Triple

T429538
Position Surface form Disambiguated ID Type / Status
Subject Whitney embedding theorem E9682 entity
Predicate hasVariant P455 FINISHED
Object Whitney immersion theorem E9682 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: Whitney immersion theorem | Statement: [Whitney embedding theorem, hasVariant, Whitney immersion theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Whitney immersion theorem
Context triple: [Whitney embedding theorem, hasVariant, Whitney immersion theorem]
  • A. Whitney embedding theorem chosen
    The Whitney embedding theorem is a fundamental result in differential topology stating that any smooth n-dimensional manifold can be embedded as a submanifold of Euclidean space of sufficiently high dimension (specifically \(\mathbb{R}^{2n}\)).
  • B. Whitney approximation theorem
    The Whitney approximation theorem is a fundamental result in differential topology stating that any continuous function between smooth manifolds can be uniformly approximated by smooth functions.
  • C. Nash embedding theorem
    The Nash embedding theorem is a fundamental result in differential geometry that shows any Riemannian manifold can be isometrically embedded into some Euclidean space, thereby realizing abstract curved spaces as concrete subsets of standard Euclidean space.
  • D. Janet–Cartan theorem
    The Janet–Cartan theorem is a fundamental result in differential geometry stating that any real-analytic Riemannian manifold can be locally isometrically embedded into a Euclidean space of sufficiently high dimension.
  • E. Whitney stratification
    Whitney stratification is a method in differential topology for decomposing singular spaces into smoothly compatible manifolds (strata) that fit together under specific regularity conditions, enabling rigorous analysis of singularities.
  • 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_69a431e1d6348190875a434414029e7d completed March 1, 2026, 12:32 p.m.
Created at: Feb. 28, 2026, 1:11 p.m.