Triple

T22668848
Position Surface form Disambiguated ID Type / Status
Subject Chevalley’s theorem in algebraic geometry E559865 entity
Predicate usesConcept P531 FINISHED
Object Zariski topology — NE NERFINISHED

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: Zariski topology | Statement: [Chevalley’s theorem in algebraic geometry, usesConcept, Zariski topology]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Zariski topology
Context triple: [Chevalley’s theorem in algebraic geometry, usesConcept, Zariski topology]
  • A. Zariski topology chosen
    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.
  • B. 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.
  • C. Noetherian space
    A Noetherian space is a topological space in which every descending chain of closed subsets stabilizes, mirroring the finiteness conditions of Noetherian rings in algebra.
  • D. Hilbert scheme theory
    Hilbert scheme theory is a branch of algebraic geometry that studies parameter spaces representing families of subschemes of projective space, capturing how such geometric objects vary in moduli.
  • E. 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.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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_69e2454a158c819093b8e35f5045efb6 completed April 17, 2026, 2:35 p.m.
NER Named-entity recognition batch_69f1781de1d48190947cb1bb9d0890d9 completed April 29, 2026, 3:16 a.m.
Created at: April 17, 2026, 3:09 p.m.