Triple

T12702500
Position Surface form Disambiguated ID Type / Status
Subject Dynamic Noncooperative Game Theory E303496 entity
Predicate subject P450 FINISHED
Object Pontryagin maximum principle 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 | Statement: [Dynamic Noncooperative Game Theory, subject, Pontryagin maximum principle]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Pontryagin maximum principle
Context triple: [Dynamic Noncooperative Game Theory, subject, Pontryagin maximum principle]
  • 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. Hamilton–Jacobi equation
    The Hamilton–Jacobi equation is a fundamental partial differential equation in classical mechanics that reformulates dynamics in terms of a generating function, providing a powerful bridge to quantum mechanics and modern analytical methods.
  • 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_69d7bdef90d48190b46b88270e780946 completed April 9, 2026, 2:55 p.m.
NER Named-entity recognition batch_69d961f0941081908a879cde0be48667 completed April 10, 2026, 8:47 p.m.
NED1 Entity disambiguation (via context triple) batch_69f671b4832c8190abc17f5f33b3552a completed May 2, 2026, 9:50 p.m.
Created at: April 9, 2026, 5:22 p.m.