Triple

T478545
Position Surface form Disambiguated ID Type / Status
Subject Girsanov theorem E9114 entity
Predicate coreConcept P533 FINISHED
Object 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.
E59639 NE FINISHED

How this triple was built (4 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: Radon–Nikodym derivative | Statement: [Girsanov theorem, coreConcept, Radon–Nikodym derivative]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Radon–Nikodym derivative
Context triple: [Girsanov theorem, coreConcept, Radon–Nikodym derivative]
  • A. 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.
  • B. Girsanov theorem
    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.
  • C. 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.
  • D. Riemann–Liouville integral
    The Riemann–Liouville integral is a fundamental operator in fractional calculus that generalizes the concept of an n-fold repeated integral to non-integer (fractional) orders.
  • E. Rényi divergence
    Rényi divergence is a family of information-theoretic measures that generalize Kullback–Leibler divergence to quantify the dissimilarity between probability distributions, parameterized by an order α.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Radon–Nikodym derivative
Triple: [Girsanov theorem, coreConcept, Radon–Nikodym derivative]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Radon–Nikodym derivative
Target entity description: 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.
  • A. 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.
  • B. Girsanov theorem
    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.
  • C. 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.
  • D. Riemann–Liouville integral
    The Riemann–Liouville integral is a fundamental operator in fractional calculus that generalizes the concept of an n-fold repeated integral to non-integer (fractional) orders.
  • E. Rényi divergence
    Rényi divergence is a family of information-theoretic measures that generalize Kullback–Leibler divergence to quantify the dissimilarity between probability distributions, parameterized by an order α.
  • F. None of above. chosen

Provenance (5 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_69a46804b90881908422851eeb9bbba1 completed March 1, 2026, 4:23 p.m.
NEDg Description generation batch_69a46901d5c08190af7ea8b01206505c completed March 1, 2026, 4:27 p.m.
NED2 Entity disambiguation (via description) batch_69a4696c35c08190890e8159983e2efb completed March 1, 2026, 4:29 p.m.
Created at: Feb. 28, 2026, 1:12 p.m.