Triple

T412551
Position Surface form Disambiguated ID Type / Status
Subject Marian Smoluchowski E9520 entity
Predicate knownFor P22 FINISHED
Object Smoluchowski coagulation equation
The Smoluchowski coagulation equation is a fundamental integro-differential equation in statistical physics that models how particles undergoing random collisions aggregate over time into larger clusters.
E52850 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: Smoluchowski coagulation equation | Statement: [Marian Smoluchowski, knownFor, Smoluchowski coagulation equation]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Smoluchowski coagulation equation
Context triple: [Marian Smoluchowski, knownFor, Smoluchowski coagulation equation]
  • A. 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.
  • 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. Stokes–Einstein relation
    The Stokes–Einstein relation is a fundamental equation in statistical physics that links the diffusion coefficient of a particle in a fluid to its size, the fluid’s viscosity, and temperature.
  • D. Boltzmann equation
    The Boltzmann equation is a fundamental kinetic theory equation that describes the statistical behavior and time evolution of a dilute gas or particle distribution in phase space due to streaming and collisions.
  • 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: Smoluchowski coagulation equation
Triple: [Marian Smoluchowski, knownFor, Smoluchowski coagulation equation]
Generated description
The Smoluchowski coagulation equation is a fundamental integro-differential equation in statistical physics that models how particles undergoing random collisions aggregate over time into larger clusters.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Smoluchowski coagulation equation
Target entity description: The Smoluchowski coagulation equation is a fundamental integro-differential equation in statistical physics that models how particles undergoing random collisions aggregate over time into larger clusters.
  • A. 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.
  • 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. Stokes–Einstein relation
    The Stokes–Einstein relation is a fundamental equation in statistical physics that links the diffusion coefficient of a particle in a fluid to its size, the fluid’s viscosity, and temperature.
  • D. Boltzmann equation
    The Boltzmann equation is a fundamental kinetic theory equation that describes the statistical behavior and time evolution of a dilute gas or particle distribution in phase space due to streaming and collisions.
  • 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_69a2e80111fc8190961d5b7c6154123f completed Feb. 28, 2026, 1:05 p.m.
NER Named-entity recognition batch_69a2ecdafa2481908111accc918ff2e8 completed Feb. 28, 2026, 1:25 p.m.
NED1 Entity disambiguation (via context triple) batch_69a423a152b0819099cfb9dd799ce755 completed March 1, 2026, 11:31 a.m.
NEDg Description generation batch_69a423fc21188190bacc03bfae9ac401 completed March 1, 2026, 11:33 a.m.
NED2 Entity disambiguation (via description) batch_69a42486e1e08190b7603c34d625da7c completed March 1, 2026, 11:35 a.m.
Created at: Feb. 28, 2026, 1:09 p.m.