Triple

T10313524
Position Surface form Disambiguated ID Type / Status
Subject Herbert Busemann E241955 entity
Predicate notableWork P4 FINISHED
Object The Geometry of Geodesics
The Geometry of Geodesics is a foundational mathematical monograph that systematically develops the theory of geodesics and metric geometry, particularly in non-Riemannian settings.
E855792 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: The Geometry of Geodesics | Statement: [Herbert Busemann, notableWork, The Geometry of Geodesics]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: The Geometry of Geodesics
Context triple: [Herbert Busemann, notableWork, The Geometry of Geodesics]
  • A. On the Principles of Geometry
    "On the Principles of Geometry" is Nikolai Lobachevsky’s foundational work that introduced non-Euclidean (hyperbolic) geometry, challenging the universality of Euclid’s parallel postulate.
  • B. Vorlesungen über Geometrie
    Vorlesungen über Geometrie is a foundational 19th-century textbook on geometry authored by German mathematician Alfred Clebsch.
  • 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. The Foundations of Geometry
    The Foundations of Geometry is a seminal mathematical text by Oswald Veblen that rigorously develops the axiomatic basis of geometry in a modern, logical framework.
  • 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: The Geometry of Geodesics
Triple: [Herbert Busemann, notableWork, The Geometry of Geodesics]
Generated description
The Geometry of Geodesics is a foundational mathematical monograph that systematically develops the theory of geodesics and metric geometry, particularly in non-Riemannian settings.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: The Geometry of Geodesics
Target entity description: The Geometry of Geodesics is a foundational mathematical monograph that systematically develops the theory of geodesics and metric geometry, particularly in non-Riemannian settings.
  • A. On the Principles of Geometry
    "On the Principles of Geometry" is Nikolai Lobachevsky’s foundational work that introduced non-Euclidean (hyperbolic) geometry, challenging the universality of Euclid’s parallel postulate.
  • B. Vorlesungen über Geometrie
    Vorlesungen über Geometrie is a foundational 19th-century textbook on geometry authored by German mathematician Alfred Clebsch.
  • 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. The Foundations of Geometry
    The Foundations of Geometry is a seminal mathematical text by Oswald Veblen that rigorously develops the axiomatic basis of geometry in a modern, logical framework.
  • 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_69d381ac38808190a8ca7457c85b625b completed April 6, 2026, 9:49 a.m.
NER Named-entity recognition batch_69d4d35a292c8190bc8c467e522bba92 completed April 7, 2026, 9:50 a.m.
NED1 Entity disambiguation (via context triple) batch_69d71d801978819097293b5c98350fef completed April 9, 2026, 3:31 a.m.
NEDg Description generation batch_69d73186831481909555e2205d8783a7 completed April 9, 2026, 4:56 a.m.
NED2 Entity disambiguation (via description) batch_69d732bfc76c819089287477b54a7b77 completed April 9, 2026, 5:01 a.m.
Created at: April 6, 2026, 11:48 a.m.