Triple

T7648336
Position Surface form Disambiguated ID Type / Status
Subject Heinz Hopf E173181 entity
Predicate notablePublication P4 FINISHED
Object "Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche" (1931)
"Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche" (1931) is Heinz Hopf’s seminal paper in which he introduced the Hopf fibration, a foundational concept in algebraic topology describing a nontrivial mapping from the 3-sphere to the 2-sphere.
E679325 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: "Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche" (1931) | Statement: [Heinz Hopf, notablePublication, "Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche" (1931)]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: "Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche" (1931)
Context triple: [Heinz Hopf, notablePublication, "Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche" (1931)]
  • A. 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.
  • B. 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.
  • C. 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.
  • D. “Solutio problematis ad geometriam situs pertinentis”
    “Solutio problematis ad geometriam situs pertinentis” is Leonhard Euler’s 1736 Latin paper that founded graph theory and topology by solving the Seven Bridges of Königsberg problem.
  • E. On the Curvature of Space
    "On the Curvature of Space" is a pioneering 1922 paper by Alexander Friedmann that introduced non-static, expanding-universe solutions to Einstein’s field equations, laying the theoretical foundation for modern cosmology.
  • 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: "Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche" (1931)
Triple: [Heinz Hopf, notablePublication, "Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche" (1931)]
Generated description
"Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche" (1931) is Heinz Hopf’s seminal paper in which he introduced the Hopf fibration, a foundational concept in algebraic topology describing a nontrivial mapping from the 3-sphere to the 2-sphere.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: "Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche" (1931)
Target entity description: "Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche" (1931) is Heinz Hopf’s seminal paper in which he introduced the Hopf fibration, a foundational concept in algebraic topology describing a nontrivial mapping from the 3-sphere to the 2-sphere.
  • A. 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.
  • B. 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.
  • C. 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.
  • D. “Solutio problematis ad geometriam situs pertinentis”
    “Solutio problematis ad geometriam situs pertinentis” is Leonhard Euler’s 1736 Latin paper that founded graph theory and topology by solving the Seven Bridges of Königsberg problem.
  • E. On the Curvature of Space
    "On the Curvature of Space" is a pioneering 1922 paper by Alexander Friedmann that introduced non-static, expanding-universe solutions to Einstein’s field equations, laying the theoretical foundation for modern cosmology.
  • 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.