The revised proposition

The proposition is a statement about what this source patch establishes. It is not a theorem that no lift exists. Likewise, it is not a theorem that the unnamed residual bundle cannot be chosen. It says that the patch has not recovered the frozen choice and has not constructed the lift.

The omission of a separately printed fiber rank would not by itself prevent a definition if the bundle were otherwise specified. The present failure concerns the missing identification of the output object and pairing. More importantly, even a later choice of that bundle would not remove the independent presentation, coefficient, correction-map, and composition obligations.