Triple

T21047373
Position Surface form Disambiguated ID Type / Status
Subject Le calcul des résidus et ses applications à la théorie des fonctions E518482 entity
Predicate relatedTo P37 FINISHED
Object Cauchy’s integral theorem — NE NERFINISHED

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’s integral theorem | Statement: [Le calcul des résidus et ses applications à la théorie des fonctions, relatedTo, Cauchy’s integral theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Cauchy’s integral theorem
Context triple: [Le calcul des résidus et ses applications à la théorie des fonctions, relatedTo, Cauchy’s integral theorem]
  • A. Cauchy integral theorem chosen
    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.
  • 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 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–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.
  • E. Morera's theorem
    Morera's theorem is a fundamental result in complex analysis that characterizes holomorphic functions by stating that a continuous function with zero integral over every closed contour in a domain must be analytic there.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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_69e0b50438e08190917e2538bb8bc034 completed April 16, 2026, 10:08 a.m.
NER Named-entity recognition batch_69e6fcf4d26481908b639996500a8319 completed April 21, 2026, 4:28 a.m.
Created at: April 16, 2026, 2:34 p.m.