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.