Triple

T2631375
Position Surface form Disambiguated ID Type / Status
Subject Doob–Meyer decomposition E59636 entity
Predicate hasVersion P455 FINISHED
Object discrete-time Doob 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: discrete-time Doob decomposition | Statement: [Doob–Meyer decomposition, hasVersion, discrete-time Doob decomposition]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: discrete-time Doob decomposition
Context triple: [Doob–Meyer decomposition, hasVersion, discrete-time Doob 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. 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).
  • C. 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.
  • 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. Chapman–Kolmogorov equation
    The Chapman–Kolmogorov equation is a fundamental relation in the theory of stochastic processes that expresses how transition probabilities of a Markov process over longer time intervals can be obtained by integrating over intermediate states.
  • 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.