Triple

T100607
Position Surface form Disambiguated ID Type / Status
Subject Feynman–Kac formula E2031 entity
Predicate relatedTo P37 FINISHED
Object 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.
E9114 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: Girsanov theorem | Statement: [Feynman–Kac formula, relatedTo, Girsanov theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Girsanov theorem
Context triple: [Feynman–Kac formula, relatedTo, Girsanov theorem]
  • 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. Fokker–Planck equation
    The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
  • C. Feynman–Hellmann theorem
    The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
  • D. Einstein–Smoluchowski relation
    The Einstein–Smoluchowski relation is a fundamental equation in statistical physics that links the diffusion coefficient of particles undergoing Brownian motion to their mobility and thermal energy.
  • E. Brownian motion
    Brownian motion is the random, jittery movement of microscopic particles suspended in a fluid, whose explanation provided key evidence for the existence of atoms and the molecular nature of matter.
  • 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: Girsanov theorem
Triple: [Feynman–Kac formula, relatedTo, Girsanov theorem]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Girsanov theorem
Target entity description: 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.
  • 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. Fokker–Planck equation
    The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
  • C. Feynman–Hellmann theorem
    The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
  • D. Einstein–Smoluchowski relation
    The Einstein–Smoluchowski relation is a fundamental equation in statistical physics that links the diffusion coefficient of particles undergoing Brownian motion to their mobility and thermal energy.
  • E. Brownian motion
    Brownian motion is the random, jittery movement of microscopic particles suspended in a fluid, whose explanation provided key evidence for the existence of atoms and the molecular nature of matter.
  • 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_69a24d4862f881908cc8b89d3a78031d completed Feb. 28, 2026, 2:04 a.m.
NER Named-entity recognition batch_69a24ff1a8cc8190843d4c6807cebd09 completed Feb. 28, 2026, 2:16 a.m.
NED1 Entity disambiguation (via context triple) batch_69a266ee56548190a781e2d0ea7fac2b completed Feb. 28, 2026, 3:54 a.m.
NEDg Description generation batch_69a2678d1b808190aa9e6451d7945f58 completed Feb. 28, 2026, 3:57 a.m.
NED2 Entity disambiguation (via description) batch_69a26853ed9881909e55192266bfd0b4 completed Feb. 28, 2026, 4 a.m.
Created at: Feb. 28, 2026, 2:09 a.m.