It is assumed. Let me give you an example of an analysis that has fewer assumptions than yours.

First of all you assume a coordinate system and further assume that you analysis is independent of the coordinate system. As far as I can tell this is equivalent to assuming a space-time structure. Later in the your analysis, but still in the first chapter if I remember correctly, your identify what parameter time is. Those are all assumptions.

The example of an analysis that does not contain any of the above assumptions is called "Loop Quantum Theory". It actually derives the space-time structure from may basic axioms. It's founder if Aksterker (sp?) of UPENN and has been further developed by Smolin and others who I forget. Rubin is one other. So there is an example of physics that has fewer assumptions than your analysis.