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.