Triple

T8119294
Position Surface form Disambiguated ID Type / Status
Subject Routh–Hurwitz stability criterion E189565 entity
Predicate uses P98 FINISHED
Object Routh array
The Routh array is a tabular method used in control theory to determine the stability of a linear time-invariant system by examining the locations of its characteristic polynomial roots.
E189565 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: Routh array | Statement: [Routh–Hurwitz stability criterion, uses, Routh array]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Routh array
Context triple: [Routh–Hurwitz stability criterion, uses, Routh array]
  • A. Routh–Hurwitz stability criterion
    The Routh–Hurwitz stability criterion is a mathematical test in control theory that determines whether all roots of a system’s characteristic polynomial lie in the left half of the complex plane, ensuring system stability without explicitly computing the roots.
  • B. Nyquist stability criterion
    The Nyquist stability criterion is a graphical frequency-domain method in control theory used to determine the stability of feedback systems by analyzing how their open-loop transfer function encircles a critical point in the complex plane.
  • C. Bode plot
    A Bode plot is a graphical representation of a linear system’s frequency response, showing magnitude and phase versus frequency on logarithmic scales, widely used in control and amplifier design.
  • D. Nichols chart
    A Nichols chart is a graphical design tool used in control engineering to analyze and shape the closed-loop frequency response by plotting open-loop gain versus phase on contour maps of constant closed-loop magnitude.
  • E. Sylvester matrix
    The Sylvester matrix is a structured matrix constructed from the coefficients of two polynomials, commonly used to compute their resultant and study common roots in algebra.
  • 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: Routh array
Triple: [Routh–Hurwitz stability criterion, uses, Routh array]
Generated description
The Routh array is a tabular method used in control theory to determine the stability of a linear time-invariant system by examining the locations of its characteristic polynomial roots.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Routh array
Target entity description: The Routh array is a tabular method used in control theory to determine the stability of a linear time-invariant system by examining the locations of its characteristic polynomial roots.
  • A. Routh–Hurwitz stability criterion chosen
    The Routh–Hurwitz stability criterion is a mathematical test in control theory that determines whether all roots of a system’s characteristic polynomial lie in the left half of the complex plane, ensuring system stability without explicitly computing the roots.
  • B. Nyquist stability criterion
    The Nyquist stability criterion is a graphical frequency-domain method in control theory used to determine the stability of feedback systems by analyzing how their open-loop transfer function encircles a critical point in the complex plane.
  • C. Bode plot
    A Bode plot is a graphical representation of a linear system’s frequency response, showing magnitude and phase versus frequency on logarithmic scales, widely used in control and amplifier design.
  • D. Nichols chart
    A Nichols chart is a graphical design tool used in control engineering to analyze and shape the closed-loop frequency response by plotting open-loop gain versus phase on contour maps of constant closed-loop magnitude.
  • E. Sylvester matrix
    The Sylvester matrix is a structured matrix constructed from the coefficients of two polynomials, commonly used to compute their resultant and study common roots in algebra.
  • F. None of above.

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_69ca82baad008190ab2859712b9b1607 completed March 30, 2026, 2:03 p.m.
NER Named-entity recognition batch_69cb4358e1688190940b98114225113b completed March 31, 2026, 3:45 a.m.
NED1 Entity disambiguation (via context triple) batch_69cc944d009c81908ceb37b6922efb59 completed April 1, 2026, 3:43 a.m.
NEDg Description generation batch_69cc96f2220881909d752d4088bd375a completed April 1, 2026, 3:54 a.m.
NED2 Entity disambiguation (via description) batch_69cca843fbc0819098d1841fcef25eaa completed April 1, 2026, 5:08 a.m.
Created at: March 30, 2026, 5:33 p.m.