Triple

T14334411
Position Surface form Disambiguated ID Type / Status
Subject Ramanujan tau function E355432 entity
Predicate relatedTo P37 FINISHED
Object Galois representations E534413 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: Galois representations | Statement: [Ramanujan tau function, relatedTo, Galois representations]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Galois representations
Context triple: [Ramanujan tau function, relatedTo, 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. 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.
  • D. Iwasawa theory
    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.
  • 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_69d8278fa2108190bc0d0e7939c1eb03 completed April 9, 2026, 10:26 p.m.
NER Named-entity recognition batch_69de8c20d2148190bb534bef338e871d completed April 14, 2026, 6:49 p.m.
NED1 Entity disambiguation (via context triple) batch_69fd469634688190980df59ee482b792 completed May 8, 2026, 2:12 a.m.
Created at: April 10, 2026, 1:13 a.m.