I want to use VirtualBox to set up a stable software environment, which I may then export to other systems running VirtualBox. I also want to install guest additions.
Are guest additions host system independent, or are they somehow tailored to the host system, thus installing them may compromise portability of my virtual machine?
They are not tailored to the host system that is to say, the installation of the guest additions inside a VM doesnt vary based on the host system.
There is one link between the host and VMs: the recommendation is to install the version of the guest additions matching the version of VirtualBox on the host, but even that is not strictly required:
Each version of Oracle VM VirtualBox, even minor releases, ship with their own version of the Guest Additions. While the interfaces through which the Oracle VM VirtualBox core communicates with the Guest Additions are kept stable so that Guest Additions already installed in a VM should continue to work when Oracle VM VirtualBox is upgraded on the host, for best results, it is recommended to keep the Guest Additions at the same version.
If the two versions are different, theres a greater risk of problems if the guest additions are newer than the host VirtualBox, but even that risk is small.
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