Triple

T6735780

Position	Surface form	Disambiguated ID	Type / Status
Subject	Roger W. Brockett	`E153749`	entity
Predicate	notableWork	`P4`	FINISHED
Object	Brockett’s condition for smooth feedback stabilization Brockett’s condition for smooth feedback stabilization is a fundamental result in nonlinear control theory that provides a necessary topological criterion for when a nonlinear system can be stabilized by a smooth state-feedback law.	`E615222`	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: Brockett’s condition for smooth feedback stabilization | Statement: [Roger W. Brockett, notableWork, Brockett’s condition for smooth feedback stabilization]

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Brockett’s condition for smooth feedback stabilization
Context triple: [Roger W. Brockett, notableWork, Brockett’s condition for smooth feedback stabilization]

A. Nonlinear Control Systems
Nonlinear Control Systems is a foundational textbook by Alberto Isidori that systematically develops the theory and design methods for controlling nonlinear dynamical systems.
B. 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.
C. Stability of Linear Systems
"Stability of Linear Systems" is a foundational book by Eliahu I. Jury that systematically develops the theory and criteria for determining the stability of linear dynamical and control systems.
D. Inners and Stability of Dynamic Systems
"Inners and Stability of Dynamic Systems" is a seminal work in control theory by Eliahu I. Jury that analyzes the role of inner functions in determining the stability properties of dynamic systems.
E. Zames–Falb multipliers
Zames–Falb multipliers are a class of frequency-domain operators used in control theory to analyze and guarantee the stability of nonlinear and time-varying feedback systems.
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: Brockett’s condition for smooth feedback stabilization
Triple: [Roger W. Brockett, notableWork, Brockett’s condition for smooth feedback stabilization]

Generated description

Brockett’s condition for smooth feedback stabilization is a fundamental result in nonlinear control theory that provides a necessary topological criterion for when a nonlinear system can be stabilized by a smooth state-feedback law.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Brockett’s condition for smooth feedback stabilization
Target entity description: Brockett’s condition for smooth feedback stabilization is a fundamental result in nonlinear control theory that provides a necessary topological criterion for when a nonlinear system can be stabilized by a smooth state-feedback law.

A. Nonlinear Control Systems
Nonlinear Control Systems is a foundational textbook by Alberto Isidori that systematically develops the theory and design methods for controlling nonlinear dynamical systems.
B. 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.
C. Stability of Linear Systems
"Stability of Linear Systems" is a foundational book by Eliahu I. Jury that systematically develops the theory and criteria for determining the stability of linear dynamical and control systems.
D. Inners and Stability of Dynamic Systems
"Inners and Stability of Dynamic Systems" is a seminal work in control theory by Eliahu I. Jury that analyzes the role of inner functions in determining the stability properties of dynamic systems.
E. Zames–Falb multipliers
Zames–Falb multipliers are a class of frequency-domain operators used in control theory to analyze and guarantee the stability of nonlinear and time-varying feedback systems.
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_69c6880bdd68819097de8b6099992682`	completed	March 27, 2026, 1:37 p.m.
NER	Named-entity recognition	`batch_69c6d18369d88190a73349075462202b`	completed	March 27, 2026, 6:50 p.m.
NED1	Entity disambiguation (via context triple)	`batch_69c70b0703288190906cfcaba9d9c85a`	completed	March 27, 2026, 10:56 p.m.
NEDg	Description generation	`batch_69c70bffe7b48190bbe217bc9fbb08ab`	completed	March 27, 2026, 11 p.m.
NED2	Entity disambiguation (via description)	`batch_69c70c84de7081908d86c6f710410443`	completed	March 27, 2026, 11:02 p.m.

Created at: March 27, 2026, 2:09 p.m.