Triple

T79809
Position Surface form Disambiguated ID Type / Status
Subject Brownian motion E1601 entity
Predicate usedIn P98 FINISHED
Object 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.
E4990 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: Einstein–Smoluchowski relation | Statement: [Brownian motion, usedIn, Einstein–Smoluchowski relation]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Einstein–Smoluchowski relation
Context triple: [Brownian motion, usedIn, Einstein–Smoluchowski relation]
  • A. 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.
  • B. On the Motion of Small Particles Suspended in Liquids at Rest Required by the Molecular-Kinetic Theory of Heat
    "On the Motion of Small Particles Suspended in Liquids at Rest Required by the Molecular-Kinetic Theory of Heat" is Albert Einstein’s 1905 paper that provided a theoretical explanation of Brownian motion, offering strong evidence for the existence of atoms and molecules.
  • C. 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.
  • D. 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.
  • E. Einstein coefficients
    Einstein coefficients are parameters in quantum theory that quantify the probabilities of absorption, spontaneous emission, and stimulated emission of radiation by atoms or molecules.
  • 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: Einstein–Smoluchowski relation
Triple: [Brownian motion, usedIn, Einstein–Smoluchowski relation]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Einstein–Smoluchowski relation
Target entity description: 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.
  • A. 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.
  • B. On the Motion of Small Particles Suspended in Liquids at Rest Required by the Molecular-Kinetic Theory of Heat
    "On the Motion of Small Particles Suspended in Liquids at Rest Required by the Molecular-Kinetic Theory of Heat" is Albert Einstein’s 1905 paper that provided a theoretical explanation of Brownian motion, offering strong evidence for the existence of atoms and molecules.
  • C. 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.
  • D. 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.
  • E. Einstein coefficients
    Einstein coefficients are parameters in quantum theory that quantify the probabilities of absorption, spontaneous emission, and stimulated emission of radiation by atoms or molecules.
  • 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_69a24c60d19c8190a1b6c105ca59ef5b completed Feb. 28, 2026, 2:01 a.m.
NER Named-entity recognition batch_69a24f335b5c8190bf2158d884890ac2 completed Feb. 28, 2026, 2:13 a.m.
NED1 Entity disambiguation (via context triple) batch_69a255522b0081909f8a02667108a6d3 completed Feb. 28, 2026, 2:39 a.m.
NEDg Description generation batch_69a255ef9b1081909fe71530250bd68b completed Feb. 28, 2026, 2:41 a.m.
NED2 Entity disambiguation (via description) batch_69a256c673748190abb6b556701b4a2a completed Feb. 28, 2026, 2:45 a.m.
Created at: Feb. 28, 2026, 2:06 a.m.