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.