Triple

T4290526
Position Surface form Disambiguated ID Type / Status
Subject Augustus De Morgan E97376 entity
Predicate notableWork P4 FINISHED
Object Elements of Arithmetic
Elements of Arithmetic is a foundational 19th-century mathematics textbook by Augustus De Morgan that systematically develops the principles of arithmetic and number theory.
E428889 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: Elements of Arithmetic | Statement: [Augustus De Morgan, notableWork, Elements of Arithmetic]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Elements of Arithmetic
Context triple: [Augustus De Morgan, notableWork, Elements of Arithmetic]
  • A. The Higher Arithmetic
    The Higher Arithmetic is a classic introductory textbook on number theory, widely regarded for its clear exposition and influence on generations of mathematicians.
  • B. Die Grundlagen der Arithmetik
    Die Grundlagen der Arithmetik is Gottlob Frege’s seminal philosophical work that lays the logical foundations of arithmetic and advances the logicist thesis that arithmetic is reducible to pure logic.
  • C. Elementary Mathematics from an Advanced Standpoint
    "Elementary Mathematics from an Advanced Standpoint" is a classic three-volume work by Felix Klein that reexamines school-level mathematics through the lens of modern, rigorous mathematical theory and pedagogy.
  • D. Philosophy and Fun of Algebra
    Philosophy and Fun of Algebra is an accessible, imaginative book that introduces algebraic ideas and mathematical thinking to children and lay readers through stories, puzzles, and philosophical reflections.
  • E. Arithmetic, Algebra, Analysis
    "Arithmetic, Algebra, Analysis" is a foundational mathematics text that systematically develops core topics in number theory, algebraic structures, and real analysis from a rigorous, advanced perspective.
  • 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: Elements of Arithmetic
Triple: [Augustus De Morgan, notableWork, Elements of Arithmetic]
Generated description
Elements of Arithmetic is a foundational 19th-century mathematics textbook by Augustus De Morgan that systematically develops the principles of arithmetic and number theory.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Elements of Arithmetic
Target entity description: Elements of Arithmetic is a foundational 19th-century mathematics textbook by Augustus De Morgan that systematically develops the principles of arithmetic and number theory.
  • A. The Higher Arithmetic
    The Higher Arithmetic is a classic introductory textbook on number theory, widely regarded for its clear exposition and influence on generations of mathematicians.
  • B. Die Grundlagen der Arithmetik
    Die Grundlagen der Arithmetik is Gottlob Frege’s seminal philosophical work that lays the logical foundations of arithmetic and advances the logicist thesis that arithmetic is reducible to pure logic.
  • C. Elementary Mathematics from an Advanced Standpoint
    "Elementary Mathematics from an Advanced Standpoint" is a classic three-volume work by Felix Klein that reexamines school-level mathematics through the lens of modern, rigorous mathematical theory and pedagogy.
  • D. Philosophy and Fun of Algebra
    Philosophy and Fun of Algebra is an accessible, imaginative book that introduces algebraic ideas and mathematical thinking to children and lay readers through stories, puzzles, and philosophical reflections.
  • E. Arithmetic, Algebra, Analysis
    "Arithmetic, Algebra, Analysis" is a foundational mathematics text that systematically develops core topics in number theory, algebraic structures, and real analysis from a rigorous, advanced perspective.
  • 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_69b3454595848190a0e6bbb6a2bea040 completed March 12, 2026, 10:59 p.m.
NER Named-entity recognition batch_69b3507efb28819091a9d5b9161a5008 completed March 12, 2026, 11:47 p.m.
NED1 Entity disambiguation (via context triple) batch_69b5c73501f4819088bf87f3c4d0f23b completed March 14, 2026, 8:38 p.m.
NEDg Description generation batch_69b5c83c4b088190864f4bd5d32b0a29 completed March 14, 2026, 8:42 p.m.
NED2 Entity disambiguation (via description) batch_69b5c8a0c0bc8190beba56664874ed9b completed March 14, 2026, 8:44 p.m.
Created at: March 12, 2026, 11:08 p.m.