Triple

T22668864
Position Surface form Disambiguated ID Type / Status
Subject Chevalley’s theorem in algebraic geometry E559865 entity
Predicate hasVariant P455 FINISHED
Object Chevalley’s theorem for morphisms of finite type of Noetherian schemes — 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: Chevalley’s theorem for morphisms of finite type of Noetherian schemes | Statement: [Chevalley’s theorem in algebraic geometry, hasVariant, Chevalley’s theorem for morphisms of finite type of Noetherian schemes]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Chevalley’s theorem for morphisms of finite type of Noetherian schemes
Context triple: [Chevalley’s theorem in algebraic geometry, hasVariant, Chevalley’s theorem for morphisms of finite type of Noetherian schemes]
  • A. Chevalley’s theorem in algebraic geometry chosen
    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.
  • B. Zariski’s Main Theorem
    Zariski’s Main Theorem is a fundamental result in algebraic geometry that characterizes finite-type morphisms between varieties by relating birationality, normality, and the structure of fibers.
  • C. The Geometry of Schemes
    The Geometry of Schemes is a graduate-level textbook by David Eisenbud and Joe Harris that provides an accessible, example-driven introduction to the language and techniques of scheme theory in modern algebraic geometry.
  • D. 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.
  • E. Serre’s cohomological methods in algebraic geometry
    Serre’s cohomological methods in algebraic geometry are foundational techniques that use sheaf cohomology to relate and study algebraic and analytic geometry, profoundly influencing modern algebraic geometry and complex geometry.
  • 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.