Triple

T2314441
Position Surface form Disambiguated ID Type / Status
Subject Oswald Veblen E51030 entity
Predicate notableWork P4 FINISHED
Object 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.
E255570 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 Foundations of Geometry | Statement: [Oswald Veblen, notableWork, The Foundations of Geometry]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: The Foundations of Geometry
Context triple: [Oswald Veblen, notableWork, The Foundations of Geometry]
  • A. Commentary on the Difficulties of Certain Postulates of Euclid
    Commentary on the Difficulties of Certain Postulates of Euclid is a mathematical treatise by Omar Khayyam in which he critically examines and attempts to resolve issues in Euclid’s postulates, especially the parallel postulate, laying early groundwork for later developments in geometry.
  • B. Über die Hypothesen, welche der Geometrie zu Grunde liegen
    "Über die Hypothesen, welche der Geometrie zu Grunde liegen" is Bernhard Riemann’s seminal 1854 lecture that founded Riemannian geometry and revolutionized the understanding of space in mathematics and physics.
  • C. Grundlagen der Geometrie
    Grundlagen der Geometrie is David Hilbert’s foundational 1899 treatise that rigorously axiomatizes Euclidean geometry and helped shape modern mathematical logic and the axiomatic method.
  • D. Book I of Geometry (Descartes)
    Book I of Geometry (Descartes) is the opening section of René Descartes’ seminal work where he introduces his method of applying algebra to geometry, laying the foundations of analytic geometry.
  • E. Euclides adauctus et methodicus
    Euclides adauctus et methodicus is a 17th-century mathematical treatise by Guarino Guarini that expands and systematizes Euclidean geometry for advanced study and architectural application.
  • 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 Foundations of Geometry
Triple: [Oswald Veblen, notableWork, The Foundations of Geometry]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: The Foundations of Geometry
Target entity description: 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.
  • A. Commentary on the Difficulties of Certain Postulates of Euclid
    Commentary on the Difficulties of Certain Postulates of Euclid is a mathematical treatise by Omar Khayyam in which he critically examines and attempts to resolve issues in Euclid’s postulates, especially the parallel postulate, laying early groundwork for later developments in geometry.
  • B. Über die Hypothesen, welche der Geometrie zu Grunde liegen
    "Über die Hypothesen, welche der Geometrie zu Grunde liegen" is Bernhard Riemann’s seminal 1854 lecture that founded Riemannian geometry and revolutionized the understanding of space in mathematics and physics.
  • C. Grundlagen der Geometrie
    Grundlagen der Geometrie is David Hilbert’s foundational 1899 treatise that rigorously axiomatizes Euclidean geometry and helped shape modern mathematical logic and the axiomatic method.
  • D. Book I of Geometry (Descartes)
    Book I of Geometry (Descartes) is the opening section of René Descartes’ seminal work where he introduces his method of applying algebra to geometry, laying the foundations of analytic geometry.
  • E. Euclides adauctus et methodicus
    Euclides adauctus et methodicus is a 17th-century mathematical treatise by Guarino Guarini that expands and systematizes Euclidean geometry for advanced study and architectural application.
  • 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_69a88b074b908190ae983dbca7757d88 completed March 4, 2026, 7:41 p.m.
NER Named-entity recognition batch_69abc61d41f88190983f8947667b4c7a completed March 7, 2026, 6:30 a.m.
NED1 Entity disambiguation (via context triple) batch_69ae895f5420819087b403e9772dce9a completed March 9, 2026, 8:48 a.m.
NEDg Description generation batch_69ae8af65eb88190b17d74e7411967cc completed March 9, 2026, 8:55 a.m.
NED2 Entity disambiguation (via description) batch_69ae8ba02cec8190917c0e17d3fedb0e completed March 9, 2026, 8:58 a.m.
Created at: March 4, 2026, 7:49 p.m.