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.