Triple

T13614782
Position Surface form Disambiguated ID Type / Status
Subject Differential Analysis on Complex Manifolds E325283 entity
Predicate topic P261 FINISHED
Object Cauchy–Riemann equations E239285 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–Riemann equations | Statement: [Differential Analysis on Complex Manifolds, topic, Cauchy–Riemann equations]

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–Riemann equations
Context triple: [Differential Analysis on Complex Manifolds, topic, Cauchy–Riemann equations]
  • A. Cauchy–Riemann equations chosen
    The Cauchy–Riemann equations are fundamental conditions in complex analysis that characterize when a complex-valued function is holomorphic (complex differentiable).
  • B. Cauchy–Pompeiu formula
    The Cauchy–Pompeiu formula is a fundamental result in complex analysis that extends the Cauchy integral formula to functions that are not necessarily holomorphic by expressing them via both boundary and area integrals.
  • C. Wirtinger derivatives
    Wirtinger derivatives are complex differential operators that treat a complex variable and its conjugate as independent, providing a convenient formalism for expressing and analyzing holomorphicity and the Cauchy–Riemann equations.
  • D. Christoffel–Schwarz formula
    The Christoffel–Schwarz formula is a fundamental result in complex analysis that provides an explicit conformal mapping from the upper half-plane onto polygonal regions in the complex plane.
  • E. Laplace equation
    The Laplace equation is a fundamental second-order partial differential equation widely used in physics and engineering to describe steady-state phenomena such as electrostatics, gravitation, and heat conduction.
  • 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_69d8076aae28819092cf636190ee5529 elicitation completed
NER batch_69dbb0ad0a7c81909c7972187202db96 ner completed
NED1 batch_69f77f9cbc388190972e949324144d2f ned_source_triple completed
Created at: April 9, 2026, 9:50 p.m.