Triple

T9843581
Position Surface form Disambiguated ID Type / Status
Subject Cauchy integral theorem E239284 entity
Predicate relatedTo P37 FINISHED
Object Green's theorem E620783 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: Green's theorem | Statement: [Cauchy integral theorem, relatedTo, Green's theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Green's theorem
Context triple: [Cauchy integral theorem, relatedTo, Green's theorem]
  • A. Green's theorem chosen
    Green's theorem is a fundamental result in vector calculus that relates a line integral around a simple closed curve in the plane to a double integral over the region it encloses.
  • B. Stokes' theorem
    Stokes' theorem is a fundamental result in vector calculus that relates the surface integral of the curl of a vector field over a surface to the line integral of the field around the surface’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. Fubini's theorem
    Fubini's theorem is a fundamental result in measure theory that allows the evaluation of double integrals as iterated integrals under suitable integrability conditions.
  • E. Poincaré lemma
    The Poincaré lemma is a fundamental result in differential geometry and topology stating that every closed differential form on a star-shaped (or more generally, contractible) domain is locally exact.
  • 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_69ca84e3f0c48190ada72a65ebd50efd completed March 30, 2026, 2:12 p.m.
NER Named-entity recognition batch_69cdb35c8e348190aa090c71bf6f30eb completed April 2, 2026, 12:07 a.m.
NED1 Entity disambiguation (via context triple) batch_69d1d5dda4b0819092703270e87bee5a completed April 5, 2026, 3:24 a.m.
Created at: March 30, 2026, 8:33 p.m.