Triple

T2290632
Position Surface form Disambiguated ID Type / Status
Subject Alexander Grothendieck E51493 entity
Predicate doctoralThesisTitle P1860 FINISHED
Object Produits tensoriels topologiques et espaces nucléaires
"Produits tensoriels topologiques et espaces nucléaires" is a foundational 1953 doctoral thesis in functional analysis that introduced and developed the theory of nuclear spaces and topological tensor products.
E254122 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: Produits tensoriels topologiques et espaces nucléaires | Statement: [Alexander Grothendieck, doctoralThesisTitle, Produits tensoriels topologiques et espaces nucléaires]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Produits tensoriels topologiques et espaces nucléaires
Context triple: [Alexander Grothendieck, doctoralThesisTitle, Produits tensoriels topologiques et espaces nucléaires]
  • A. L’intégration dans les groupes topologiques et ses applications
    L’intégration dans les groupes topologiques et ses applications is a foundational mathematical monograph by André Weil that develops the theory of integration on topological groups and explores its far-reaching applications in analysis and number theory.
  • 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. Banach spaces
    Banach spaces are complete normed vector spaces that provide a fundamental framework for functional analysis and the study of infinite-dimensional linear phenomena.
  • D. Topologie (with Heinz Hopf)
    "Topologie" is a foundational 1935 textbook on general topology co-authored by Pavel Alexandrov and Heinz Hopf that helped shape the modern development of the field.
  • E. Hilbert spaces
    Hilbert spaces are complete inner product spaces that provide the fundamental framework for modern functional analysis and many areas of mathematical physics.
  • 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: Produits tensoriels topologiques et espaces nucléaires
Triple: [Alexander Grothendieck, doctoralThesisTitle, Produits tensoriels topologiques et espaces nucléaires]
Generated description
"Produits tensoriels topologiques et espaces nucléaires" is a foundational 1953 doctoral thesis in functional analysis that introduced and developed the theory of nuclear spaces and topological tensor products.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Produits tensoriels topologiques et espaces nucléaires
Target entity description: "Produits tensoriels topologiques et espaces nucléaires" is a foundational 1953 doctoral thesis in functional analysis that introduced and developed the theory of nuclear spaces and topological tensor products.
  • A. L’intégration dans les groupes topologiques et ses applications
    L’intégration dans les groupes topologiques et ses applications is a foundational mathematical monograph by André Weil that develops the theory of integration on topological groups and explores its far-reaching applications in analysis and number theory.
  • 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. Banach spaces
    Banach spaces are complete normed vector spaces that provide a fundamental framework for functional analysis and the study of infinite-dimensional linear phenomena.
  • D. Topologie (with Heinz Hopf)
    "Topologie" is a foundational 1935 textbook on general topology co-authored by Pavel Alexandrov and Heinz Hopf that helped shape the modern development of the field.
  • E. Hilbert spaces
    Hilbert spaces are complete inner product spaces that provide the fundamental framework for modern functional analysis and many areas of mathematical physics.
  • 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.