Triple

T8119326
Position Surface form Disambiguated ID Type / Status
Subject Routh–Hurwitz stability criterion E189565 entity
Predicate characterizes P662 FINISHED
Object Hurwitz polynomials E189565 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: Hurwitz polynomials | Statement: [Routh–Hurwitz stability criterion, characterizes, Hurwitz polynomials]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Hurwitz polynomials
Context triple: [Routh–Hurwitz stability criterion, characterizes, Hurwitz polynomials]
  • A. Hermite–Biehler theorem
    The Hermite–Biehler theorem is a result in complex analysis and control theory that characterizes when a complex polynomial has all its zeros in the open upper half-plane in terms of the interlacing of zeros of two associated real polynomials.
  • B. 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.
  • C. Hurwitz theorem
    Hurwitz theorem is a fundamental result in Diophantine approximation that gives an optimal bound on how well any irrational real number can be approximated by infinitely many rational numbers.
  • D. Carathéodory–Fejér interpolation
    Carathéodory–Fejér interpolation is a classical result in complex analysis and approximation theory that concerns constructing analytic functions, typically with bounded or positive real part, that match prescribed initial Taylor coefficients.
  • E. Symanzik polynomials
    Symanzik polynomials are graph-based polynomials that arise in the parametric representation of Feynman integrals in quantum field theory, encoding the topology and kinematic dependence of Feynman diagrams.
  • 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_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.
Created at: March 30, 2026, 5:33 p.m.