Triple

T12442792
Position Surface form Disambiguated ID Type / Status
Subject Luigi Bianchi E297317 entity
Predicate notableWork P4 FINISHED
Object Lezioni sulla teoria dei gruppi continui finiti di trasformazioni
Lezioni sulla teoria dei gruppi continui finiti di trasformazioni is a foundational mathematical treatise by Luigi Bianchi on the theory of finite continuous transformation groups, contributing significantly to the development of group theory and differential geometry.
E984864 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: Lezioni sulla teoria dei gruppi continui finiti di trasformazioni | Statement: [Luigi Bianchi, notableWork, Lezioni sulla teoria dei gruppi continui finiti di trasformazioni]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Lezioni sulla teoria dei gruppi continui finiti di trasformazioni
Context triple: [Luigi Bianchi, notableWork, Lezioni sulla teoria dei gruppi continui finiti di trasformazioni]
  • A. Theorie der Transformationsgruppen
    Theorie der Transformationsgruppen is Sophus Lie’s foundational multi-volume work that established the theory of continuous transformation groups, now known as Lie groups, and their applications to differential equations and geometry.
  • B. Theorie der Gruppen von endlicher Ordnung
    "Theorie der Gruppen von endlicher Ordnung" is a foundational mathematical monograph on finite group theory that helped shape the modern development of abstract algebra.
  • C. 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.
  • D. Erlangen Program
    The Erlangen Program is Felix Klein’s influential 1872 framework that classifies and studies geometries based on their underlying symmetry groups and transformation properties.
  • E. Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra
    "Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra" is a foundational monograph by Eugene Wigner that systematically applies group-theoretical methods to analyze the symmetries and energy levels of atomic systems in quantum mechanics.
  • 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: Lezioni sulla teoria dei gruppi continui finiti di trasformazioni
Triple: [Luigi Bianchi, notableWork, Lezioni sulla teoria dei gruppi continui finiti di trasformazioni]
Generated description
Lezioni sulla teoria dei gruppi continui finiti di trasformazioni is a foundational mathematical treatise by Luigi Bianchi on the theory of finite continuous transformation groups, contributing significantly to the development of group theory and differential geometry.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Lezioni sulla teoria dei gruppi continui finiti di trasformazioni
Target entity description: Lezioni sulla teoria dei gruppi continui finiti di trasformazioni is a foundational mathematical treatise by Luigi Bianchi on the theory of finite continuous transformation groups, contributing significantly to the development of group theory and differential geometry.
  • A. Theorie der Transformationsgruppen
    Theorie der Transformationsgruppen is Sophus Lie’s foundational multi-volume work that established the theory of continuous transformation groups, now known as Lie groups, and their applications to differential equations and geometry.
  • B. Theorie der Gruppen von endlicher Ordnung
    "Theorie der Gruppen von endlicher Ordnung" is a foundational mathematical monograph on finite group theory that helped shape the modern development of abstract algebra.
  • C. 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.
  • D. Erlangen Program
    The Erlangen Program is Felix Klein’s influential 1872 framework that classifies and studies geometries based on their underlying symmetry groups and transformation properties.
  • E. Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra
    "Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra" is a foundational monograph by Eugene Wigner that systematically applies group-theoretical methods to analyze the symmetries and energy levels of atomic systems in quantum mechanics.
  • 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_69d6ada166c48190b902972cd2408fa3 completed April 8, 2026, 7:33 p.m.
NER Named-entity recognition batch_69d94d8fd9848190a83410353d88ea8d completed April 10, 2026, 7:20 p.m.
NED1 Entity disambiguation (via context triple) batch_69f63f10926881909ffc641f8d19f93a completed May 2, 2026, 6:14 p.m.
NEDg Description generation batch_69f640874a0481908d9203b48304d866 completed May 2, 2026, 6:20 p.m.
NED2 Entity disambiguation (via description) batch_69f641287f888190bc7000c256c362d3 completed May 2, 2026, 6:23 p.m.
Created at: April 8, 2026, 9:55 p.m.