Triple

T2290646
Position Surface form Disambiguated ID Type / Status
Subject Alexander Grothendieck E51493 entity
Predicate notableWork P4 FINISHED
Object Éléments de géométrie algébrique
Éléments de géométrie algébrique is a foundational multi-volume treatise that reshaped modern algebraic geometry by developing the theory of schemes and cohomology in a highly general, abstract framework.
E254127 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: Éléments de géométrie algébrique | Statement: [Alexander Grothendieck, notableWork, Éléments de géométrie algébrique]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Éléments de géométrie algébrique
Context triple: [Alexander Grothendieck, notableWork, Éléments de géométrie algébrique]
  • A. Sur les courbes algébriques et les variétés qui s’en déduisent
    Sur les courbes algébriques et les variétés qui s’en déduisent is a foundational 1948 monograph by André Weil that helped establish modern algebraic geometry and introduced key ideas leading to the Weil conjectures.
  • B. Méthodes de calcul différentiel absolu et leurs applications
    Méthodes de calcul différentiel absolu et leurs applications is a foundational mathematical work that systematically develops the theory of tensor calculus and its applications, laying groundwork later used in general relativity.
  • C. Cours d’Analyse
    Cours d’Analyse is a foundational 19th-century mathematics textbook by Augustin-Louis Cauchy that rigorously developed the theory of functions, limits, and continuity, helping to formalize modern analysis.
  • D. Treatise on Demonstration of Problems of Algebra
    Treatise on Demonstration of Problems of Algebra is a seminal mathematical work by Omar Khayyam in which he systematically analyzes and geometrically solves cubic equations.
  • E. Sheaves in Geometry and Logic
    Sheaves in Geometry and Logic is a foundational monograph that develops the theory of sheaves and topos theory and explores their deep connections to geometry, logic, and the foundations of mathematics.
  • 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: Éléments de géométrie algébrique
Triple: [Alexander Grothendieck, notableWork, Éléments de géométrie algébrique]
Generated description
Éléments de géométrie algébrique is a foundational multi-volume treatise that reshaped modern algebraic geometry by developing the theory of schemes and cohomology in a highly general, abstract framework.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Éléments de géométrie algébrique
Target entity description: Éléments de géométrie algébrique is a foundational multi-volume treatise that reshaped modern algebraic geometry by developing the theory of schemes and cohomology in a highly general, abstract framework.
  • A. Sur les courbes algébriques et les variétés qui s’en déduisent
    Sur les courbes algébriques et les variétés qui s’en déduisent is a foundational 1948 monograph by André Weil that helped establish modern algebraic geometry and introduced key ideas leading to the Weil conjectures.
  • B. Méthodes de calcul différentiel absolu et leurs applications
    Méthodes de calcul différentiel absolu et leurs applications is a foundational mathematical work that systematically develops the theory of tensor calculus and its applications, laying groundwork later used in general relativity.
  • C. Cours d’Analyse
    Cours d’Analyse is a foundational 19th-century mathematics textbook by Augustin-Louis Cauchy that rigorously developed the theory of functions, limits, and continuity, helping to formalize modern analysis.
  • D. Treatise on Demonstration of Problems of Algebra
    Treatise on Demonstration of Problems of Algebra is a seminal mathematical work by Omar Khayyam in which he systematically analyzes and geometrically solves cubic equations.
  • E. Sheaves in Geometry and Logic
    Sheaves in Geometry and Logic is a foundational monograph that develops the theory of sheaves and topos theory and explores their deep connections to geometry, logic, and the foundations of mathematics.
  • F. None of above. chosen

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_69a88b09c644819090b503456d96bf70 completed March 4, 2026, 7:42 p.m.
NER Named-entity recognition batch_69abc27536588190a74731b5537c90ee completed March 7, 2026, 6:15 a.m.
NED1 Entity disambiguation (via context triple) batch_69ae7f210bb881909086b86b2c3017a7 completed March 9, 2026, 8:04 a.m.
NEDg Description generation batch_69ae8018c2e88190aaacaad9adc442cf completed March 9, 2026, 8:08 a.m.
NED2 Entity disambiguation (via description) batch_69ae806fd8008190bfd6c6bcd1d0ddbd completed March 9, 2026, 8:10 a.m.
Created at: March 4, 2026, 7:48 p.m.