Triple

T10772991
Position Surface form Disambiguated ID Type / Status
Subject Éléments de géométrie algébrique E254127 entity
Predicate predecessor P97 FINISHED
Object Foundations of Algebraic Geometry E244836 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: Foundations of Algebraic Geometry | Statement: [Éléments de géométrie algébrique, predecessor, Foundations of Algebraic Geometry]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Foundations of Algebraic Geometry
Context triple: [Éléments de géométrie algébrique, predecessor, Foundations of Algebraic Geometry]
  • A. Foundations of Algebraic Geometry chosen
    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.
  • 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. 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. 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.
  • E. 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.
  • 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_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.
Created at: April 8, 2026, 9:16 p.m.