Triple
T10304989
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Cauchy integral formula |
E241728
|
entity |
| Predicate | hasGeneralization |
P2372
|
FINISHED |
| Object | Cauchy integral theorem |
E239284
|
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 theorem | Statement: [Cauchy integral formula, hasGeneralization, Cauchy integral theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Cauchy integral theorem Context triple: [Cauchy integral formula, hasGeneralization, Cauchy integral theorem]
-
A.
Cauchy integral theorem
chosen
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.
-
B.
Cauchy integral formula
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.
-
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.
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.
-
E.
Riemann mapping theorem
The Riemann mapping theorem is a fundamental result in complex analysis stating that any non-empty simply connected open subset of the complex plane (other than the whole plane) can be conformally mapped onto the open unit disk.
- 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_69d381ac38808190a8ca7457c85b625b |
completed | April 6, 2026, 9:49 a.m. |
| NER | Named-entity recognition | batch_69d4d309a4508190ad9de37171a64dba |
completed | April 7, 2026, 9:48 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69d71d58416081909a010e905d70e934 |
completed | April 9, 2026, 3:30 a.m. |
Created at: April 6, 2026, 11:46 a.m.