Triple

T7685071
Position Surface form Disambiguated ID Type / Status
Subject Lev Pontryagin E174094 entity
Predicate notableIdea P4 FINISHED
Object Pontryagin maximum principle in optimal control E681627 NE FINISHED

How this triple was built (2 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: Pontryagin maximum principle in optimal control | Statement: [Lev Pontryagin, notableIdea, Pontryagin maximum principle in optimal control]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Pontryagin maximum principle in optimal control
Context triple: [Lev Pontryagin, notableIdea, Pontryagin maximum principle in optimal control]
  • A. Pontryagin maximum principle chosen
    The Pontryagin maximum principle is a fundamental result in optimal control theory that provides necessary conditions for an optimal control process by characterizing optimal trajectories via a Hamiltonian maximization condition.
  • 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. 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.
  • D. 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.
  • 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.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69c8aca0b5b08190b178f0908612164c completed March 29, 2026, 4:37 a.m.
Created at: March 27, 2026, 4:02 p.m.