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.