Triple

T9843561
Position Surface form Disambiguated ID Type / Status
Subject Cauchy integral theorem E239284 entity
Predicate implies P1661 FINISHED
Object 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.
E825426 NE FINISHED

How this triple was built (4 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: Morera's theorem | Statement: [Cauchy integral theorem, implies, Morera's theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Morera's theorem
Context triple: [Cauchy integral theorem, implies, Morera's theorem]
  • A. Mittag-Leffler theorem
    The Mittag-Leffler theorem is a fundamental result in complex analysis that characterizes meromorphic functions by allowing the construction of such functions with prescribed principal parts at given poles.
  • B. Montel theorem
    Montel's theorem is a fundamental result in complex analysis stating that a family of holomorphic functions that is uniformly bounded on every compact subset of a domain is a normal family, meaning every sequence in it has a subsequence that converges uniformly on compact sets.
  • 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. Lindelöf theorem in complex analysis
    The Lindelöf theorem in complex analysis is a result that refines the maximum modulus principle by controlling the boundary growth of analytic functions, particularly along paths approaching boundary points of their domain.
  • E. Picard theorem
    Picard theorem is a fundamental result in complex analysis stating that entire non-constant functions take on all possible complex values, with at most one exception.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Morera's theorem
Triple: [Cauchy integral theorem, implies, Morera's theorem]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Morera's theorem
Target entity description: 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.
  • A. Mittag-Leffler theorem
    The Mittag-Leffler theorem is a fundamental result in complex analysis that characterizes meromorphic functions by allowing the construction of such functions with prescribed principal parts at given poles.
  • B. Montel theorem
    Montel's theorem is a fundamental result in complex analysis stating that a family of holomorphic functions that is uniformly bounded on every compact subset of a domain is a normal family, meaning every sequence in it has a subsequence that converges uniformly on compact sets.
  • 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. Lindelöf theorem in complex analysis
    The Lindelöf theorem in complex analysis is a result that refines the maximum modulus principle by controlling the boundary growth of analytic functions, particularly along paths approaching boundary points of their domain.
  • E. Picard theorem
    Picard theorem is a fundamental result in complex analysis stating that entire non-constant functions take on all possible complex values, with at most one exception.
  • F. None of above. chosen

Provenance (5 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.
NEDg Description generation batch_69d1d6815e28819081788393cda63bc0 completed April 5, 2026, 3:26 a.m.
NED2 Entity disambiguation (via description) batch_69d1d74e7a148190a9470745bfd7ad42 completed April 5, 2026, 3:30 a.m.
Created at: March 30, 2026, 8:33 p.m.