Triple
T3365583
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Kiyoshi Itô |
E70827
|
entity |
| Predicate | knownFor |
P22
|
FINISHED |
| Object |
Itô isometry
Itô isometry is a fundamental result in stochastic calculus that relates the L² norm of a stochastic integral with respect to Brownian motion to the L² norm of its integrand, enabling rigorous analysis of stochastic processes.
|
E351146
|
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 isometry | Statement: [Kiyoshi Itô, knownFor, Itô isometry]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Itô isometry Context triple: [Kiyoshi Itô, knownFor, Itô isometry]
-
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.
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.
-
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.
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.
-
E.
Stratonovich integral
The Stratonovich integral is a formulation of stochastic integration that preserves the classical chain rule of calculus and is widely used in physics and engineering for modeling systems with noise.
- 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 isometry Triple: [Kiyoshi Itô, knownFor, Itô isometry]
Generated description
Itô isometry is a fundamental result in stochastic calculus that relates the L² norm of a stochastic integral with respect to Brownian motion to the L² norm of its integrand, enabling rigorous analysis of stochastic processes.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Itô isometry Target entity description: Itô isometry is a fundamental result in stochastic calculus that relates the L² norm of a stochastic integral with respect to Brownian motion to the L² norm of its integrand, enabling rigorous analysis of stochastic processes.
-
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.
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.
-
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.
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.
-
E.
Stratonovich integral
The Stratonovich integral is a formulation of stochastic integration that preserves the classical chain rule of calculus and is widely used in physics and engineering for modeling systems with noise.
- 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_69ad85a729d48190afd789cd8417f289 |
completed | March 8, 2026, 2:20 p.m. |
| NER | Named-entity recognition | batch_69adb28643f48190b78b0222f8323344 |
completed | March 8, 2026, 5:31 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69b3254daf8c8190b2141682503c111e |
completed | March 12, 2026, 8:42 p.m. |
| NEDg | Description generation | batch_69b326f94db481908560b64f701dd433 |
completed | March 12, 2026, 8:50 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69b3276b55a0819094face2e56001921 |
completed | March 12, 2026, 8:51 p.m. |
Created at: March 8, 2026, 3:13 p.m.