Triple

T10061982
Position Surface form Disambiguated ID Type / Status
Subject Hilbert’s twelfth problem E213012 entity
Predicate generalizes P2372 FINISHED
Object Kronecker’s Jugendtraum
Kronecker’s Jugendtraum is a classical conjectural vision in number theory describing how special values of analytic functions, such as elliptic and modular functions, generate abelian extensions of number fields.
E213012 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: Kronecker’s Jugendtraum | Statement: [Hilbert’s twelfth problem, generalizes, Kronecker’s Jugendtraum]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Kronecker’s Jugendtraum
Context triple: [Hilbert’s twelfth problem, generalizes, Kronecker’s Jugendtraum]
  • A. Hilbert’s twelfth problem
    Hilbert’s twelfth problem is one of David Hilbert’s famous list of 23 problems, asking for a general explicit class field theory that would generate all abelian extensions of a given number field using special values of analytic functions.
  • B. Furtwängler’s theorem in class field theory
    Furtwängler’s theorem in class field theory is a fundamental result in algebraic number theory that refines the principal ideal theorem by describing how ideal classes capitulate (become principal) in certain abelian extensions of number fields.
  • C. 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.
  • D. Algebraic Groups and Class Fields
    "Algebraic Groups and Class Fields" is a influential mathematical monograph that develops the deep connections between algebraic group theory and class field theory within number theory and arithmetic geometry.
  • E. Artin–Schreier theory
    Artin–Schreier theory is a branch of algebraic number theory and field theory that characterizes cyclic extensions of prime degree in fields of characteristic p using additive 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: Kronecker’s Jugendtraum
Triple: [Hilbert’s twelfth problem, generalizes, Kronecker’s Jugendtraum]
Generated description
Kronecker’s Jugendtraum is a classical conjectural vision in number theory describing how special values of analytic functions, such as elliptic and modular functions, generate abelian extensions of number fields.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Kronecker’s Jugendtraum
Target entity description: Kronecker’s Jugendtraum is a classical conjectural vision in number theory describing how special values of analytic functions, such as elliptic and modular functions, generate abelian extensions of number fields.
  • A. Hilbert’s twelfth problem chosen
    Hilbert’s twelfth problem is one of David Hilbert’s famous list of 23 problems, asking for a general explicit class field theory that would generate all abelian extensions of a given number field using special values of analytic functions.
  • B. Furtwängler’s theorem in class field theory
    Furtwängler’s theorem in class field theory is a fundamental result in algebraic number theory that refines the principal ideal theorem by describing how ideal classes capitulate (become principal) in certain abelian extensions of number fields.
  • C. 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.
  • D. Algebraic Groups and Class Fields
    "Algebraic Groups and Class Fields" is a influential mathematical monograph that develops the deep connections between algebraic group theory and class field theory within number theory and arithmetic geometry.
  • E. Artin–Schreier theory
    Artin–Schreier theory is a branch of algebraic number theory and field theory that characterizes cyclic extensions of prime degree in fields of characteristic p using additive polynomials.
  • F. None of above.

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_69ca83977128819084084eb7d1d8c52a completed March 30, 2026, 2:07 p.m.
NER Named-entity recognition batch_69cdcfd3c6bc8190a21ed3566f9c08d1 completed April 2, 2026, 2:09 a.m.
NED1 Entity disambiguation (via context triple) batch_69d29a717f008190907089e1acb32361 completed April 5, 2026, 5:22 p.m.
NEDg Description generation batch_69d29b75634c819088c8ef750b1691d2 completed April 5, 2026, 5:27 p.m.
NED2 Entity disambiguation (via description) batch_69d29f5007f88190b0330d1a8c551905 completed April 5, 2026, 5:43 p.m.
Created at: March 30, 2026, 8:58 p.m.