Triple

T10304988
Position Surface form Disambiguated ID Type / Status
Subject Cauchy integral formula E241728 entity
Predicate hasGeneralization P2372 FINISHED
Object Cauchy integral formula for higher derivatives E241728 NE FINISHED

How this triple was built (2 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 higher derivatives | Statement: [Cauchy integral formula, hasGeneralization, Cauchy integral formula for higher derivatives]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Cauchy integral formula for higher derivatives
Context triple: [Cauchy integral formula, hasGeneralization, Cauchy integral formula for higher derivatives]
  • 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–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.
  • 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. 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.
  • E. 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.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69d75026fb0881908e4d16b3fde531c0 completed April 9, 2026, 7:07 a.m.
Created at: April 6, 2026, 11:46 a.m.