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.