Triple

T17105179
Position Surface form Disambiguated ID Type / Status
Subject Kramers–Kronig relations E415080 entity
Predicate basedOn P98 FINISHED
Object Cauchy integral formula 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 | Statement: [Kramers–Kronig relations, basedOn, Cauchy integral formula]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Cauchy integral formula
Context triple: [Kramers–Kronig relations, basedOn, Cauchy integral formula]
  • 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 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.
  • 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 (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_69d886cfc8e88190b05ba466edd35591 completed April 10, 2026, 5:12 a.m.
NER Named-entity recognition batch_69e3dc2683fc81908af2df9012addecb completed April 18, 2026, 7:31 p.m.
NED1 Entity disambiguation (via context triple) batch_6a0139ffbe808190a24e827331ee4a6c completed May 11, 2026, 2:07 a.m.
Created at: April 10, 2026, 5:35 a.m.