Triple
T11086027
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Grothendieck–Ogg–Shafarevich formula |
E262121
|
entity |
| Predicate | language |
P15
|
FINISHED |
| Object | étale topology |
E254130
|
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 topology | Statement: [Grothendieck–Ogg–Shafarevich formula, language, étale topology]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: étale topology Context triple: [Grothendieck–Ogg–Shafarevich formula, language, étale topology]
-
A.
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.
-
B.
Grothendieck topology
chosen
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.
-
C.
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.
-
D.
Théorie des topos et cohomologie étale des schémas
Théorie des topos et cohomologie étale des schémas is a foundational multi-volume work in algebraic geometry, originating from Grothendieck’s Séminaire de Géométrie Algébrique, that develops topos theory and étale cohomology of schemes.
-
E.
Grothendieck toposes
Grothendieck toposes are highly structured categories that generalize topological spaces and serve as a unifying framework for geometry, logic, and cohomology in modern mathematics.
- 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_69d6aa9983c08190b0ef61603b69feac |
completed | April 8, 2026, 7:20 p.m. |
| NER | Named-entity recognition | batch_69d799c3ed9c8190a3f5cdf1fe0e74a2 |
completed | April 9, 2026, 12:21 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69e3e7a6dfa8819096f822294eb64dd1 |
completed | April 18, 2026, 8:20 p.m. |
Created at: April 8, 2026, 9:27 p.m.