Triple

T33361854
Position Surface form Disambiguated ID Type / Status
Subject Liouville's theorem (complex analysis) E854242 entity
Predicate corollaryOf P45604 FINISHED
Object Cauchy integral formula and Cauchy estimates LITERAL 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 and Cauchy estimates | Statement: [Liouville's theorem (complex analysis), corollaryOf, Cauchy integral formula and Cauchy estimates]
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: corollaryOf
Context triple: [Liouville's theorem (complex analysis), corollaryOf, Cauchy integral formula and Cauchy estimates]
  • A. hasCorollary chosen
    Indicates that one statement, result, or proposition follows as a corollary from another, typically more general, statement.
  • B. relatedTheorem
    Indicates that one theorem is connected to another through a logical, thematic, or derivational relationship.
  • C. alsoAppealsTo
    Indicates that something attracts, interests, or is pleasing to an additional person, group, or audience beyond the primary one.
  • D. provesTo
    Indicates that one entity demonstrates or establishes the truth or validity of something to another entity.
  • E. hasTheorem
    Indicates that one entity (typically a mathematical theory, field, or work) includes, establishes, or is associated with a particular theorem.
  • F. None of above.

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_69f3496bda8c8190bfc8fade9d1b791c completed April 30, 2026, 12:22 p.m.
NER Named-entity recognition batch_69f6e3156ea48190b604e414665ef351 completed May 3, 2026, 5:54 a.m.
PD Predicate disambiguation batch_69f6de0b9ba48190887c9eb5d06a2e94 completed May 3, 2026, 5:32 a.m.
Created at: May 1, 2026, 1:34 a.m.