Triple

T14438347
Position Surface form Disambiguated ID Type / Status
Subject Iwasawa theory E358023 entity
Predicate relatedTo P37 FINISHED
Object Langlands program E753154 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: Langlands program | Statement: [Iwasawa theory, relatedTo, Langlands program]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Langlands program
Context triple: [Iwasawa theory, relatedTo, Langlands program]
  • A. Langlands program chosen
    The Langlands program is a far-reaching web of conjectures and theories in number theory and representation theory that seeks deep connections between Galois groups and automorphic forms, unifying many areas of modern mathematics.
  • B. Langlands classification
    The Langlands classification is a fundamental framework in representation theory that systematically describes all irreducible admissible representations of a real or p-adic reductive group in terms of data from its parabolic subgroups and their characters.
  • C. Fontaine–Mazur conjecture
    The Fontaine–Mazur conjecture is a central open problem in number theory that predicts which p-adic Galois representations of number fields arise from geometry or from automorphic forms.
  • D. Bloch–Kato conjecture
    The Bloch–Kato conjecture is a deep statement in arithmetic geometry and K-theory that predicts an exact correspondence between Galois cohomology and Milnor K-theory, linking algebraic K-groups to field arithmetic.
  • E. Automorphic Forms and Representations
    Automorphic Forms and Representations is a foundational mathematical monograph that develops the theory of automorphic forms and their connections to representation theory and number theory.
  • 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_69d8279402a88190821ffa39ae15bccf completed April 9, 2026, 10:26 p.m.
NER Named-entity recognition batch_69de914a45ec81909ab8ccf302047d7f completed April 14, 2026, 7:11 p.m.
NED1 Entity disambiguation (via context triple) batch_69fd5bd7f46881908df1a1cea7b6af9b completed May 8, 2026, 3:43 a.m.
Created at: April 10, 2026, 1:18 a.m.