Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 098-01. A doubling Hilbert subset with no finite-dimensional bi-Lipschitz embedding
Manuscript map · lines 4355–4364
OpenAI@2026-10-07#rem:oai-p-098-01
Authors: OpenAI. Family 098.
Title: A doubling Hilbert subset with no finite-dimensional bi-Lipschitz embedding.
Abstract: Every infinite-dimensional real Banach space contains a compact doubling subset that admits no bi-Lipschitz embedding into any finite-dimensional real normed space. The doubling constant has a universal bound, independent of the ambient Banach space. This answers the Lang–Plaut problem negatively, even for compact subsets of Hilbert space.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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