Triple

T10991191
Position Surface form Disambiguated ID Type / Status
Subject random matrix theory E259756 entity
Predicate hasKeyConcept P533 FINISHED
Object Dyson Brownian motion
Dyson Brownian motion is a stochastic process describing the time evolution of eigenvalues of random matrices as if they were interacting particles undergoing Brownian motion, fundamental in random matrix theory.
E898465 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: Dyson Brownian motion | Statement: [random matrix theory, hasKeyConcept, Dyson Brownian motion]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Dyson Brownian motion
Context triple: [random matrix theory, hasKeyConcept, Dyson Brownian motion]
  • A. Dyson’s formula
    Dyson’s formula is a key expression in quantum field theory that provides the perturbative expansion of time-ordered exponentials, forming the basis of the Dyson series used to compute interaction effects.
  • B. 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.
  • C. 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.
  • D. Freidlin–Wentzell theory
    Freidlin–Wentzell theory is a mathematical framework in probability that analyzes the behavior of stochastic dynamical systems under small random perturbations using large deviation principles.
  • E. Boltzmann–Kac equation
    The Boltzmann–Kac equation is a kinetic equation in statistical mechanics that models the evolution of the velocity distribution of particles in a gas, providing a probabilistic framework related to the classical Boltzmann equation.
  • 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: Dyson Brownian motion
Triple: [random matrix theory, hasKeyConcept, Dyson Brownian motion]
Generated description
Dyson Brownian motion is a stochastic process describing the time evolution of eigenvalues of random matrices as if they were interacting particles undergoing Brownian motion, fundamental in random matrix theory.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Dyson Brownian motion
Target entity description: Dyson Brownian motion is a stochastic process describing the time evolution of eigenvalues of random matrices as if they were interacting particles undergoing Brownian motion, fundamental in random matrix theory.
  • A. Dyson’s formula
    Dyson’s formula is a key expression in quantum field theory that provides the perturbative expansion of time-ordered exponentials, forming the basis of the Dyson series used to compute interaction effects.
  • B. 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.
  • C. 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.
  • D. Freidlin–Wentzell theory
    Freidlin–Wentzell theory is a mathematical framework in probability that analyzes the behavior of stochastic dynamical systems under small random perturbations using large deviation principles.
  • E. Boltzmann–Kac equation
    The Boltzmann–Kac equation is a kinetic equation in statistical mechanics that models the evolution of the velocity distribution of particles in a gas, providing a probabilistic framework related to the classical Boltzmann equation.
  • 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_69d6aa8a6a548190a750f944ccdc8064 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d787b8d7088190b7d6b63c3bac4ad1 completed April 9, 2026, 11:04 a.m.
NED1 Entity disambiguation (via context triple) batch_69e34504ebec8190a78e4795765b0c24 completed April 18, 2026, 8:47 a.m.
NEDg Description generation batch_69e3556fd3548190a33f04604be947cf completed April 18, 2026, 9:57 a.m.
NED2 Entity disambiguation (via description) batch_69e3593b0f8481909ed7a90f8bb9839d completed April 18, 2026, 10:13 a.m.
Created at: April 8, 2026, 9:24 p.m.