Triple

T10062000
Position Surface form Disambiguated ID Type / Status
Subject Hilbert’s twelfth problem E213012 entity
Predicate relatedTo P37 FINISHED
Object Iwasawa theory E358023 NE FINISHED

How this triple was built (2 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: Iwasawa theory | Statement: [Hilbert’s twelfth problem, relatedTo, Iwasawa theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Iwasawa theory
Context triple: [Hilbert’s twelfth problem, relatedTo, Iwasawa theory]
  • A. Iwasawa theory chosen
    Iwasawa theory is a branch of number theory that studies the growth of arithmetic invariants in infinite towers of number fields, particularly using p-adic methods.
  • B. Arakelov theory
    Arakelov theory is a framework in arithmetic geometry that extends intersection theory to arithmetic surfaces by incorporating both finite and infinite places, enabling analytic tools to study Diophantine problems.
  • C. Galois representations
    Galois representations are homomorphisms from Galois groups of field extensions into matrix groups that encode deep arithmetic information and link number theory with algebraic geometry and modular forms.
  • D. Artin reciprocity law
    The Artin reciprocity law is a fundamental theorem in class field theory that generalizes quadratic reciprocity by describing abelian extensions of number fields in terms of characters of their idele class groups.
  • E. algebraic number theory
    Algebraic number theory is a branch of mathematics that studies algebraic structures related to algebraic integers and number fields, focusing on properties of integers through tools from abstract algebra.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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.
Created at: March 30, 2026, 8:58 p.m.