Triple

T10829046
Position Surface form Disambiguated ID Type / Status
Subject Veblen axioms for projective geometry E255568 entity
Predicate assumes P1458 FINISHED
Object Veblen–Young axiom (Veblen axiom of 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 axiom (Veblen axiom of projective geometry) | Statement: [Veblen axioms for projective geometry, assumes, Veblen–Young axiom (Veblen axiom of projective geometry)]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Veblen–Young axiom (Veblen axiom of projective geometry)
Context triple: [Veblen axioms for projective geometry, assumes, Veblen–Young axiom (Veblen axiom of 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. Playfair's axiom
    Playfair's axiom is a reformulation of Euclid’s parallel postulate stating that through a point not on a given line there is exactly one line parallel to the given line, fundamental to Euclidean geometry.
  • C. Fano plane
    The Fano plane is the smallest finite projective plane, consisting of seven points and seven lines with rich symmetrical and combinatorial properties.
  • D. Sylvester–Gallai theorem
    The Sylvester–Gallai theorem is a result in incidence geometry stating that for any finite set of points in the Euclidean plane not all on a single line, there exists a line that passes through exactly two of the points.
  • E. 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.
  • 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.