Triple
T14168723
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Itô isometry |
E351146
|
entity |
| Predicate | foundationFor |
P1450
|
FINISHED |
| Object | stochastic Fubini theorems |
E284675
|
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: stochastic Fubini theorems | Statement: [Itô isometry, foundationFor, stochastic Fubini theorems]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: stochastic Fubini theorems Context triple: [Itô isometry, foundationFor, stochastic Fubini theorems]
-
A.
Fubini's theorem
chosen
Fubini's theorem is a fundamental result in measure theory that allows the evaluation of double integrals as iterated integrals under suitable integrability conditions.
-
B.
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.
-
C.
Skorokhod integral
The Skorokhod integral is a stochastic integral extending the Itô integral to non-adapted processes, playing a central role in Malliavin calculus and anticipating stochastic analysis.
-
D.
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.
-
E.
Malliavin calculus
Malliavin calculus is a branch of stochastic analysis that extends differential calculus to functionals of stochastic processes, particularly Brownian motion, enabling probabilistic proofs of regularity and smoothness for solutions to stochastic differential equations.
- 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_69fcf7f779248190921c85f99f587296 |
completed | May 7, 2026, 8:37 p.m. |
Created at: April 10, 2026, 1 a.m.