Triple

T6908933
Position Surface form Disambiguated ID Type / Status
Subject Zariski topology E159881 entity
Predicate contrastWith P278 FINISHED
Object Zariski–Riemann space topologies E159881 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: Zariski–Riemann space topologies | Statement: [Zariski topology, contrastWith, Zariski–Riemann space topologies]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Zariski–Riemann space topologies
Context triple: [Zariski topology, contrastWith, Zariski–Riemann space topologies]
  • 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. Topological Methods in Algebraic Geometry
    Topological Methods in Algebraic Geometry is a foundational mathematical monograph by Friedrich Hirzebruch that applies topological techniques, particularly characteristic classes and cobordism theory, to problems in algebraic geometry.
  • C. Chevalley’s theorem in algebraic geometry
    Chevalley’s theorem in algebraic geometry is a fundamental result stating that the image of a morphism of finite type between schemes (or varieties) is a constructible set, playing a key role in understanding how geometric properties behave under mappings.
  • D. Krull–Gabriel dimension
    Krull–Gabriel dimension is a refinement of Krull dimension used in the representation theory of rings and abelian categories to measure the complexity of their subobject lattices and module categories.
  • E. Foundations of Algebraic Geometry
    Foundations of Algebraic Geometry is a landmark mathematical treatise that systematically developed the modern foundations of algebraic geometry and profoundly influenced the field’s subsequent evolution.
  • 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_69c68839ccb88190b4aa5cc1aca3448f completed March 27, 2026, 1:38 p.m.
NER Named-entity recognition batch_69c6d9be98748190b5cb698e66e3aa42 completed March 27, 2026, 7:25 p.m.
NED1 Entity disambiguation (via context triple) batch_69c749076f6c819088b0b40dd3e208b0 completed March 28, 2026, 3:20 a.m.
Created at: March 27, 2026, 2:25 p.m.