Triple

T10773143
Position Surface form Disambiguated ID Type / Status
Subject Grothendieck topology E254130 entity
Predicate generalizes P2372 FINISHED
Object Nisnevich topology
The Nisnevich topology is a Grothendieck topology on schemes tailored to capture étale-local algebraic information while ensuring strong local lifting properties over points.
E884926 NE FINISHED

How this triple was built (4 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: Nisnevich topology | Statement: [Grothendieck topology, generalizes, Nisnevich topology]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Nisnevich topology
Context triple: [Grothendieck topology, generalizes, Nisnevich topology]
  • A. Grothendieck topology
    A Grothendieck topology is an abstract framework in category theory that generalizes the notion of open covers in topology to define sheaves on arbitrary categories.
  • B. Zariski topology
    The Zariski topology is a fundamental topology in algebraic geometry, defined on the spectrum of a ring or an algebraic variety, whose closed sets correspond to solution sets of polynomial equations.
  • C. Grothendieck’s scheme-theoretic framework
    Grothendieck’s scheme-theoretic framework is a foundational reformulation of algebraic geometry that generalizes varieties using schemes, enabling powerful tools like sheaf theory, cohomology, and modern number-theoretic applications.
  • D. étale cohomology
    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.
  • E. 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.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Nisnevich topology
Triple: [Grothendieck topology, generalizes, Nisnevich topology]
Generated description
The Nisnevich topology is a Grothendieck topology on schemes tailored to capture étale-local algebraic information while ensuring strong local lifting properties over points.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Nisnevich topology
Target entity description: The Nisnevich topology is a Grothendieck topology on schemes tailored to capture étale-local algebraic information while ensuring strong local lifting properties over points.
  • A. Grothendieck topology
    A Grothendieck topology is an abstract framework in category theory that generalizes the notion of open covers in topology to define sheaves on arbitrary categories.
  • B. Zariski topology
    The Zariski topology is a fundamental topology in algebraic geometry, defined on the spectrum of a ring or an algebraic variety, whose closed sets correspond to solution sets of polynomial equations.
  • C. Grothendieck’s scheme-theoretic framework
    Grothendieck’s scheme-theoretic framework is a foundational reformulation of algebraic geometry that generalizes varieties using schemes, enabling powerful tools like sheaf theory, cohomology, and modern number-theoretic applications.
  • D. étale cohomology
    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.
  • E. 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.
  • F. None of above. chosen

Provenance (5 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_69d6aa5f54f4819082d0bbcb6f8797e6 completed April 8, 2026, 7:19 p.m.
NER Named-entity recognition batch_69d7329b27748190bd0e2569c7972fd1 completed April 9, 2026, 5:01 a.m.
NED1 Entity disambiguation (via context triple) batch_69de238559b48190abc759e744ab0f8e completed April 14, 2026, 11:22 a.m.
NEDg Description generation batch_69de271fb08c8190a44c547083226fd8 completed April 14, 2026, 11:38 a.m.
NED2 Entity disambiguation (via description) batch_69de2cecc24c8190a240366e0600426a completed April 14, 2026, 12:02 p.m.
Created at: April 8, 2026, 9:16 p.m.