a.m.
Created at: April 17, 2026, 4:05 p.m.