Triple

T9843842
Position Surface form Disambiguated ID Type / Status
Subject Cauchy–Schwarz inequality E239290 entity
Predicate namedAfter P63 FINISHED
Object Hermann Amandus Schwarz
Hermann Amandus Schwarz was a German mathematician known for his fundamental contributions to complex analysis and for co-formulating the Cauchy–Schwarz inequality.
E827207 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: Hermann Amandus Schwarz | Statement: [Cauchy–Schwarz inequality, namedAfter, Hermann Amandus Schwarz]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Hermann Amandus Schwarz
Context triple: [Cauchy–Schwarz inequality, namedAfter, Hermann Amandus Schwarz]
  • A. Rudolf Lipschitz
    Rudolf Lipschitz was a 19th-century German mathematician known for foundational work in analysis and differential equations, including the Lipschitz continuity condition that underpins key existence and uniqueness results.
  • B. Alfred Clebsch
    Alfred Clebsch was a 19th-century German mathematician known for his influential work in algebraic geometry and invariant theory.
  • C. Karl Weierstrass
    Karl Weierstrass was a 19th-century German mathematician renowned as a founder of modern analysis, particularly for his rigorous formulation of calculus and the theory of functions.
  • D. Adolf Hurwitz
    Adolf Hurwitz was a German mathematician known for his influential work in complex analysis, algebra, and number theory, including foundational contributions to the theory of Riemann surfaces and algebraic functions.
  • E. Bernhard Riemann
    Bernhard Riemann was a 19th-century German mathematician whose groundbreaking work in analysis, number theory, and differential geometry laid the foundations for modern mathematics and general relativity.
  • 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: Hermann Amandus Schwarz
Triple: [Cauchy–Schwarz inequality, namedAfter, Hermann Amandus Schwarz]
Generated description
Hermann Amandus Schwarz was a German mathematician known for his fundamental contributions to complex analysis and for co-formulating the Cauchy–Schwarz inequality.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Hermann Amandus Schwarz
Target entity description: Hermann Amandus Schwarz was a German mathematician known for his fundamental contributions to complex analysis and for co-formulating the Cauchy–Schwarz inequality.
  • A. Rudolf Lipschitz
    Rudolf Lipschitz was a 19th-century German mathematician known for foundational work in analysis and differential equations, including the Lipschitz continuity condition that underpins key existence and uniqueness results.
  • B. Alfred Clebsch
    Alfred Clebsch was a 19th-century German mathematician known for his influential work in algebraic geometry and invariant theory.
  • C. Karl Weierstrass
    Karl Weierstrass was a 19th-century German mathematician renowned as a founder of modern analysis, particularly for his rigorous formulation of calculus and the theory of functions.
  • D. Adolf Hurwitz
    Adolf Hurwitz was a German mathematician known for his influential work in complex analysis, algebra, and number theory, including foundational contributions to the theory of Riemann surfaces and algebraic functions.
  • E. Bernhard Riemann
    Bernhard Riemann was a 19th-century German mathematician whose groundbreaking work in analysis, number theory, and differential geometry laid the foundations for modern mathematics and general relativity.
  • 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_69cdb35dc29c819080203be5b904dc9d completed April 2, 2026, 12:07 a.m.
NED1 Entity disambiguation (via context triple) batch_69d1ead49b14819086a9bbd256f298a9 completed April 5, 2026, 4:53 a.m.
NEDg Description generation batch_69d1eb79be388190853e0e7c29287294 completed April 5, 2026, 4:56 a.m.
NED2 Entity disambiguation (via description) batch_69d1ebf0a99081908ae0c4bceadc42bc completed April 5, 2026, 4:58 a.m.
Created at: March 30, 2026, 8:33 p.m.