Triple

T11977899
Position Surface form Disambiguated ID Type / Status
Subject John G. Kemeny E285081 entity
Predicate knownFor P22 FINISHED
Object Kemeny–Snell finite Markov chain theory
Kemeny–Snell finite Markov chain theory is a foundational mathematical framework that rigorously develops the behavior and long-term properties of finite-state Markov chains, widely used in probability theory and stochastic processes.
E957994 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: Kemeny–Snell finite Markov chain theory | Statement: [John G. Kemeny, knownFor, Kemeny–Snell finite Markov chain theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Kemeny–Snell finite Markov chain theory
Context triple: [John G. Kemeny, knownFor, Kemeny–Snell finite Markov chain theory]
  • A. Foundations of a General Theory of Sequential Decision Functions
    Foundations of a General Theory of Sequential Decision Functions is a seminal work in statistics that established the mathematical foundations of sequential analysis and optimal decision-making under uncertainty.
  • B. Modern Probability Theory and Its Applications
    "Modern Probability Theory and Its Applications" is a foundational textbook by Emanuel Parzen that systematically develops modern probability theory and demonstrates its use in a wide range of statistical and applied contexts.
  • C. Pólya’s theorem on random walks
    Pólya’s theorem on random walks is a fundamental result in probability theory stating that simple random walks on one- and two-dimensional lattices are recurrent (almost surely return to the starting point infinitely often), while in three or more dimensions they are transient.
  • D. Pólya’s urn model
    Pólya’s urn model is a classic probabilistic scheme in which drawing and then reinforcing the color of balls in an urn produces rich-get-richer dynamics and illustrates concepts like contagion, dependence, and random reinforcement.
  • E. Introduction to Stochastic Control Theory
    Introduction to Stochastic Control Theory is a foundational textbook that systematically develops the theory and methods for controlling dynamical systems under uncertainty using probabilistic and stochastic-process tools.
  • 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: Kemeny–Snell finite Markov chain theory
Triple: [John G. Kemeny, knownFor, Kemeny–Snell finite Markov chain theory]
Generated description
Kemeny–Snell finite Markov chain theory is a foundational mathematical framework that rigorously develops the behavior and long-term properties of finite-state Markov chains, widely used in probability theory and stochastic processes.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Kemeny–Snell finite Markov chain theory
Target entity description: Kemeny–Snell finite Markov chain theory is a foundational mathematical framework that rigorously develops the behavior and long-term properties of finite-state Markov chains, widely used in probability theory and stochastic processes.
  • A. Foundations of a General Theory of Sequential Decision Functions
    Foundations of a General Theory of Sequential Decision Functions is a seminal work in statistics that established the mathematical foundations of sequential analysis and optimal decision-making under uncertainty.
  • B. Modern Probability Theory and Its Applications
    "Modern Probability Theory and Its Applications" is a foundational textbook by Emanuel Parzen that systematically develops modern probability theory and demonstrates its use in a wide range of statistical and applied contexts.
  • C. Pólya’s theorem on random walks
    Pólya’s theorem on random walks is a fundamental result in probability theory stating that simple random walks on one- and two-dimensional lattices are recurrent (almost surely return to the starting point infinitely often), while in three or more dimensions they are transient.
  • D. Pólya’s urn model
    Pólya’s urn model is a classic probabilistic scheme in which drawing and then reinforcing the color of balls in an urn produces rich-get-richer dynamics and illustrates concepts like contagion, dependence, and random reinforcement.
  • E. Introduction to Stochastic Control Theory
    Introduction to Stochastic Control Theory is a foundational textbook that systematically develops the theory and methods for controlling dynamical systems under uncertainty using probabilistic and stochastic-process tools.
  • 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_69d6ab2eaeb881909f7914758f859413 completed April 8, 2026, 7:23 p.m.
NER Named-entity recognition batch_69d90393cfb08190b5b45d3e5e32fad3 completed April 10, 2026, 2:05 p.m.
NED1 Entity disambiguation (via context triple) batch_69f471f6afc48190856a0f7c486b28aa completed May 1, 2026, 9:27 a.m.
NEDg Description generation batch_69f47b7ac4048190ae09f18f1a90338f completed May 1, 2026, 10:07 a.m.
NED2 Entity disambiguation (via description) batch_69f47db91f38819092b7b5c5e2bb489b completed May 1, 2026, 10:17 a.m.
Created at: April 8, 2026, 9:46 p.m.