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.