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Conditional Hilbert-space classification of Gromov--Hausdorff space

Yoshito Ishiki

Palomar Registrypalomar/PALOMAR-2026-09-28-000004Sep 28, 2026math.GNscore 0

A Lean formalization of the implication from five explicitly stated literature inputs to a homeomorphism between the ordinary Gromov--Hausdorff space of nonempty compact metric spaces and real square-summable sequences. The proof constructs invariant full-support probability assignments, finite dimensional local models, global AR domination and discrete approximation. The five literature inputs are assumptions, not theorems proved in this snapshot.

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