Remark: Exact scope

This is an explicit map from operational data to a genuine same-patch boundary form, with a direct identification proof on its restricted class. It is not a derivation of that class from unknown boundary physics. The reference Euclidean form and the one-parameter metric ansatz are installed in the comparator dictionary.

Consequently this theorem does not establish general metric emergence, general smooth anisotropic uniqueness, or a physical boundary acquisition instrument. It does not invoke 365-01 or 365-02.