Triple

T14334581
Position Surface form Disambiguated ID Type / Status
Subject Ramanujan–Petersson conjecture E355436 entity
Predicate proofUses P27215 FINISHED
Object étale cohomology E254118 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: étale cohomology | Statement: [Ramanujan–Petersson conjecture, proofUses, étale cohomology]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: étale cohomology
Context triple: [Ramanujan–Petersson conjecture, proofUses, étale cohomology]
  • A. étale cohomology chosen
    Étale cohomology is a cohomology theory in algebraic geometry that allows one to apply topological and cohomological methods to schemes, particularly over fields with nontrivial arithmetic such as finite fields.
  • B. Weil cohomology
    Weil cohomology is a type of cohomology theory for algebraic varieties that satisfies specific axioms enabling the proof of the Weil conjectures and the development of modern algebraic geometry.
  • 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. Deligne cohomology
    Deligne cohomology is a refined cohomology theory in algebraic geometry that combines singular cohomology and differential forms to capture both topological and arithmetic information about complex algebraic varieties.
  • E. Tate cohomology
    Tate cohomology is a refinement of group cohomology that extends cohomology and homology to negative degrees, playing a key role in algebraic number theory and Galois cohomology.
  • 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.