Triple

T10304990
Position Surface form Disambiguated ID Type / Status
Subject Cauchy integral formula E241728 entity
Predicate hasGeneralization P2372 FINISHED
Object Cauchy–Pompeiu formula
The Cauchy–Pompeiu formula is a fundamental result in complex analysis that extends the Cauchy integral formula to functions that are not necessarily holomorphic by expressing them via both boundary and area integrals.
E854243 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–Pompeiu formula | Statement: [Cauchy integral formula, hasGeneralization, Cauchy–Pompeiu formula]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Cauchy–Pompeiu formula
Context triple: [Cauchy integral formula, hasGeneralization, Cauchy–Pompeiu formula]
  • A. 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.
  • B. 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.
  • C. 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.
  • D. Poisson integral
    The Poisson integral is a fundamental formula in harmonic analysis that reconstructs harmonic functions inside a disk (or half-plane) from their boundary values using the Poisson kernel.
  • E. Cauchy–Riemann equations
    The Cauchy–Riemann equations are fundamental conditions in complex analysis that characterize when a complex-valued function is holomorphic (complex differentiable).
  • 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–Pompeiu formula
Triple: [Cauchy integral formula, hasGeneralization, Cauchy–Pompeiu formula]
Generated description
The Cauchy–Pompeiu formula is a fundamental result in complex analysis that extends the Cauchy integral formula to functions that are not necessarily holomorphic by expressing them via both boundary and area integrals.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Cauchy–Pompeiu formula
Target entity description: The Cauchy–Pompeiu formula is a fundamental result in complex analysis that extends the Cauchy integral formula to functions that are not necessarily holomorphic by expressing them via both boundary and area integrals.
  • A. 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.
  • B. 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.
  • C. 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.
  • D. Poisson integral
    The Poisson integral is a fundamental formula in harmonic analysis that reconstructs harmonic functions inside a disk (or half-plane) from their boundary values using the Poisson kernel.
  • E. Cauchy–Riemann equations
    The Cauchy–Riemann equations are fundamental conditions in complex analysis that characterize when a complex-valued function is holomorphic (complex differentiable).
  • 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_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.