Triple

T12146179
Position Surface form Disambiguated ID Type / Status
Subject Peng Shige E289326 entity
Predicate notableConcept P201 FINISHED
Object G-expectation
G-expectation is a nonlinear expectation framework in probability theory that models uncertainty in volatility and leads to the development of G-Brownian motion and related stochastic calculus.
E965112 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: G-expectation | Statement: [Peng Shige, notableConcept, G-expectation]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: G-expectation
Context triple: [Peng Shige, notableConcept, G-expectation]
  • A. Snell envelope
    The Snell envelope is a stochastic process that represents the smallest supermartingale dominating a given process and is fundamental in optimal stopping theory and the valuation of American-style options.
  • B. Clark–Ocone formula
    The Clark–Ocone formula is a key result in stochastic calculus and Malliavin calculus that provides an explicit integral representation of square-integrable random variables with respect to Brownian motion.
  • C. 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.
  • 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. 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.
  • 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: G-expectation
Triple: [Peng Shige, notableConcept, G-expectation]
Generated description
G-expectation is a nonlinear expectation framework in probability theory that models uncertainty in volatility and leads to the development of G-Brownian motion and related stochastic calculus.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: G-expectation
Target entity description: G-expectation is a nonlinear expectation framework in probability theory that models uncertainty in volatility and leads to the development of G-Brownian motion and related stochastic calculus.
  • A. Snell envelope
    The Snell envelope is a stochastic process that represents the smallest supermartingale dominating a given process and is fundamental in optimal stopping theory and the valuation of American-style options.
  • B. Clark–Ocone formula
    The Clark–Ocone formula is a key result in stochastic calculus and Malliavin calculus that provides an explicit integral representation of square-integrable random variables with respect to Brownian motion.
  • C. 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.
  • 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. 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.
  • 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_69d6ab4c6710819097a9d228382dde43 completed April 8, 2026, 7:23 p.m.
NER Named-entity recognition batch_69d915ac2ebc81909155f9b2fb4a2252 completed April 10, 2026, 3:22 p.m.
NED1 Entity disambiguation (via context triple) batch_69f5f696ec648190aa43655ac8a2b312 completed May 2, 2026, 1:05 p.m.
NEDg Description generation batch_69f600b7385881909ddb86a1d39ff5d4 completed May 2, 2026, 1:48 p.m.
NED2 Entity disambiguation (via description) batch_69f601e7f3b0819098a2245b9f9316b9 completed May 2, 2026, 1:53 p.m.
Created at: April 8, 2026, 9:49 p.m.