Triple

T2171644
Position Surface form Disambiguated ID Type / Status
Subject Augustin-Louis Cauchy E48438 entity
Predicate knownFor P22 FINISHED
Object 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.
E239284 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 integral theorem | Statement: [Augustin-Louis Cauchy, knownFor, Cauchy integral theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Cauchy integral theorem
Context triple: [Augustin-Louis Cauchy, knownFor, Cauchy integral theorem]
  • A. 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.
  • B. Cauchy–Kovalevskaya theorem
    The Cauchy–Kovalevskaya theorem is a fundamental result in partial differential equations that guarantees the existence and uniqueness of analytic solutions to certain initial value problems under appropriate analyticity conditions.
  • C. Cauchy-à-la-Tour
    Cauchy-à-la-Tour is a small commune in the Pas-de-Calais department of northern France.
  • D. Weierstrass preparation theorem
    The Weierstrass preparation theorem is a fundamental result in complex analysis and analytic geometry that locally expresses analytic functions near a zero as a product of a polynomial and a unit, enabling a power-series analogue of factorization.
  • E. Weierstrass factorization theorem
    The Weierstrass factorization theorem is a fundamental result in complex analysis that expresses any entire function as an infinite product determined by its zeros, generalizing the factorization of polynomials.
  • 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 integral theorem
Triple: [Augustin-Louis Cauchy, knownFor, Cauchy integral theorem]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Cauchy integral theorem
Target entity description: 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.
  • A. 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.
  • B. Cauchy–Kovalevskaya theorem
    The Cauchy–Kovalevskaya theorem is a fundamental result in partial differential equations that guarantees the existence and uniqueness of analytic solutions to certain initial value problems under appropriate analyticity conditions.
  • C. Cauchy-à-la-Tour
    Cauchy-à-la-Tour is a small commune in the Pas-de-Calais department of northern France.
  • D. Weierstrass preparation theorem
    The Weierstrass preparation theorem is a fundamental result in complex analysis and analytic geometry that locally expresses analytic functions near a zero as a product of a polynomial and a unit, enabling a power-series analogue of factorization.
  • E. Weierstrass factorization theorem
    The Weierstrass factorization theorem is a fundamental result in complex analysis that expresses any entire function as an infinite product determined by its zeros, generalizing the factorization of polynomials.
  • 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_69a88aa3faa48190995b233af6525815 completed March 4, 2026, 7:40 p.m.
NER Named-entity recognition batch_69abbec7f9088190b32127421e340788 completed March 7, 2026, 5:59 a.m.
NED1 Entity disambiguation (via context triple) batch_69ae58f6c8c8819081a06861f6133fe9 completed March 9, 2026, 5:21 a.m.
NEDg Description generation batch_69ae5989f054819082f36e5515bec3ca completed March 9, 2026, 5:24 a.m.
NED2 Entity disambiguation (via description) batch_69ae5a12f11c81908cc345905f0a485e completed March 9, 2026, 5:26 a.m.
Created at: March 4, 2026, 7:45 p.m.