Triple

T10082389
Position Surface form Disambiguated ID Type / Status
Subject William George Spencer E213932 entity
Predicate notableWork P4 FINISHED
Object Inventional Geometry
Inventional Geometry is an educational work by William George Spencer that introduces geometric concepts through intuitive, discovery-based learning rather than formal proofs.
E840721 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: Inventional Geometry | Statement: [William George Spencer, notableWork, Inventional Geometry]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Inventional Geometry
Context triple: [William George Spencer, notableWork, Inventional Geometry]
  • 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. 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.
  • C. Elements of Geometry
    Elements of Geometry is a widely used 18th-century textbook by John Playfair that modernized and clarified Euclid’s geometric principles for mathematical education.
  • D. Introduction to Geometry
    "Introduction to Geometry" is a classic textbook by H. S. M. Coxeter that systematically develops both Euclidean and non-Euclidean geometry with an emphasis on rigorous foundations and elegant geometric insights.
  • E. 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.
  • 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: Inventional Geometry
Triple: [William George Spencer, notableWork, Inventional Geometry]
Generated description
Inventional Geometry is an educational work by William George Spencer that introduces geometric concepts through intuitive, discovery-based learning rather than formal proofs.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Inventional Geometry
Target entity description: Inventional Geometry is an educational work by William George Spencer that introduces geometric concepts through intuitive, discovery-based learning rather than formal proofs.
  • 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. 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.
  • C. Elements of Geometry
    Elements of Geometry is a widely used 18th-century textbook by John Playfair that modernized and clarified Euclid’s geometric principles for mathematical education.
  • D. Introduction to Geometry
    "Introduction to Geometry" is a classic textbook by H. S. M. Coxeter that systematically develops both Euclidean and non-Euclidean geometry with an emphasis on rigorous foundations and elegant geometric insights.
  • E. 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.
  • 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_69ca839bf730819086900c323c9b8c95 completed March 30, 2026, 2:07 p.m.
NER Named-entity recognition batch_69cdd03482d481908b03d35dc2d16395 completed April 2, 2026, 2:11 a.m.
NED1 Entity disambiguation (via context triple) batch_69d2b66b256c8190861066f7c19008d2 completed April 5, 2026, 7:22 p.m.
NEDg Description generation batch_69d2b7901ea08190a48e984356bd3d71 completed April 5, 2026, 7:27 p.m.
NED2 Entity disambiguation (via description) batch_69d2b8813f9c8190a85462efb7a0a517 completed April 5, 2026, 7:31 p.m.
Created at: March 30, 2026, 9 p.m.