Triple

T10829061
Position Surface form Disambiguated ID Type / Status
Subject Veblen axioms for projective geometry E255568 entity
Predicate relatedTo P37 FINISHED
Object Veblen–Young axioms for projective geometry E255568 NE FINISHED

How this triple was built (2 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: Veblen–Young axioms for projective geometry | Statement: [Veblen axioms for projective geometry, relatedTo, Veblen–Young axioms for projective geometry]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Veblen–Young axioms for projective geometry
Context triple: [Veblen axioms for projective geometry, relatedTo, Veblen–Young axioms for projective geometry]
  • A. Veblen axioms for projective geometry chosen
    The Veblen axioms for projective geometry are a foundational set of incidence-based axioms introduced by Oswald Veblen to rigorously formalize the structure of projective spaces.
  • 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. 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.
  • D. Cremona group of the projective plane
    The Cremona group of the projective plane is the group of all birational self-maps of the complex projective plane, serving as a fundamental object in algebraic geometry and the study of plane transformations.
  • E. The Real Projective Plane
    The Real Projective Plane is a classic mathematical monograph by H. S. M. Coxeter that systematically develops the geometry and topology of the real projective plane, emphasizing its axiomatic foundations and non-Euclidean properties.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69d6aa8081448190a9324184f2bd1c26 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d734d3eab88190b30a3025b6b2b0bc completed April 9, 2026, 5:10 a.m.
NED1 Entity disambiguation (via context triple) batch_69de8592d8f08190ac577395ad7cc557 completed April 14, 2026, 6:21 p.m.
Created at: April 8, 2026, 9:19 p.m.