Triple

T2171645
Position Surface form Disambiguated ID Type / Status
Subject Augustin-Louis Cauchy E48438 entity
Predicate knownFor P22 FINISHED
Object 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.
E241728 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 formula | Statement: [Augustin-Louis Cauchy, knownFor, Cauchy integral formula]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Cauchy integral formula
Context triple: [Augustin-Louis Cauchy, knownFor, Cauchy integral formula]
  • A. 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.
  • B. 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.
  • C. 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.
  • D. 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.
  • E. Cauchy–Riemann equations
    The Cauchy–Riemann equations are fundamental conditions in complex analysis that characterize when a complex-valued function is holomorphic (complex differentiable).
  • 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 formula
Triple: [Augustin-Louis Cauchy, knownFor, Cauchy integral formula]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Cauchy integral formula
Target entity description: 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.
  • A. 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.
  • B. 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.
  • C. 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.
  • D. 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.
  • E. Cauchy–Riemann equations
    The Cauchy–Riemann equations are fundamental conditions in complex analysis that characterize when a complex-valued function is holomorphic (complex differentiable).
  • 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_69ae5d9a74e081909d8945fe03c8d0fa completed March 9, 2026, 5:41 a.m.
NEDg Description generation batch_69ae5e30a69c8190a3f77e784401f671 completed March 9, 2026, 5:44 a.m.
NED2 Entity disambiguation (via description) batch_69ae5ea4edcc81908829e4bd64ce0aea completed March 9, 2026, 5:46 a.m.
Created at: March 4, 2026, 7:45 p.m.