Triple

T787817
Position Surface form Disambiguated ID Type / Status
Subject Mark Kac E16842 entity
Predicate hasPublication P80 FINISHED
Object Random Walk and the Theory of Brownian Motion
"Random Walk and the Theory of Brownian Motion" is a mathematical work by Mark Kac that rigorously develops the connection between discrete random walks and continuous Brownian motion within probability theory.
E92913 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: Random Walk and the Theory of Brownian Motion | Statement: [Mark Kac, hasPublication, Random Walk and the Theory of Brownian Motion]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Random Walk and the Theory of Brownian Motion
Context triple: [Mark Kac, hasPublication, Random Walk and the Theory of Brownian Motion]
  • 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. Illustrations of the Dynamical Theory of Gases
    Illustrations of the Dynamical Theory of Gases is a foundational 1860 scientific paper by James Clerk Maxwell that introduced key ideas of kinetic theory and the statistical behavior of gas molecules.
  • 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. On a Heuristic Point of View Concerning the Production and Transformation of Light
    "On a Heuristic Point of View Concerning the Production and Transformation of Light" is Albert Einstein’s 1905 paper that introduced the concept of light quanta (photons), laying the foundation for quantum theory and explaining the photoelectric effect.
  • 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: Random Walk and the Theory of Brownian Motion
Triple: [Mark Kac, hasPublication, Random Walk and the Theory of Brownian Motion]
Generated description
"Random Walk and the Theory of Brownian Motion" is a mathematical work by Mark Kac that rigorously develops the connection between discrete random walks and continuous Brownian motion within probability theory.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Random Walk and the Theory of Brownian Motion
Target entity description: "Random Walk and the Theory of Brownian Motion" is a mathematical work by Mark Kac that rigorously develops the connection between discrete random walks and continuous Brownian motion within probability theory.
  • 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. Illustrations of the Dynamical Theory of Gases
    Illustrations of the Dynamical Theory of Gases is a foundational 1860 scientific paper by James Clerk Maxwell that introduced key ideas of kinetic theory and the statistical behavior of gas molecules.
  • 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. On a Heuristic Point of View Concerning the Production and Transformation of Light
    "On a Heuristic Point of View Concerning the Production and Transformation of Light" is Albert Einstein’s 1905 paper that introduced the concept of light quanta (photons), laying the foundation for quantum theory and explaining the photoelectric effect.
  • 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_69a4936cb7448190914f5fe4b8d81607 completed March 1, 2026, 7:28 p.m.
NER Named-entity recognition batch_69a4a78171908190a38a70274bfbebf9 completed March 1, 2026, 8:54 p.m.
NED1 Entity disambiguation (via context triple) batch_69a6733e47148190bad0ac71cf45dd85 completed March 3, 2026, 5:35 a.m.
NEDg Description generation batch_69a673afbd308190863aea2ff0f650cb completed March 3, 2026, 5:37 a.m.
NED2 Entity disambiguation (via description) batch_69a6743f50d0819089885836b9668466 completed March 3, 2026, 5:40 a.m.
Created at: March 1, 2026, 7:38 p.m.