Triple
T10304987
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Cauchy integral formula |
E241728
|
entity |
| Predicate | hasGeneralization |
P2372
|
FINISHED |
| Object |
Cauchy integral formula for derivatives
The Cauchy integral formula for derivatives is a fundamental result in complex analysis that expresses the nth derivative of a holomorphic function inside a contour as a contour integral of the function over that curve.
|
E241728
|
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: Cauchy integral formula for derivatives | Statement: [Cauchy integral formula, hasGeneralization, Cauchy integral formula for derivatives]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Cauchy integral formula for derivatives Context triple: [Cauchy integral formula, hasGeneralization, Cauchy integral formula for derivatives]
-
A.
Cauchy integral formula
The Cauchy integral formula is a fundamental result in complex analysis that expresses the value of a holomorphic function inside a disk in terms of a contour integral of the function around the disk’s boundary.
-
B.
Cauchy integral theorem
The Cauchy integral theorem is a fundamental result in complex analysis stating that the integral of a holomorphic function over any closed contour in a simply connected domain is zero.
-
C.
Cauchy residue theorem
The Cauchy residue theorem is a fundamental result in complex analysis that relates contour integrals of analytic functions around singularities to the sum of their residues, greatly simplifying the evaluation of many complex and real integrals.
-
D.
Cauchy–Riemann equations
The Cauchy–Riemann equations are fundamental conditions in complex analysis that characterize when a complex-valued function is holomorphic (complex differentiable).
-
E.
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.
- 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: Cauchy integral formula for derivatives Triple: [Cauchy integral formula, hasGeneralization, Cauchy integral formula for derivatives]
Generated description
The Cauchy integral formula for derivatives is a fundamental result in complex analysis that expresses the nth derivative of a holomorphic function inside a contour as a contour integral of the function over that curve.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Cauchy integral formula for derivatives Target entity description: The Cauchy integral formula for derivatives is a fundamental result in complex analysis that expresses the nth derivative of a holomorphic function inside a contour as a contour integral of the function over that curve.
-
A.
Cauchy integral formula
chosen
The Cauchy integral formula is a fundamental result in complex analysis that expresses the value of a holomorphic function inside a disk in terms of a contour integral of the function around the disk’s boundary.
-
B.
Cauchy integral theorem
The Cauchy integral theorem is a fundamental result in complex analysis stating that the integral of a holomorphic function over any closed contour in a simply connected domain is zero.
-
C.
Cauchy residue theorem
The Cauchy residue theorem is a fundamental result in complex analysis that relates contour integrals of analytic functions around singularities to the sum of their residues, greatly simplifying the evaluation of many complex and real integrals.
-
D.
Cauchy–Riemann equations
The Cauchy–Riemann equations are fundamental conditions in complex analysis that characterize when a complex-valued function is holomorphic (complex differentiable).
-
E.
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.
- F. None of above.
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_69d381ac38808190a8ca7457c85b625b |
completed | April 6, 2026, 9:49 a.m. |
| NER | Named-entity recognition | batch_69d4d309a4508190ad9de37171a64dba |
completed | April 7, 2026, 9:48 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69d71d58416081909a010e905d70e934 |
completed | April 9, 2026, 3:30 a.m. |
| NEDg | Description generation | batch_69d73185266481909e79eddc33469d8d |
completed | April 9, 2026, 4:56 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69d73279922c8190b616e1a61df4d227 |
completed | April 9, 2026, 5 a.m. |
Created at: April 6, 2026, 11:46 a.m.