Proposition: No global transfer from the chart

The developing chart does not supply a global Minkowski representation, an intrinsic Newton inverse on the cone, or a global field-controlled unitary.

Proof. Parallel transport around the missing conical axis has nontrivial rotational holonomy for $0<{\delta }_{\mathrm{c}}<2\pi$. A global isometry into Minkowski space would identify this connection with one having trivial holonomy, which is impossible.

A local isometry also does not fix nonlocal inverse boundary conditions. For example, two flat-completion sources agreeing in a chart but differing by a nonnegative bump outside it can have different Newton potentials inside it. Finally, a chart supplies neither a field representation nor a coupling Hamiltonian or controlled unitary on such a representation.