Triple

T21858365
Position Surface form Disambiguated ID Type / Status
Subject Artin’s conjecture on L-functions E539691 entity
Predicate concerns P1256 FINISHED
Object Galois representations — 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: Galois representations | Statement: [Artin’s conjecture on L-functions, concerns, Galois representations]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Galois representations
Context triple: [Artin’s conjecture on L-functions, concerns, Galois representations]
  • A. Galois representations chosen
    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.
  • B. 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.
  • C. Weil–Deligne representations
    Weil–Deligne representations are algebraic objects combining a representation of the Weil group with a nilpotent operator, used to describe local Galois representations and formulate the local Langlands correspondence.
  • D. Mazur's deformation theory of Galois representations
    Mazur's deformation theory of Galois representations is a foundational framework in number theory that systematically studies how p-adic Galois representations can be deformed, with deep applications to modular forms and the proof of Fermat’s Last Theorem.
  • E. Galois cohomology
    Galois cohomology is a branch of mathematics that studies Galois groups and their actions on modules using cohomological methods, providing powerful tools for understanding field extensions, algebraic number theory, and arithmetic geometry.
  • 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_69e0c47829648190bbe2d1d7033768ec completed April 16, 2026, 11:14 a.m.
NER Named-entity recognition batch_69f0d638721c8190918fc6ad9c5d5bf6 completed April 28, 2026, 3:46 p.m.
Created at: April 16, 2026, 6:56 p.m.