Triple

T478567
Position Surface form Disambiguated ID Type / Status
Subject Girsanov theorem E9114 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: [Girsanov theorem, relatedTo, Doob–Meyer decomposition]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Doob–Meyer decomposition
Context triple: [Girsanov theorem, 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. 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. 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).
  • D. Kolmogorov backward equation
    The Kolmogorov backward equation is a fundamental partial differential equation in stochastic processes that characterizes the time evolution of expected values of functionals of Markov processes, complementary to the Fokker–Planck (forward) equation.
  • E. Radon–Nikodym derivative
    The Radon–Nikodym derivative is a function that represents how one measure changes with respect to another absolutely continuous measure, playing a central role in modern probability theory and measure theory.
  • 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_69a2e7ff81708190b0507a24a997232c completed Feb. 28, 2026, 1:05 p.m.
NER Named-entity recognition batch_69a2f056459881909749764cc4a7f9e8 completed Feb. 28, 2026, 1:40 p.m.
NED1 Entity disambiguation (via context triple) batch_69a46c5f07808190aeafebb8e7cd7df9 completed March 1, 2026, 4:42 p.m.
Created at: Feb. 28, 2026, 1:12 p.m.