Triple
T7150465
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Milstein method |
E166677
|
entity |
| Predicate | relatedConcept |
P37
|
FINISHED |
| Object |
Itô–Taylor expansion
The Itô–Taylor expansion is a stochastic generalization of the Taylor series that expresses solutions of stochastic differential equations as series involving iterated Itô integrals, forming the basis for higher-order numerical schemes.
|
E645107
|
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: Itô–Taylor expansion | Statement: [Milstein method, relatedConcept, Itô–Taylor expansion]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Itô–Taylor expansion Context triple: [Milstein method, relatedConcept, Itô–Taylor expansion]
-
A.
Itô’s lemma
Itô’s lemma is a fundamental result in stochastic calculus that generalizes the chain rule to functions of stochastic processes, especially Brownian motion.
-
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.
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.
-
D.
Itô calculus
Itô calculus is a branch of stochastic analysis that extends classical calculus to functions of stochastic processes, particularly Brownian motion, enabling rigorous treatment of stochastic differential equations.
-
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: Itô–Taylor expansion Triple: [Milstein method, relatedConcept, Itô–Taylor expansion]
Generated description
The Itô–Taylor expansion is a stochastic generalization of the Taylor series that expresses solutions of stochastic differential equations as series involving iterated Itô integrals, forming the basis for higher-order numerical schemes.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Itô–Taylor expansion Target entity description: The Itô–Taylor expansion is a stochastic generalization of the Taylor series that expresses solutions of stochastic differential equations as series involving iterated Itô integrals, forming the basis for higher-order numerical schemes.
-
A.
Itô’s lemma
Itô’s lemma is a fundamental result in stochastic calculus that generalizes the chain rule to functions of stochastic processes, especially Brownian motion.
-
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.
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.
-
D.
Itô calculus
Itô calculus is a branch of stochastic analysis that extends classical calculus to functions of stochastic processes, particularly Brownian motion, enabling rigorous treatment of stochastic differential equations.
-
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_69c68886779c8190a8e3fbabffe68253 |
completed | March 27, 2026, 1:39 p.m. |
| NER | Named-entity recognition | batch_69c6e7f28b188190b1732ca711666531 |
completed | March 27, 2026, 8:26 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c7ada940e08190b16e97e363801e75 |
completed | March 28, 2026, 10:30 a.m. |
| NEDg | Description generation | batch_69c7ae5767408190860c1c7bc3a769fa |
completed | March 28, 2026, 10:32 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69c7aeb68c3481909c6dff8ee51349ab |
completed | March 28, 2026, 10:34 a.m. |
Created at: March 27, 2026, 2:46 p.m.