Triple

T2646020
Position Surface form Disambiguated ID Type / Status
Subject Karl J. Åström E62984 entity
Predicate notableWork P4 FINISHED
Object 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.
E285086 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: Introduction to Stochastic Control Theory | Statement: [Karl J. Åström, notableWork, Introduction to Stochastic Control Theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Introduction to Stochastic Control Theory
Context triple: [Karl J. Åström, notableWork, Introduction to Stochastic Control 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. Hamilton’s maximum principle
    Hamilton’s maximum principle is a fundamental analytical tool in geometric analysis that extends the classical maximum principle to tensor-valued quantities, playing a key role in studying the behavior of solutions to the Ricci flow and related geometric evolution equations.
  • C. Lyapunov stability theory
    Lyapunov stability theory is a fundamental framework in dynamical systems and control theory that uses energy-like functions to assess the stability of equilibrium points without explicitly solving differential equations.
  • D. 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.
  • E. 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.
  • 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: Introduction to Stochastic Control Theory
Triple: [Karl J. Åström, notableWork, Introduction to Stochastic Control Theory]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Introduction to Stochastic Control Theory
Target entity description: 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.
  • 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. Hamilton’s maximum principle
    Hamilton’s maximum principle is a fundamental analytical tool in geometric analysis that extends the classical maximum principle to tensor-valued quantities, playing a key role in studying the behavior of solutions to the Ricci flow and related geometric evolution equations.
  • C. Lyapunov stability theory
    Lyapunov stability theory is a fundamental framework in dynamical systems and control theory that uses energy-like functions to assess the stability of equilibrium points without explicitly solving differential equations.
  • D. 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.
  • E. 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.
  • 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_69ab4c3f2dcc819082df80f5e032f690 completed March 6, 2026, 9:50 p.m.
NER Named-entity recognition batch_69abd91846b4819093a063c15e1ee6af completed March 7, 2026, 7:51 a.m.
NED1 Entity disambiguation (via context triple) batch_69af98c721b08190b380d3625126cb55 completed March 10, 2026, 4:06 a.m.
NEDg Description generation batch_69af996e93f08190ac4b8faa64fb0550 completed March 10, 2026, 4:09 a.m.
NED2 Entity disambiguation (via description) batch_69af99d58744819098633b2b51f7943e completed March 10, 2026, 4:11 a.m.
Created at: March 6, 2026, 9:53 p.m.