Triple

T21077308
Position Surface form Disambiguated ID Type / Status
Subject Playfair's axiom E519271 entity
Predicate parallelLineCountInHyperbolicGeometry P131877 FINISHED
Object infinitely many parallels through a point not on a given line LITERAL 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: infinitely many parallels through a point not on a given line | Statement: [Playfair's axiom, parallelLineCountInHyperbolicGeometry, infinitely many parallels through a point not on a given line]
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: parallelLineCountInHyperbolicGeometry
Context triple: [Playfair's axiom, parallelLineCountInHyperbolicGeometry, infinitely many parallels through a point not on a given line]
  • A. hasHyperbolicArea
    Indicates that one entity possesses or is associated with a specific area measured in hyperbolic geometry.
  • B. hasParallelPostulateFormulation chosen
    Indicates that one formulation of the parallel postulate corresponds to or can be expressed equivalently as another formulation.
  • C. hasLinesThroughEachPoint
    Indicates that for every point in the relevant space or set, there exists at least one line that passes through that point.
  • D. parallelOfLatitude
    Indicates that one entity is a line or circle on a sphere (typically Earth) that is at a constant latitude relative to another reference.
  • E. hasStraightLines
    Indicates that the related entity possesses or is characterized by straight, non-curved lines.
  • F. None of above.

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_69e0b506e59c8190849b71ed07929215 completed April 16, 2026, 10:08 a.m.
NER Named-entity recognition batch_69e702d77b8081908ecfb05ab391fd39 completed April 21, 2026, 4:53 a.m.
PD Predicate disambiguation batch_69e5dbfcd5e881908f1e4e0d2d237856 completed April 20, 2026, 7:55 a.m.
Created at: April 16, 2026, 2:49 p.m.