Triple

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).

Phrase: Nash C1 embedding theorem | Statement: [Nash embedding theorem, hasVersion, Nash C1 embedding theorem]

Target entity: Nash C1 embedding theorem
Context triple: [Nash embedding theorem, hasVersion, Nash C1 embedding theorem]

• A. Nash embedding theorem chosen
  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.
• B. Feynman–Kac formula
  The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
• C. Hilbert spaces
  Hilbert spaces are complete inner product spaces that provide the fundamental framework for modern functional analysis and many areas of mathematical physics.
• D. Wholly New Forms of Encyclopedias
  "Wholly New Forms of Encyclopedias" is a section of Vannevar Bush’s essay "As We May Think" that envisions future, highly interconnected and dynamically organized knowledge systems beyond traditional printed encyclopedias.
• E. Differential analyzer
  The Differential Analyzer is an early analog mechanical computer designed to solve differential equations using interconnected rotating shafts and wheels.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: hasVersion
Context triple: [Nash embedding theorem, hasVersion, Nash C1 embedding theorem]

• A. hasVariant chosen
  Indicates that one entity exists as an alternative form, version, or variation of another entity.
• B. hasMajorBranch
  Indicates that one entity possesses or includes another entity as a primary or principal subdivision or branch.
• C. hasLegacy
  Indicates that an entity leaves behind a lasting impact, influence, or inheritance that continues to exist or be recognized over time.
• D. hasFeature
  Indicates that an entity possesses, exhibits, or includes a particular characteristic, attribute, or component.
• E. hasOfficialStateTree
  Indicates that a political entity has a designated tree recognized as its official state symbol.
• F. None of above.