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.