Triple
T10304991
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Cauchy integral formula |
E241728
|
entity |
| Predicate | hasGeneralization |
P2372
|
FINISHED |
| Object |
Cauchy–Green formula
The Cauchy–Green formula is a generalization of the Cauchy integral formula that represents sufficiently smooth complex functions inside a domain in terms of both boundary integrals and area integrals involving their partial derivatives.
|
E613405
|
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–Green formula | Statement: [Cauchy integral formula, hasGeneralization, Cauchy–Green formula]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Cauchy–Green formula Context triple: [Cauchy integral formula, hasGeneralization, Cauchy–Green formula]
-
A.
Green's theorem
Green's theorem is a fundamental result in vector calculus that relates a line integral around a simple closed curve in the plane to a double integral over the region it encloses.
-
B.
Cauchy–Binet formula
The Cauchy–Binet formula is a fundamental result in linear algebra that expresses the determinant of a product of two rectangular matrices as a sum of products of determinants of their square submatrices.
-
C.
Cauchy–Riemann equations
The Cauchy–Riemann equations are fundamental conditions in complex analysis that characterize when a complex-valued function is holomorphic (complex differentiable).
-
D.
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.
-
E.
Kubo formula
The Kubo formula is a fundamental result in linear response theory that expresses transport coefficients and response functions in terms of equilibrium correlation functions in statistical mechanics and quantum many-body physics.
- 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–Green formula Triple: [Cauchy integral formula, hasGeneralization, Cauchy–Green formula]
Generated description
The Cauchy–Green formula is a generalization of the Cauchy integral formula that represents sufficiently smooth complex functions inside a domain in terms of both boundary integrals and area integrals involving their partial derivatives.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Cauchy–Green formula Target entity description: The Cauchy–Green formula is a generalization of the Cauchy integral formula that represents sufficiently smooth complex functions inside a domain in terms of both boundary integrals and area integrals involving their partial derivatives.
-
A.
Green's theorem
Green's theorem is a fundamental result in vector calculus that relates a line integral around a simple closed curve in the plane to a double integral over the region it encloses.
-
B.
Cauchy–Binet formula
The Cauchy–Binet formula is a fundamental result in linear algebra that expresses the determinant of a product of two rectangular matrices as a sum of products of determinants of their square submatrices.
-
C.
Cauchy–Riemann equations
The Cauchy–Riemann equations are fundamental conditions in complex analysis that characterize when a complex-valued function is holomorphic (complex differentiable).
-
D.
Bochner–Martinelli formula
chosen
The Bochner–Martinelli formula is a fundamental integral representation in several complex variables that generalizes the Cauchy integral formula to higher dimensions.
-
E.
Kubo formula
The Kubo formula is a fundamental result in linear response theory that expresses transport coefficients and response functions in terms of equilibrium correlation functions in statistical mechanics and quantum many-body physics.
- 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.