Triple

T4962221
Position Surface form Disambiguated ID Type / Status
Subject Kurt Hensel E111434 entity
Predicate publication P80 FINISHED
Object Theorie der algebraischen Zahlen
"Theorie der algebraischen Zahlen" is Kurt Hensel’s foundational work in algebraic number theory, notable for introducing and developing the concept of p-adic numbers.
E483406 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: Theorie der algebraischen Zahlen | Statement: [Kurt Hensel, publication, Theorie der algebraischen Zahlen]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Theorie der algebraischen Zahlen
Context triple: [Kurt Hensel, publication, Theorie der algebraischen Zahlen]
  • A. Die Theorie der algebraischen Zahlkörper
    "Die Theorie der algebraischen Zahlkörper" is a foundational mathematical monograph on algebraic number fields, authored by David Hilbert and published as part of his influential Zahlbericht.
  • B. Disquisitiones Arithmeticae
    Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
  • C. An Introduction to the Theory of Numbers
    An Introduction to the Theory of Numbers is a classic textbook in number theory, co-authored by G. H. Hardy, that systematically develops fundamental concepts such as divisibility, prime numbers, Diophantine equations, and quadratic forms.
  • D. Theorie der algebraischen Kurven
    "Theorie der algebraischen Kurven" is a foundational 19th-century mathematical treatise by Julius Plücker that systematically develops the geometry and classification of algebraic curves.
  • E. Neukirch: Algebraic Number Theory
    "Neukirch: Algebraic Number Theory" is a widely respected graduate-level textbook that provides a rigorous, modern introduction to algebraic number theory, including class field theory and foundational results such as the Kronecker–Weber theorem.
  • 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: Theorie der algebraischen Zahlen
Triple: [Kurt Hensel, publication, Theorie der algebraischen Zahlen]
Generated description
"Theorie der algebraischen Zahlen" is Kurt Hensel’s foundational work in algebraic number theory, notable for introducing and developing the concept of p-adic numbers.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Theorie der algebraischen Zahlen
Target entity description: "Theorie der algebraischen Zahlen" is Kurt Hensel’s foundational work in algebraic number theory, notable for introducing and developing the concept of p-adic numbers.
  • A. Die Theorie der algebraischen Zahlkörper
    "Die Theorie der algebraischen Zahlkörper" is a foundational mathematical monograph on algebraic number fields, authored by David Hilbert and published as part of his influential Zahlbericht.
  • B. Disquisitiones Arithmeticae
    Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
  • C. An Introduction to the Theory of Numbers
    An Introduction to the Theory of Numbers is a classic textbook in number theory, co-authored by G. H. Hardy, that systematically develops fundamental concepts such as divisibility, prime numbers, Diophantine equations, and quadratic forms.
  • D. Theorie der algebraischen Kurven
    "Theorie der algebraischen Kurven" is a foundational 19th-century mathematical treatise by Julius Plücker that systematically develops the geometry and classification of algebraic curves.
  • E. Neukirch: Algebraic Number Theory
    "Neukirch: Algebraic Number Theory" is a widely respected graduate-level textbook that provides a rigorous, modern introduction to algebraic number theory, including class field theory and foundational results such as the Kronecker–Weber theorem.
  • 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_69bd4419393c819086319a6fe4bf8542 completed March 20, 2026, 12:56 p.m.
NER Named-entity recognition batch_69bd71f3e6148190b99f35734220ffc3 completed March 20, 2026, 4:12 p.m.
NED1 Entity disambiguation (via context triple) batch_69be81ea8cc08190af40098ca99364f1 completed March 21, 2026, 11:32 a.m.
NEDg Description generation batch_69be82dcc280819098eac824370b1af0 completed March 21, 2026, 11:37 a.m.
NED2 Entity disambiguation (via description) batch_69be8349507481908643591de7f03f42 completed March 21, 2026, 11:38 a.m.
Created at: March 20, 2026, 1:32 p.m.