Triple
T14168722
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Itô isometry |
E351146
|
entity |
| Predicate | foundationFor |
P1450
|
FINISHED |
| Object | Itô’s lemma |
E59984
|
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’s lemma | Statement: [Itô isometry, foundationFor, Itô’s lemma]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Itô’s lemma Context triple: [Itô isometry, foundationFor, Itô’s lemma]
-
A.
Itô’s lemma
chosen
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 integral
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.
-
D.
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.
-
E.
Itô–Stratonovich conversion formula
The Itô–Stratonovich conversion formula is a key result in stochastic calculus that provides the explicit relationship for transforming stochastic integrals between the Itô and Stratonovich interpretations.
- 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_69d8278775fc8190b0802d22ca2f495d |
completed | April 9, 2026, 10:26 p.m. |
| NER | Named-entity recognition | batch_69de61b472288190b4a271daa54aa6cd |
completed | April 14, 2026, 3:48 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69fd193dbbcc819082043d92c174164c |
completed | May 7, 2026, 10:59 p.m. |
Created at: April 10, 2026, 1 a.m.