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.