Triple

T9843638
Position Surface form Disambiguated ID Type / Status
Subject Cauchy–Riemann equations E239285 entity
Predicate relatedConcept P37 FINISHED
Object 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.
E825427 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: Wirtinger derivatives | Statement: [Cauchy–Riemann equations, relatedConcept, Wirtinger derivatives]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Wirtinger derivatives
Context triple: [Cauchy–Riemann equations, relatedConcept, Wirtinger derivatives]
  • A. Cauchy–Riemann equations
    The Cauchy–Riemann equations are fundamental conditions in complex analysis that characterize when a complex-valued function is holomorphic (complex differentiable).
  • B. Bochner–Martinelli formula
    The Bochner–Martinelli formula is a fundamental integral representation in several complex variables that generalizes the Cauchy integral formula to higher dimensions.
  • C. Sommerfeld-Watson transform
    The Sommerfeld-Watson transform is a complex-analysis technique that converts discrete sums over angular momentum into contour integrals, widely used in scattering theory and Regge theory to study analytic properties of amplitudes.
  • D. Weyl fractional integral
    The Weyl fractional integral is a generalization of the classical integral to arbitrary (including non-integer) orders, defined on periodic functions or the whole real line and used in fractional calculus to model memory and hereditary properties in various systems.
  • E. Wirtinger
    Wirtinger is a surname most notably associated with Austrian mathematician Wilhelm Wirtinger, known for his contributions to complex analysis and knot theory.
  • 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: Wirtinger derivatives
Triple: [Cauchy–Riemann equations, relatedConcept, Wirtinger derivatives]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Wirtinger derivatives
Target entity description: 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.
  • A. Cauchy–Riemann equations
    The Cauchy–Riemann equations are fundamental conditions in complex analysis that characterize when a complex-valued function is holomorphic (complex differentiable).
  • B. Bochner–Martinelli formula
    The Bochner–Martinelli formula is a fundamental integral representation in several complex variables that generalizes the Cauchy integral formula to higher dimensions.
  • C. Sommerfeld-Watson transform
    The Sommerfeld-Watson transform is a complex-analysis technique that converts discrete sums over angular momentum into contour integrals, widely used in scattering theory and Regge theory to study analytic properties of amplitudes.
  • D. Weyl fractional integral
    The Weyl fractional integral is a generalization of the classical integral to arbitrary (including non-integer) orders, defined on periodic functions or the whole real line and used in fractional calculus to model memory and hereditary properties in various systems.
  • E. Wirtinger
    Wirtinger is a surname most notably associated with Austrian mathematician Wilhelm Wirtinger, known for his contributions to complex analysis and knot theory.
  • F. None of above. chosen

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_69ca84e3f0c48190ada72a65ebd50efd completed March 30, 2026, 2:12 p.m.
NER Named-entity recognition batch_69cdb35c8e348190aa090c71bf6f30eb completed April 2, 2026, 12:07 a.m.
NED1 Entity disambiguation (via context triple) batch_69d1d5dda4b0819092703270e87bee5a completed April 5, 2026, 3:24 a.m.
NEDg Description generation batch_69d1d6815e28819081788393cda63bc0 completed April 5, 2026, 3:26 a.m.
NED2 Entity disambiguation (via description) batch_69d1d74e7a148190a9470745bfd7ad42 completed April 5, 2026, 3:30 a.m.
Created at: March 30, 2026, 8:33 p.m.