Triple
T2631371
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Doob–Meyer decomposition |
E59636
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Girsanov theorem |
E9114
|
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: Girsanov theorem | Statement: [Doob–Meyer decomposition, relatedTo, Girsanov theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Girsanov theorem Context triple: [Doob–Meyer decomposition, relatedTo, Girsanov theorem]
-
A.
Girsanov theorem
chosen
Girsanov theorem is a fundamental result in stochastic calculus that describes how the dynamics of stochastic processes, particularly Brownian motion, change under an equivalent change of probability measure.
-
B.
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.
-
C.
Cameron–Martin theorem
The Cameron–Martin theorem is a fundamental result in probability theory and functional analysis that characterizes how Gaussian measures on infinite-dimensional spaces change under shifts by elements of a special Hilbert subspace (the Cameron–Martin space).
-
D.
martingale representation theorem
The martingale representation theorem is a fundamental result in stochastic calculus stating that, under suitable conditions, every martingale can be expressed as a stochastic integral with respect to a Brownian motion (or more generally, a fundamental martingale).
-
E.
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.
- 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_69ab4ac8596c8190b34997e73d9e991c |
completed | March 6, 2026, 9:44 p.m. |
| NER | Named-entity recognition | batch_69abd8c6e540819087c7f92432b27b0f |
completed | March 7, 2026, 7:50 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69af90a7021081909f81c4ddb48fa00c |
completed | March 10, 2026, 3:31 a.m. |
Created at: March 6, 2026, 9:50 p.m.