Triple

T10772990
Position Surface form Disambiguated ID Type / Status
Subject Éléments de géométrie algébrique E254127 entity
Predicate influenced P9 FINISHED
Object Grothendieck school of algebraic geometry
The Grothendieck school of algebraic geometry is a mid-20th-century mathematical movement led by Alexander Grothendieck that revolutionized algebraic geometry through the development of schemes, sheaf theory, and cohomological methods.
E627992 NE FINISHED

How this triple was built (4 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: Grothendieck school of algebraic geometry | Statement: [Éléments de géométrie algébrique, influenced, Grothendieck school of algebraic geometry]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Grothendieck school of algebraic geometry
Context triple: [Éléments de géométrie algébrique, influenced, Grothendieck school of algebraic geometry]
  • A. 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.
  • B. 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.
  • C. Bourbaki school of mathematics
    The Bourbaki school of mathematics is a collective pseudonymous group of mainly French mathematicians known for their rigorous, abstract, and axiomatic reformulation of modern mathematics through influential multi-volume treatises.
  • D. 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.
  • E. 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.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Grothendieck school of algebraic geometry
Triple: [Éléments de géométrie algébrique, influenced, Grothendieck school of algebraic geometry]
Generated description
The Grothendieck school of algebraic geometry is a mid-20th-century mathematical movement led by Alexander Grothendieck that revolutionized algebraic geometry through the development of schemes, sheaf theory, and cohomological methods.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Grothendieck school of algebraic geometry
Target entity description: The Grothendieck school of algebraic geometry is a mid-20th-century mathematical movement led by Alexander Grothendieck that revolutionized algebraic geometry through the development of schemes, sheaf theory, and cohomological methods.
  • A. Grothendieck’s scheme-theoretic framework chosen
    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.
  • B. 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.
  • C. Bourbaki school of mathematics
    The Bourbaki school of mathematics is a collective pseudonymous group of mainly French mathematicians known for their rigorous, abstract, and axiomatic reformulation of modern mathematics through influential multi-volume treatises.
  • D. 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.
  • E. 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.
  • F. None of above.

Provenance (5 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.
NEDg Description generation batch_69de271fb08c8190a44c547083226fd8 completed April 14, 2026, 11:38 a.m.
NED2 Entity disambiguation (via description) batch_69de2cecc24c8190a240366e0600426a completed April 14, 2026, 12:02 p.m.
Created at: April 8, 2026, 9:16 p.m.