Triple

T9843480
Position Surface form Disambiguated ID Type / Status
Subject Augustin-Louis Cauchy E239282 entity
Predicate notableFor P22 FINISHED
Object Cauchy–Euler equation E239291 NE FINISHED

Named-entity recognition

Before disambiguation, gpt-5-mini classified whether the object phrase is a named entity — the step behind the object's NE type shown above.

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: Cauchy–Euler equation | Statement: [Augustin-Louis Cauchy, notableFor, Cauchy–Euler equation]

Disambiguation candidates (1 decision)

The exact options the model was shown at each disambiguation step, with the option it chose highlighted — the evidence behind this triple's disambiguated ids.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Cauchy–Euler equation
Context triple: [Augustin-Louis Cauchy, notableFor, Cauchy–Euler equation]
  • A. Cauchy–Euler equation chosen
    The Cauchy–Euler equation is a type of linear ordinary differential equation with variable coefficients that often appears in problems with power-law or scale-invariant behavior.
  • B. Bernoulli differential equations
    Bernoulli differential equations are a class of first-order nonlinear differential equations that can be transformed into linear form and are fundamental in the study of ordinary differential equations.
  • C. Riccati equation
    A Riccati equation is a type of nonlinear differential or difference equation, often quadratic in the unknown function, that plays a central role in control theory, filtering, and various areas of applied mathematics.
  • D. Fuchsian differential equation
    A Fuchsian differential equation is a type of linear ordinary differential equation characterized by having only regular singular points, extensively studied in complex analysis and the theory of special functions.
  • E. Sturm–Liouville problem
    The Sturm–Liouville problem is a class of second-order linear differential equations with boundary conditions that yield real eigenvalues and orthogonal eigenfunctions forming a basis for function expansions in mathematical physics and engineering.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 batches)

Stage Batch ID Job type Status
creating batch_69ca84e3f0c48190ada72a65ebd50efd elicitation completed
NER batch_69cdb35c8e348190aa090c71bf6f30eb ner completed
NED1 batch_69d1d5dda4b0819092703270e87bee5a ned_source_triple completed
Created at: March 30, 2026, 8:33 p.m.