Triple

T10061997
Position Surface form Disambiguated ID Type / Status
Subject Hilbert’s twelfth problem E213012 entity
Predicate relatedTo P37 FINISHED
Object Stark conjectures
The Stark conjectures are a set of deep conjectures in algebraic number theory that predict precise connections between special values of L-functions and the arithmetic of number fields, particularly units and class fields.
E839485 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: Stark conjectures | Statement: [Hilbert’s twelfth problem, relatedTo, Stark conjectures]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Stark conjectures
Context triple: [Hilbert’s twelfth problem, relatedTo, Stark conjectures]
  • A. Tate Conjecture
    The Tate Conjecture is a major open problem in arithmetic geometry that predicts a deep connection between algebraic cycles on varieties over finite fields and their Galois-invariant étale cohomology classes.
  • B. Beilinson conjectures
    Beilinson conjectures are a set of deep conjectures in arithmetic geometry that relate special values of L-functions to algebraic K-theory and motivic cohomology, generalizing phenomena seen in cases like the Birch and Swinnerton-Dyer conjecture.
  • C. Serre’s conjecture on Galois representations
    Serre’s conjecture on Galois representations is a landmark statement in number theory that predicts which two-dimensional mod p Galois representations of the absolute Galois group of the rationals arise from modular forms.
  • D. Birch and Swinnerton-Dyer Conjecture
    The Birch and Swinnerton-Dyer Conjecture is a central unsolved problem in number theory that predicts a deep connection between the arithmetic of rational points on an elliptic curve and the behavior of its associated L-function at a specific value.
  • E. Artin’s conjecture on L-functions
    Artin’s conjecture on L-functions is a major unproven hypothesis in number theory asserting that nontrivial Artin L-functions associated to Galois representations are entire, with deep implications for the distribution of primes and the structure of number fields.
  • 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: Stark conjectures
Triple: [Hilbert’s twelfth problem, relatedTo, Stark conjectures]
Generated description
The Stark conjectures are a set of deep conjectures in algebraic number theory that predict precise connections between special values of L-functions and the arithmetic of number fields, particularly units and class fields.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Stark conjectures
Target entity description: The Stark conjectures are a set of deep conjectures in algebraic number theory that predict precise connections between special values of L-functions and the arithmetic of number fields, particularly units and class fields.
  • A. Tate Conjecture
    The Tate Conjecture is a major open problem in arithmetic geometry that predicts a deep connection between algebraic cycles on varieties over finite fields and their Galois-invariant étale cohomology classes.
  • B. Beilinson conjectures
    Beilinson conjectures are a set of deep conjectures in arithmetic geometry that relate special values of L-functions to algebraic K-theory and motivic cohomology, generalizing phenomena seen in cases like the Birch and Swinnerton-Dyer conjecture.
  • C. Serre’s conjecture on Galois representations
    Serre’s conjecture on Galois representations is a landmark statement in number theory that predicts which two-dimensional mod p Galois representations of the absolute Galois group of the rationals arise from modular forms.
  • D. Birch and Swinnerton-Dyer Conjecture
    The Birch and Swinnerton-Dyer Conjecture is a central unsolved problem in number theory that predicts a deep connection between the arithmetic of rational points on an elliptic curve and the behavior of its associated L-function at a specific value.
  • E. Artin’s conjecture on L-functions
    Artin’s conjecture on L-functions is a major unproven hypothesis in number theory asserting that nontrivial Artin L-functions associated to Galois representations are entire, with deep implications for the distribution of primes and the structure of number fields.
  • 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_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.