Triple

T429531
Position Surface form Disambiguated ID Type / Status
Subject Whitney embedding theorem E9682 entity
Predicate concerns P1256 FINISHED
Object Euclidean space E22816 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: Euclidean space | Statement: [Whitney embedding theorem, concerns, Euclidean space]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Euclidean space
Context triple: [Whitney embedding theorem, concerns, Euclidean space]
  • A. Euclidean space chosen
    Euclidean space is the standard flat, n-dimensional geometric setting of classical geometry and vector calculus, characterized by straight lines, right angles, and the usual distance and dot product.
  • B. Minkowski space-time
    Minkowski space-time is a four-dimensional geometric framework that unifies three-dimensional space and time into a single continuum used to describe events and motion in special relativity.
  • C. Cartesian coordinate system
    The Cartesian coordinate system is a mathematical framework that uses perpendicular axes to represent points in a plane or space with ordered numerical coordinates.
  • D. 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.
  • E. Erlangen Program
    The Erlangen Program is Felix Klein’s influential 1872 framework that classifies and studies geometries based on their underlying symmetry groups and transformation 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_69a2e801e1d48190b505d1dd336b52ac completed Feb. 28, 2026, 1:05 p.m.
NER Named-entity recognition batch_69a2eeedf68c81908473d6c6600961bd completed Feb. 28, 2026, 1:34 p.m.
NED1 Entity disambiguation (via context triple) batch_69a42f67dc3881908d4b1c2f1fbc2aaa completed March 1, 2026, 12:22 p.m.
Created at: Feb. 28, 2026, 1:11 p.m.