Full faithfulness of the functor from analytic adic spaces to solid D-stacks

Determine whether the canonical functor from the category of analytic adic spaces AnAdic to the category of solid D-stacks Shv_D(Aff_{Z_□}), sending an analytic adic space X to the associated object X_□, is fully faithful for all analytic adic spaces (not only affinoid ones).

Background

The paper constructs a natural functor from the category of analytic adic spaces to the category of solid D-stacks by sending an analytic adic space X to X_□. This encodes rigid-analytic geometry within the solid/condensed analytic framework and is used throughout the work to compare geometric and categorical structures.

It is known (by Andreatta, cited as [And21, Proposition 3.34]) that the functor is fully faithful when restricted to the full subcategory of affinoid analytic adic spaces. However, extending this to general (non-affinoid) analytic adic spaces presents difficulties: the functor does not necessarily preserve fiber products, and canonical covers in the solid D-topology may not refine to affinoid open covers, complicating descent arguments.

Resolving full faithfulness beyond the affinoid case would clarify the relationship between classical adic geometry and solid D-stacks and strengthen foundational aspects of the 6-functor formalism in this setting.