Triple

T7648337
Position Surface form Disambiguated ID Type / Status
Subject Heinz Hopf E173181 entity
Predicate notablePublication P4 FINISHED
Object "Vorlesungen über Differentialgeometrie"
"Vorlesungen über Differentialgeometrie" is a foundational textbook on differential geometry authored by the influential German mathematician Heinz Hopf.
E679326 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: "Vorlesungen über Differentialgeometrie" | Statement: [Heinz Hopf, notablePublication, "Vorlesungen über Differentialgeometrie"]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: "Vorlesungen über Differentialgeometrie"
Context triple: [Heinz Hopf, notablePublication, "Vorlesungen über Differentialgeometrie"]
  • A. Vorlesungen über Geometrie
    Vorlesungen über Geometrie is a foundational 19th-century textbook on geometry authored by German mathematician Alfred Clebsch.
  • B. Disquisitiones Generales Circa Superficies Curvas
    Disquisitiones Generales Circa Superficies Curvas is Carl Friedrich Gauss’s foundational 1827 work on differential geometry, in which he developed the intrinsic theory of curved surfaces and introduced concepts such as Gaussian curvature.
  • C. Neue Geometrie des Raumes
    Neue Geometrie des Raumes is a foundational 19th-century mathematical work by Julius Plücker that develops projective and line geometry in three-dimensional space.
  • D. Lezioni di calcolo differenziale assoluto
    "Lezioni di calcolo differenziale assoluto" is a foundational mathematical text by Tullio Levi-Civita that systematically develops the theory of absolute differential calculus, now known as tensor calculus, with applications to geometry and physics.
  • E. Geometrical Methods of Mathematical Physics
    Geometrical Methods of Mathematical Physics is a widely used textbook that introduces the differential geometric foundations underlying modern theoretical physics, including topics such as manifolds, tensors, and symmetries.
  • 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: "Vorlesungen über Differentialgeometrie"
Triple: [Heinz Hopf, notablePublication, "Vorlesungen über Differentialgeometrie"]
Generated description
"Vorlesungen über Differentialgeometrie" is a foundational textbook on differential geometry authored by the influential German mathematician Heinz Hopf.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: "Vorlesungen über Differentialgeometrie"
Target entity description: "Vorlesungen über Differentialgeometrie" is a foundational textbook on differential geometry authored by the influential German mathematician Heinz Hopf.
  • A. Vorlesungen über Geometrie
    Vorlesungen über Geometrie is a foundational 19th-century textbook on geometry authored by German mathematician Alfred Clebsch.
  • B. Disquisitiones Generales Circa Superficies Curvas
    Disquisitiones Generales Circa Superficies Curvas is Carl Friedrich Gauss’s foundational 1827 work on differential geometry, in which he developed the intrinsic theory of curved surfaces and introduced concepts such as Gaussian curvature.
  • C. Neue Geometrie des Raumes
    Neue Geometrie des Raumes is a foundational 19th-century mathematical work by Julius Plücker that develops projective and line geometry in three-dimensional space.
  • D. Lezioni di calcolo differenziale assoluto
    "Lezioni di calcolo differenziale assoluto" is a foundational mathematical text by Tullio Levi-Civita that systematically develops the theory of absolute differential calculus, now known as tensor calculus, with applications to geometry and physics.
  • E. Geometrical Methods of Mathematical Physics
    Geometrical Methods of Mathematical Physics is a widely used textbook that introduces the differential geometric foundations underlying modern theoretical physics, including topics such as manifolds, tensors, and symmetries.
  • 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_69c6995473348190a4f41d110d619a18 completed March 27, 2026, 2:51 p.m.
NER Named-entity recognition batch_69c6fb134a40819097f9de5f24d1df0f completed March 27, 2026, 9:48 p.m.
NED1 Entity disambiguation (via context triple) batch_69c89ada2a54819098672d45ab56f784 completed March 29, 2026, 3:22 a.m.
NEDg Description generation batch_69c89b7c27988190b78be7f249bda554 completed March 29, 2026, 3:24 a.m.
NED2 Entity disambiguation (via description) batch_69c89c56d9688190bd14badc319f9c44 completed March 29, 2026, 3:28 a.m.
Created at: March 27, 2026, 3:58 p.m.