Triple

T7685050
Position Surface form Disambiguated ID Type / Status
Subject Lev Pontryagin E174094 entity
Predicate notableWork P4 FINISHED
Object Mathematical Theory of Optimal Processes
Mathematical Theory of Optimal Processes is a foundational work in control theory that systematically develops the mathematical principles of optimal control, including what is now known as Pontryagin’s maximum principle.
E681631 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: Mathematical Theory of Optimal Processes | Statement: [Lev Pontryagin, notableWork, Mathematical Theory of Optimal Processes]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Mathematical Theory of Optimal Processes
Context triple: [Lev Pontryagin, notableWork, Mathematical Theory of Optimal Processes]
  • A. 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.
  • 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. 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.
  • D. Theory of Linear Operations
    Theory of Linear Operations is a foundational 1932 monograph by Stefan Banach that systematically developed functional analysis and the theory of Banach spaces.
  • E. 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.
  • 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: Mathematical Theory of Optimal Processes
Triple: [Lev Pontryagin, notableWork, Mathematical Theory of Optimal Processes]
Generated description
Mathematical Theory of Optimal Processes is a foundational work in control theory that systematically develops the mathematical principles of optimal control, including what is now known as Pontryagin’s maximum principle.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Mathematical Theory of Optimal Processes
Target entity description: Mathematical Theory of Optimal Processes is a foundational work in control theory that systematically develops the mathematical principles of optimal control, including what is now known as Pontryagin’s maximum principle.
  • A. 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.
  • 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. 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.
  • D. Theory of Linear Operations
    Theory of Linear Operations is a foundational 1932 monograph by Stefan Banach that systematically developed functional analysis and the theory of Banach spaces.
  • E. 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.
  • 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_69c6995840408190a19de6c51090f46f completed March 27, 2026, 2:51 p.m.
NER Named-entity recognition batch_69c7022118908190a3a93cfda79be0a4 completed March 27, 2026, 10:18 p.m.
NED1 Entity disambiguation (via context triple) batch_69c8a25c2a308190908ffdd2f0b7262f completed March 29, 2026, 3:54 a.m.
NEDg Description generation batch_69c8a37c995881908c71791c6cc002f3 completed March 29, 2026, 3:58 a.m.
NED2 Entity disambiguation (via description) batch_69c8a3fe63a4819086bcb5f80cdbd30b completed March 29, 2026, 4:01 a.m.
Created at: March 27, 2026, 4:02 p.m.