Triple
T11961931
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Clark–Ocone formula |
E284688
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Itô integral |
E351145
|
NE FINISHED |
How this triple was built (2 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 integral | Statement: [Clark–Ocone formula, relatedTo, Itô integral]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Itô integral Context triple: [Clark–Ocone formula, relatedTo, Itô integral]
-
A.
Itô integral
chosen
The Itô integral is a fundamental stochastic integral used in probability theory and mathematical finance to rigorously define integration with respect to Brownian motion and more general semimartingales.
-
B.
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.
-
C.
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.
-
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.
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.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (3 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_69d6ab2eaeb881909f7914758f859413 |
completed | April 8, 2026, 7:23 p.m. |
| NER | Named-entity recognition | batch_69d9037848f481908276716675464464 |
completed | April 10, 2026, 2:04 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f4592fa9a48190a0450e3d0c57c4d3 |
completed | May 1, 2026, 7:41 a.m. |
Created at: April 8, 2026, 9:45 p.m.