Triple

T21654168
Position Surface form Disambiguated ID Type / Status
Subject Galois representations E534413 entity
Predicate usedIn P98 FINISHED
Object Langlands program NE NERFINISHED

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: [Galois representations, usedIn, Langlands program]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Langlands program
Context triple: [Galois representations, usedIn, 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. Eichler–Shimura theory
    Eichler–Shimura theory is a foundational framework in number theory and arithmetic geometry that connects modular forms with the cohomology of modular curves and the theory of elliptic curves.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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_69e0c466aec88190ba39c7543dbc8ba2 completed April 16, 2026, 11:13 a.m.
NER Named-entity recognition batch_69ef59164fe081908abd2e33dcd67def completed April 27, 2026, 12:39 p.m.
Created at: April 16, 2026, 6:36 p.m.