Triple

T12282684
Position Surface form Disambiguated ID Type / Status
Subject Malliavin calculus E292751 entity
Predicate keyConcept P531 FINISHED
Object Clark–Ocone formula E284688 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: Clark–Ocone formula | Statement: [Malliavin calculus, keyConcept, Clark–Ocone formula]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Clark–Ocone formula
Context triple: [Malliavin calculus, keyConcept, Clark–Ocone formula]
  • A. Clark–Ocone formula chosen
    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.
  • 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. Doob–Meyer decomposition
    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.
  • D. 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.
  • E. Dynkin formula
    Dynkin formula is a fundamental result in the theory of Markov processes that expresses the expected value of a function of the process at a stopping time in terms of its generator and an integral over time.
  • 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.