Triple
T14168680
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Itô integral |
E351145
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Doob–Meyer decomposition |
E59636
|
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: Doob–Meyer decomposition | Statement: [Itô integral, relatedTo, Doob–Meyer decomposition]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Doob–Meyer decomposition Context triple: [Itô integral, relatedTo, Doob–Meyer decomposition]
-
A.
Doob–Meyer decomposition
chosen
The Doob–Meyer decomposition is a fundamental result in stochastic process theory that uniquely expresses a submartingale as the sum of a martingale and a predictable, increasing process.
-
B.
Lévy–Itô decomposition
The Lévy–Itô decomposition is a fundamental result in probability theory that expresses any Lévy process as the sum of a Brownian motion with drift and a jump process constructed from a Poisson random measure.
-
C.
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.
-
D.
Doob’s h-transform
Doob’s h-transform is a probabilistic technique that conditions Markov processes on future behavior by reweighting paths with a harmonic function, yielding a new process with modified transition dynamics.
-
E.
Snell envelope
The Snell envelope is a stochastic process that represents the smallest supermartingale dominating a given process and is fundamental in optimal stopping theory and the valuation of American-style options.
- 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_69de61b355f08190864c7322bbcb766d |
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.