Triple
T12282711
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Malliavin calculus |
E292751
|
entity |
| Predicate | hasOperator |
P179
|
FINISHED |
| Object | Ornstein–Uhlenbeck operator |
E48273
|
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: Ornstein–Uhlenbeck operator | Statement: [Malliavin calculus, hasOperator, Ornstein–Uhlenbeck operator]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Ornstein–Uhlenbeck operator Context triple: [Malliavin calculus, hasOperator, Ornstein–Uhlenbeck operator]
-
A.
Ornstein–Uhlenbeck process
chosen
The Ornstein–Uhlenbeck process is a continuous-time stochastic process that models mean-reverting random motion, widely used in physics and quantitative finance to describe systems fluctuating around a long-term equilibrium.
-
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.
Hilbert–Schmidt operators
Hilbert–Schmidt operators are a class of compact operators on Hilbert spaces characterized by having finite Hilbert–Schmidt norm, playing a central role in functional analysis and operator theory.
-
D.
Steklov operator
The Steklov operator is a boundary integral operator arising in the study of elliptic partial differential equations and spectral problems, particularly in the context of Steklov eigenvalue problems.
-
E.
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.
- 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_69d6ab690ad081908c0ed3870ec82d53 |
completed | April 8, 2026, 7:24 p.m. |
| NER | Named-entity recognition | batch_69d91cf2b09c81908a11581d33f65be0 |
completed | April 10, 2026, 3:53 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f61e70dec8819098199fbb54d888c1 |
completed | May 2, 2026, 3:55 p.m. |
Created at: April 8, 2026, 9:52 p.m.