Triple

T10304989
Position Surface form Disambiguated ID Type / Status
Subject Cauchy integral formula E241728 entity
Predicate hasGeneralization P2372 FINISHED
Object Cauchy integral theorem E239284 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 theorem | Statement: [Cauchy integral formula, hasGeneralization, Cauchy integral theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Cauchy integral theorem
Context triple: [Cauchy integral formula, hasGeneralization, Cauchy 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. 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.
  • E. Riemann mapping theorem
    The Riemann mapping theorem is a fundamental result in complex analysis stating that any non-empty simply connected open subset of the complex plane (other than the whole plane) can be conformally mapped onto the open unit disk.
  • 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_69d71d58416081909a010e905d70e934 completed April 9, 2026, 3:30 a.m.
Created at: April 6, 2026, 11:46 a.m.