Only libgranite2 is available in Ubuntu repositories, libgranite3 is not. You can get libgranite3 from the elementary-os repository by doing:

sudo add-apt-repository ppa:elementary-os/daily
sudo apt-get update
sudo apt-get install libgranite3

Then you MUST immediately remove the elementary-os repository, otherwise major problems can occur.

sudo add-apt-repository –remove ppa:elementary-os/daily

Now you can install bookworm:

sudo apt-get install bookworm

You’re seeing this error because there is a problem with the packages that you have available from the software sources on your system.

You need to download these two packages: libgranite and libgranite-common packages from Ubuntu’s package site here: https://packages.ubuntu.com/search?keywords=libgranite+&searchon=names&suite=xenial&section=all

I don’t know how familiar you are with your terminal so try using synaptic package manager to download the missing packages instead of downloading them manually.

Can you shed some light into the darkness? 🙂

Using Linux Mint Mate 18.2 (based on Ubuntu 16.04 LTS).
Thank you very much and keep up with the good work!