Triple
T9843486
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Augustin-Louis Cauchy |
E239282
|
entity |
| Predicate | notableFor |
P22
|
FINISHED |
| Object |
Cauchy’s integral test
Cauchy’s integral test is a convergence criterion in mathematical analysis that determines whether an infinite series converges by relating it to the behavior of a corresponding improper integral.
|
E825422
|
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: Cauchy’s integral test | Statement: [Augustin-Louis Cauchy, notableFor, Cauchy’s integral test]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Cauchy’s integral test Context triple: [Augustin-Louis Cauchy, notableFor, Cauchy’s integral test]
-
A.
Cauchy condensation test
The Cauchy condensation test is a convergence criterion in mathematical analysis that determines whether an infinite series with positive, nonincreasing terms converges by comparing it to a related series formed by powers of two.
-
B.
Dirichlet test
The Dirichlet test is a criterion in mathematical analysis that provides sufficient conditions for the convergence of certain infinite series, particularly those involving oscillatory terms.
-
C.
Cauchy convergence criterion
The Cauchy convergence criterion is a fundamental concept in mathematical analysis that characterizes convergence of sequences (and series) by requiring that their terms become arbitrarily close to each other beyond some index.
-
D.
Weierstrass M-test
The Weierstrass M-test is a criterion in real and complex analysis that provides a sufficient condition for the uniform convergence of a series of functions by comparing it to a convergent series of bounding constants.
-
E.
Cauchy principal value
The Cauchy principal value is a method in mathematical analysis for assigning finite values to certain improper or divergent integrals and series by symmetrically balancing their singularities.
- 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: Cauchy’s integral test Triple: [Augustin-Louis Cauchy, notableFor, Cauchy’s integral test]
Generated description
Cauchy’s integral test is a convergence criterion in mathematical analysis that determines whether an infinite series converges by relating it to the behavior of a corresponding improper integral.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Cauchy’s integral test Target entity description: Cauchy’s integral test is a convergence criterion in mathematical analysis that determines whether an infinite series converges by relating it to the behavior of a corresponding improper integral.
-
A.
Cauchy condensation test
The Cauchy condensation test is a convergence criterion in mathematical analysis that determines whether an infinite series with positive, nonincreasing terms converges by comparing it to a related series formed by powers of two.
-
B.
Dirichlet test
The Dirichlet test is a criterion in mathematical analysis that provides sufficient conditions for the convergence of certain infinite series, particularly those involving oscillatory terms.
-
C.
Cauchy convergence criterion
The Cauchy convergence criterion is a fundamental concept in mathematical analysis that characterizes convergence of sequences (and series) by requiring that their terms become arbitrarily close to each other beyond some index.
-
D.
Weierstrass M-test
The Weierstrass M-test is a criterion in real and complex analysis that provides a sufficient condition for the uniform convergence of a series of functions by comparing it to a convergent series of bounding constants.
-
E.
Cauchy principal value
The Cauchy principal value is a method in mathematical analysis for assigning finite values to certain improper or divergent integrals and series by symmetrically balancing their singularities.
- 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.